GIFT  OF 


ELEMENTS 


OF 


CHEMICAL     PHYSICS. 


JOSIAH   P.   COOKE,  JR., 

ERVING  PROFESSOK  OF  CHEMISTRY  AND  MINERALOGY   IN 
HARVARD   UNIVERSTY. 


SECOND    EDITION. 


BOSTON: 
JOHN    ALLYN,    PUBLISHER, 

LATE    SEVER,    FRANCIS,    &   CO. 

1873. 


Entered  according  to  Act  ot  Uongrass,  in  the  year  1860,  by 

JOSIAH     P.     COOKE,     JR., 
in  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


CAMBRIDGE: 

PRKSSWORK  BY  JOHN   WJLSON  AND  SON. 


PREFACE. 


THE  history  of  Chemistry  as  an  exact  science  may  be  said  to 
date  from  Lavoisier,  who  first  used  the  balance  in  investigating 
chemical  phenomena,  and  the  progress  of  the  science  since  his 
time  has  been  owing,  in  great  measure,  to  the  improvements 
which  have  been  made  in  the  processes  of  weighing  and  measur- 
ing small  quantities  of  matter.  These  processes  are  now  the 
chief  instruments  in  the  hands  of  the  chemical  investigator,  and 
it  is  evidently  essential  that  he  should  be  familiar  with  the  causes 
of  error  to  which  they  are  liable,  and  should  be  able  to  deter- 
mine the  degree  of  accuracy  of  which  they  are  capable.  All  this, 
however,  requires  a  theoretical  knowledge  of  the  principles  which 
the  processes  involve ;  and  the  chemical  investigator  who,  without 
it,  relies  on  mere  empirical  rules,  will  be  exposed  to  constant 
error. 

This  volume  is  intended  to  furnish  a  full  development  of 
these  principles,  and  it  is  hoped  that  it  will  serve  to  advance 
the  study  of  chemistry  in  the  colleges  of  this  country.  In  order 
to  adapt  the  work  to  the  purposes  of  instruction,  it  has  been  pre- 
pared on  a  strictly  inductive  method  throughout ;  and  any  stu- 
dent who  has  acquired  an  elementary  knowledge  of  mathematics 
will  be  able  to  follow  the  course  of  reasoning  without  difficulty. 
So  much  of  the  subject-matter  of  mechanics  has  been  given  at 
the  beginning  of  the  volume  as  was  necessary  to  secure  this 
object ;  and  for  the  same  reason,  each  chapter  is  followed  by  a 
large  number  of  problems,  which  are  calculated,  not  only  to  test 
the  knowledge  of  the  student,  but  also  to  extend  and  apply 

237518 


IV  PREFACE. 

the  principles  discussed  in  the  work.  Regarding  a  knowledge 
of  methods  and  principles  as  the  primary  object  in  a  course  of 
scientific  instruction,  the  author  has  developed  several  of  the 
subjects  to  a  much  greater  extent  than  is  usual  in  elementary 
works,  solely  for  the  purpose  of  illustrating  the  processes  and  the 
logic  of  physical  research.  Thus,  the  means  of  measuring  tem- 
perature and  the  defects  of  the  mercurial  thermometer  have  been 
described  at  length,  in  order  to  show  how  rapidly  the  difficulties 
multiply  when  we  attempt  to  push  scientific  observations  beyond 
a  limited  degree  of  accuracy  ;  so  also  the  history  of  Mariotte's 
law  has  been  given*  in  detail,  for  the  purpose  of  illustrating  the 
nature  of  a  -physical  law,  and  the  limitations  to  which  all  laws 
are  more  or  less  liable  ;  the  condition  of  salts  when  in  solution, 
and  the  nature  of  supersaturated  solutions,  have  in  like  manner 
been  fully  discussed  as  examples  of  scientific  theories;  and,  lastly, 
the  method  of  representing  physical  phenomena  by  empirical  for- 
mulas and  curves,  which  are  the  preliminary  substitutes  for  laws, 
has  been  illustrated  in  connection  with  Regnault's  experiments 
on  the  tension  of  aqueous  vapor. 

Although,  for  the  reason  just  given,  it  has  not  been  the  aim  of 
the  author  to  make  a  mere  digest  of  facts,  care  has  been  taken 
to  include  the  latest  results  of  science,  and  where  it  was  impos- 
sible to  enter  into  details,  references  are  given  to  the  original 
memoirs.  The  author  would  earnestly  recommend  the  advanced 
student  to  extend  his  study  to  these  memoirs,  and  not  to  spend 
much  time  in  reading  text-books.  All  compendiums  are  unavoid- 
ably incomplete.  They  can  only  give  general  results,  which  are 
necessarily  stated  in  definite  terms,  and  are  apt  to  convey  a  false 
notion  of  the  true  character  of  the  phenomena  and  laws  of  nature. 
A  student  who  desires  to  train  his  powers  of  observation  cannot 
expend  labor  more  profitably  than  in  looking  up  fully  in  a  large 
library  one  or  more  of  the  subjects  mentioned  above,  and  reading 
all  the  original  memoirs  that  have  been  written  upon  it.  It  is 
only  in  this  way  that  he  can  learn  what  scientific  investigation  has 
really  done,  as  well  as  what  can  be  expected  from  it,  and  can  thus 
prepare  himself  to  work  with  advantage  in  extending  the  bounda- 


PREFACE.  V 

ries  of  knowledge.  Moreover,  that  peculiar  scientific  power  which 
is  so  essential  to  the  "successful  interpretation  of  natural  phenom- 
ena can  be  acquired  only  at  these  fountain-heads  of  knowledge. 

In  preparing  the  work,  the  author  has  used  freely  all  the  ma- 
terials at  his  command.  Most  of  the  woodcuts  in  the  book  have 
been  transferred  from  the  pages  of  different  standard  works,  but 
especially  from  the  TraitS  de  Physique  of  Ganot.  The  excel- 
lent work  of  Buff,  Kopp,  and  Zamminer  has  been  repeatedly 
consulted,  as  well  as  those  of  Miller,  of  Graham,  of  Daguin,  of 
Jamin,  of  M  tiller,  of  Bunsen,  of  Dana,  and  of  Silliman,  and  all 
that  is  suitable  for  the  illustration  of  his  subject  has  been 
borrowed  from  them.*  Whenever  it  was  possible,  the  original 
memoirs  were  consulted,  especially  those  of  Regnault  in  the 
twenty-first  volume  of  the  Memoir es  de  I' Academic  des  Scien- 
ces. Indeed,  this  distinguished  experimentalist  has  so  greatly 
improved  the  methods  of  investigation  in  this  department  of 
Physics,  that  any  text-book  on  the  subject  must  necessarily  be 
in.  great  measure  an  abstract  of  his  labors. 

A  large  number  of  valuable  tables  are  included  in  an  Ap- 
pendix at  the  end  of  the  volume.  Several  of  these  have 
been  re-calculated  ;  but  the  rest  are  selected  with  care  from 
standard  authors.  The  authority  for  each  table,  and  the  page 
on  which  the  method  of  using  it  is  described,  are  given  at  the 
commencement  of  the  Appendix.  A  list  of  numerous  other 
tables  distributed  through  the  body  of  the  work  will  be  found, 
tinder  the  word  "Tables,"  in  the  Index.  The  author  is  in- 
debted to  Captain  Charles  Henry  Davis,  Superintendent  of 


*  Buff,  Kopp,  und   Zamminer.    Lehrbuch  dcr  physikalischen  und  theoretischen 
Chemie.     Braunschweig,  1857. 

Miller.    Elements  of  Chemistry.    Part  I.  Chemical  Physics.    London,  1855. 
Graham.    Elements  of  Chemistry.     Vol.  I.,  London,  1850.    Vol.  IL,  1857. 
Daguin.     Traite'  de  Physique.     Tom.  I.     Paris,  1855. 
Jamin.     Cours  de  Physique.     Tom.  I.    Paris,  1858. 
Miiller.     Lehrbuch  der  Physik  und  Meteorologie.    Braunschweig,  1856. 
Bunsen.     Gasometry.     Translated  by  Roscoe.     London,  1857. 
Dana.     System  of  Mineralogy.     Vol.1.     New  York,  1854. 
Silliman.    First  Principles  of  Physics.    Philadelphia,  1859. 


VI  PREFACE. 

the  Nautical  Almanac,  for  the  use  of  a  table  of  logarithms  of 
natural  numbers  to  four  places  of  decimals,  which  will  be 
found  sufficient  for  solving  most  of  the  problems  in  this  book. 
The  greater  number  of  the  problems  were  prepared  by  the 
author  ;  the  rest  have  been  selected  from  various  works,  but 
especially  from  Kahl's  Aufg-aben  aus  der  Physik,  and  from  the 
Appendix  to  Ganot's  Traite  de  Physique.  Solutions  of  these 
problems  will  be  published  hereafter,  though  for  an  obvious 
reason  they  are  not  included  in  this  volume.  For  the  purpose 
of  ready  reference,  the  sections  and  equations  have  been  num- 
bered ;  the  numbers  of  sections  are  given  in  parentheses,  those 
of  equations  in  brackets  ;  and  in  order  still  further  to  facilitate 
reference,  a  list  of  the  formulae  is  included  in  the  Index. 

Great  pains  have  been  taken  in  the  printing  of  the  book  to 
avoid  errors,  and  the  author  is  under  especial  obligation  to 
his  friend,  Professor  Henry  W.  Torrey,  for  a  careful  revision 
of  the  proof-sheets.  The  difficulties  of  securing  perfect  accu- 
racy in  printing  formulae  and  tables  are  almost  insurmountable, 
and  many  misprints  have  undoubtedly  occurred.  Such  as  may 
be  discovered  will  be  corrected  in  the  next  edition  ;  and  the 
author  will  feel  under  obligations  to  any  of  his  readers  who  will 
have  the  kindness  to  send  him  a  note  of  such  as  they  find. 

Although  the  present  volume  is  a  complete  treatise  in  itself 
of  the  principles  involved  in  the  processes  of  weighing  and  meas- 
uring, it  is  also  intended  to  serve  as  the  first  volume  of  an 
extended  work  on  the  Philosophy  of  Chemistry.  The  arrange- 
ment of  the  chapters  and  sections  has  been  adopted  with  this 
view,  and  the  inductive  method  begun  in  this  volume  will  be  con- 
tinued through  the  whole  work.  The  second  volume  will  treat 
of  Light  in  its  relations  to  Crystallography  (including  Mathemat- 
ical Crystallography),  and  also  of  Electricity  in  its  relations  to 
Chemistry.  The  third  and  last  volume  will  be  on  Stoichiometry 
and  the  principles  of  Chemical  Classification.  This  volume  is 
now  in  preparation,  and  will  be  published  next. 

J.  P.O. 

CAMBRIDGE,  February  1,  1860. 


CONTENTS 


CHAPTER    I. 

INTRODUCTION. 

(1.)  Matter,  Body,  Substance,  3.  —  (2.)  General  and  Specific  Properties,  3.  — 
(3.)  Physical  and  Chemical  Changes,  4.  —  (4.)  Physical  and  Chemical  Proper- 
ties, 5.  —  (5.)  Chemistry  and  Physics,  5.  —  (6.)  Force  and  Law,  6. 

CHAPTER   II. 

GENERAL  PROPERTIES  OF  MATTER. 

(7.)  Essential  and  Accidental  Properties,  10.  —  (8.)  Extension  and  Volume, 
10.  — (9.)  The  Measure  of  Extension,  11. 

English  System  of  Measures    .         .         .         .         .         .         .         .11 

(10.)  Units  of  Length,  11.  — (11.)  Units  of  Surface  and  of  Volume,  13. 
French  System  of  Measures          .         .         .         .         .         .         .         14 

(12.)  History, —  the  Metre,  14.  —  (13.)  Subdivisions  and  Multiples  of  the 
Metre,  17.  —  (14.)  Units  of  Surface  and  of  Volume,  17.  —  (15.)  Density  and 
Mass,  18.  —  (16.)  Impenetrability,  19. 

problems  1  to  11    .         .         .         .- 19 

Motion        .;.*...•....         20 

(17.)  Position,  20.  — (18)  Mobility,  21.  — (19.)  Time  and  Velocity,  22.  — 
(20.)  Uniform  and  Varying  Motions,  23.  —  (21.)  Uniformly  Accelerated  Mo- 
tion, 23.  — (22.)  Uniformly  Retarded  Motion,  26.— (23)  Compound  Motion, 
27. —  (24.)  Parallelogram  of  Motions,  27.  —  (25.)  Curvilinear  Motion,  29. 

Problems  12  to  24 .-.*..     31 

Force         .     '^  .\  >v*_ 32 

(26.)  Force,  32.  —  (27.)  Direction  of  Force,  32.  —  (28.)  Equilibrium,  34.  — 
(29.)  Measure  of  Forces,  34. 

Composition  of  Forces    .........     38 

(30)  Components  and  Resultant,  38.  —  (31.)  Forces  represented  by  Lines, 
38.  —  (32.)  Point  of  Application,  38.  —  (33.)  Resultant  of  Forces  acting  in 
same  Direction,  39.  —  (34.)  Parallelogram  of  Forces,  39.  —  (35.)  Decompo- 
sition of  Forces,  40.  —  (36.)  Composition  of  several  Forces,  42.  —  (37.)  Com- 
position of  Parallel  Forces,  43.  —  (38.)  Couples,  47.  —  (39.)  Composition  of 
several  Parallel  Forces,  47.  —  (40.)  Centre  of  Parallel  Forces,  48.  —  (41.)  Ac- 
tion and  Reaction,  49.  —  (42.)  Power,  or  Living  Force,  52. 

Problems  25  to  50  .  54 


Vlll  CONTENTS. 

Gravitation         ..........         56 

(43.)  Definition,  56  —  (44.)  Direction  of  the  Earth's  Attraction,  57.  — 
(45.)  Point  of  Application,  58.  —  (46  )  Centre  of  Gravity,  60.  —  (47.)  Position 
of  Centre  of  Gravity,  61.  —  (48.)  Conditions  of  Equilibrium,  62. —  (49.)  In- 
tensity of  the  Earth's  Attraction,  64  — (50.)  Pendulum,  66. —  (51.)  Simple 
Pendulum,  66.  —  (52.)  Isochronism  of  Pendulum,  68. —  (53  )  Formula  of  Pen- 
dulum, 68.  —  (54.)  Compound  Pendulum,  69.  —  (55.)  Centre  of  Oscillation, 
70.—  (56.)  Use  of  the  Pendulum  for  Measuring  Time,  71. —  (57.)  Use  of  the 
Pendulum  fur  Measuring  the  Force  of  Gravity,  73.  —  (58.)  Value  of  g,  76. — 
(59.)  Centrifugal  and  Centripetal  Force,  77.—  (60.)  The  Spheroidal  Figure  of 
the  Earth,  83.  —  (61.)  Variation  of  the  Intensity  of  Gravity,  85.  —  (62.)  Law 
of  Gravitation,  86.  —  (63.)  Absolute  Weight,  87.  —  (64)  French  System  of 
Weights,  89.  —  (65.)  System  of  Weights  of  the  United  States  and  of  England, 
89.— (66.)  Specific  Weight,  90.  — (67.)  Unit  of  Mass,  90.  — (68.)  Density, 
91.— (69.)  Specific  Gravity,  91.—  (70  j  Unit  of  Force,  93.— (71.)  Relative 
Weight,  94.— (72.)  Lever,  97.  —  (73.)  Balance,  100. 

Problems  51  to  90  . 106 

Accidental  Properties  of  Matter   .......       109 

(74.)  Divisibility,  *1 09.  — (75.)  Porosity,  110. —  (76.)  Compressibility  and 
Expansibility,  113.—  (77.)  Elasticity,  115. 


CHAPTER    III. 

THE  THREE  STATES  OF  MATTER. 
(78.)  Molecular  Forces,  117. 

MOLECULAR  FORCES  BETWEEN  HOMOGENEOUS  MOLECULES. 

I.    CHARACTERISTIC  PROPERTIES  OF  SOLIDS. 

Crystallography      .       ,, .         .         .         .         .         .         .         .         .119 

(79.)  Crystalline  Form,  119. —  (80.)  Processes  of  Crystallization,  119. — 
(81.)  Definitionsof  Terms,  121.  —  (82.)  Systems  of  Crystals,  121. —  (83.)  Cen- 
tre of  Crystal,  and  Parameters,  124.  —  (84.)  Similar  Axes,  125.  —  (85  )  Similar 
Planes,  126.  — (86.)  Holohedral  Forms,  127.— (87.)  Hemihedral  Forms,  128. 
—  (88.)  Tetartohedral  Forms,  129.— (89.)  Simple  and  Compound  Crystals, 
129.— (90.)  Dominant  and  Secondary  Forms,  130.  —  (91.)  Definition  of  terms,  * 
and  Laws  of  Modification,  131.  —  (92.)  Forms  of  Crystals  belonging  to  the  va- 
rious Systems,  132.  —  (93.)  Irregularities  of  Crystals,  170.  —  (94.)  Groups  of 
Crystals,  173. —  (95.)  Determination  of  Crystals,  174.  —  (96.)  Goniometers, 
177.  —  (97.)  Identity  of  Crystalline  Form,  183.  —  (98.)  Dimorphism  and  Poly- 
morphism, 184. 

Elasticity  .         .     r  <-.   °-     ;    .     .     •"'-.•'       .         .         .         .         .       185 

(99.)  Elasticity  of  Solids,  185. —  (100.)  Elasticity  of  Tension,  185.— (101.) 
Coefficient  of  Elasticity,  186. —  (102.)  Elasticity  of  Compression,  187.  —  (103  ) 
Elasticity  of  Flexure,  187. —  (104.)  Applications,  189. —  (105.)  Elasticity  of 
Torsion,  191.  — (106.)  Applications,  193.  — (107.)  Limit  of  Elasticity,  193.— 
(108.)  Elasticity  of  Crystals,  195.  —  (109.)  Collision  of  Elastic  Bodies,  196. 

Resistance  to  Rupture     .     ,  «     ..„->.-     .         .         .         .         .201 

(110.)  Measure  of  Resistance,  201.  —  (111.)  Tenacity,  203.  —  (112.)  Cleav- 
age, 204.  —  (113.)  Ductility  and  Malleability,  205. 

Hardness    .         .     '•':l.  .'      .     ,/.*tl' ..''7-'      »       •'*  \-  "  •••'.       •'       •       208 

(114.)  Scale  of  Hardness,  208.  —  (115.)  Sclerometer,  209.— (116.)  Anneal- 
ing and  Tempering,  211. 

Problems  91  to  105      ''  V     :  i      '  ;  V        .  .  213 


CONTENTS. 


II.    CHARACTERISTIC  PROPERTIES  OF  LIQUIDS. 

Mechanical  Condition  of  Liquids          .         .         .         .         .         .215 

(117  )   Fluidity,  215.  — (118  )  Elasticity  of  Liquids,  215. 
Consequences  of  the  Mechanical  Condition  of  Liquids      .         .          .218 

(119  )  Divisions  of  the  Subject,  218.  —  (120.)  Liquids  transmit  Pressure  in 
all  Directions,  218. —  (121.)  Direction  of  Liquid  Pressure,  219.  —  (122.)  Hy- 
kdrostatic  Press,  220.  —  (123.)  Pressure  of  Liquids  caused  by  Weight,  223. — 
'(124.)  Upward  Pressure,  225.  —  (125.)  Lateral  Pressure,  226.  —  (126.)  Gener- 
alization, 227.  — (127.)  Pressure  proportional  to  Specific  Gravity,  227.  —  (128.) 
Hydrostatic  Paradox,  228. 

Equilibrium  of  Liquids        .         .         .         .         .         .         .         .228 

(129.)  Conditions  of  Equilibrium,  228. —  (130.)  Connecting  Vessels,  230. — 
(131.)  Heights  of  Liquid  Columns  in  Connecting  Vessels,  231.  —  (132.)  Spirit- 
Level,  232.  —  (133.)  Artesian  Wells,  233.  —  (134.)  Salt  Wells,  234. 

Buoyancy  of  Liquids'      .........  235 

(135.)  Principle  of  Archimedes,  235.  — (136),  (137),  and  (138.)  Demonstra- 
tions of  Principle  of  Archimedes,  237.  —  (139.)  Centre  of  Pressure,  240. — 
(140.)  Floating  Bodies,  241.  —  (141.)  Equilibrium  of  Floating  Bodies,  242.  — 
(142.)  Stable  and  Unstable  Equilibrium,  243.  —  (143.)  Neutral  Equilibrium, 
246. 

Methods  of  determining  Specific  Gravity      .....       247 

(144.)  Definition  of  Specific  Gravity,  247. —  (145  )  Specific-Gravity  Bottle, 
247.  —  (146.)  Hydrostatic  Balance,  248.— (147.)  Hydrometers,  249. 

Problems  106  to  175 257 

III.    CHARACTERISTIC  PROPERTIES  or  GASES. 

Mechanical  Condition  of  Gases  .         .         .         .         .         .         .263 

Properties  Common  to  Gases  and  Liquids        .         .         .         .         .264 

(150.)  Pressure  independent  of  Gravity,  264. —  (151.)  Pressure  depending 
on  Gravity,  265.  —  ( 1 52.)  Pressure  of  the  Atmosphere,  266.  —  (153.)  Buoyancy 
of  the  Air,  268.  — (154.)  Weight  of  a  Body  in  Air,  268.  — (155.)  Balloons,  270. 

Differences  between  Liquids  and  Gases 273 

The  Barometer 275 

(157.)  Experiment  of  Torricelli,  275. —  (158.)    Theory  of  the  Barometer, 
278.  —  (159.)  Regnault's  Barometer,  280. —  (160.)  Barometer  of  Fortin,  282. 
(161.)  Common  Barometer,  284.  — (162.)  Uses  of  the  Barometer,  285. 
Mariotte's  Law  ..........       287 

(163)  Statement  of  Mariotte's  Law,  287. —  (164)  Experimental  Illustra- 
tion, 288. —  (165.)  History,  290. —  (166.)  Limit  to  the  Compressibility  of 
Gases,  301. 

Application  of  Mariotte's  Law         .         .         .         .         .         .         .301 

(167.)  Pressure  of  the  Atmosphere  at  different  Heights,  301. 
Instruments  illustrating  the  Properties  of  Gases    ....       307 

(168.)  Manometers,  307. —  (169.)  Pneumatic  Trough,  311.  — (170.)  Gas- 
ometers. 314.  —  (171.)  Safety-Tubes,  315.  — (172.)  Siphon,  320.  —  ( 1 73  )  Ma- 
riotte's Flask,  323.— (174.)  Wash-Bottle,  325. 

Machines  for  fiarefying  and  Condensing  Air  .....  325 

(175.)  The  Air-Pump,  325.  — (176.)  Degree  of  Exhaustion,  327.  — (177.) 
Air-Pump  with  Valves,  329.  —  (178.)  Condensing-Pump,  333.  —  (179.)  Water- 
Pump,  334. 

Problems  176  to  239  .  336 


X  CONTENTS. 

MOLECULAR  FORCES  BETWEEN  HETEROGENEOUS  MOLECULES. 

ADHESION. 

Solids  and  Solids        .         .         .        ./     .  •         -         •         •         .342 
(181.)  Adhesion  between  Solids,  342.  —  (182.)  Cements,  343. 

Solids  and  Liquids         ..         ...»         ...  344 

(183.)  Adhesion  of  Liquids  to  Solids,  344.  —  (184.)  Capillary  Attraction, 
346. —  (185.)  Form  of  the  Meniscus,  349.  —  (186.)  Molecular  Pressure,  349.  — 
(187.)  Amount  of  Molecular  Pressure,  351.  —  (188.)  Effects  of  Molecular  Pres-  ' 
sure,  352.  —  (189.)  Numerical  Laws  of  Capillarity,  355.  —  (190.)  Verification 
of  the  Laws,  357.  —  (191.)  Influence  of  Temperature,  360-  —  (192.)  Spheroidal 
Condition  of  Liquids,  361. —  (193.)  Examples  and  Illustrations  of  Capillarity, 
362.  — (194.)  Absorption,  363.  — (195.)  Solution,  365. —(196.)  Determination 
of  Solubilities,  369.  —  ( 1 97.)  Solution  aud  Chemical  Change, 371. —  (1 98.)  Su- 
persaturated Solutions,  376. 

Solids  and  Gases 879 

(199.)  Absorption  of  Gases,  379. 

Liquids  and  Liquids      .         .         .         .         »         .         .         .         .383 

(200.)  Liquid  Diffusion,  383.  — (201.)  Experiments  of  Graham,  384.— 
(202.)  Osmose,  387. 

Liquids  and  Gases     .         .         .         .         .         .         .         .         .391 

(203.)  Adhesion  of  Liquids  to  Gases,  391  —  (204.)  Solution  of  Gases,  392. 
—  (205.)  Variation  with  Temperature,  393.  —  (206.)  Variation  with  Pressure, 
394.  —  (207.)  Influence  of  Salts  in  Solution.  398.  —  (208.)  Determination  of 
Coefficient  of  Absorption,  398.  —  (209  )  Partial  Pressure,  405.—  (210.)  Analy- 
sis of  Mixed  Gases  by  Absorption  Meter,  409. 

Gases  and  Gases   ..........  412 

(211.)  Effusion,  412.— (212.)  Application  of  the  Law  of  Effusion,  414.— 
(213.)  Transpiration,  417.  — (214.)  Diffusion,  419.— (215.)  Passage  of  Gases 
through  Membrane,  425. 


CHAPTER  iv. 

HEAT. 

Action  of  Heat  on  Matter,  and  Theories  concerning  Heat  .         .426 

Thermometers     .         .      ;  v        .         .         .         .         .         .         .       432 

(217.)  Mercurial  Thermometer,  432. —  (218.)  Graduation  of  Thermometer, 
433. —  (219.)  Defects  of  Mercurtal  Thermometer,  436. —  (220.)  Change  of  the 
Zero  Point,  441.  —  (221.)  Standard  Thermometers,  442. — (222)  and  (223.) 
Correction  of  Observation.  448.  —  (224.)  House'  Thermometers,  450.  —  (225.) 
Thermometers  filled  with  other  Liquids,  451.  — (226.)  Maximum  and  Mini- 
mum Thermometers,  452. 

Thermoscopes         .         .    .     . -"-'."  -    •     .         •      *?J?  \';  *|i*v    .         .  455 

(227.)  Air  Thermometers,  455.  —  (228.)  Thermo-multiplier,  457. 
Problems  272  to  290  .         .     '  V;      V     *S*|     .     f '  V^- v    r   .       461 
Specific  Heat          .         .         .         ...         .      //;    > -'.'\         .  463 

(229.)  Temperature,  463  —  (230.)  Thermal  Equilibrium,  463.  —  (231  ) 
Unit  of  Heat,  464. —  (232.)  Specific  Heat,  464. —  (233.)  Determination  pf 
Specific  Heat,  466.  —  (234.)  General  Results,  471. —  (235.)  Specific  Heat  of 
(Gases,  476.  —  (236.)  Specific  Heat  of  Gases  under  Constant  Pressure,  477. — 
(237.)  Specific  Heat  of  Gases  under  Constant  Volume,  480.—  (238.)  Mechan- 
ical  Equivalent  of  Heat,  484. 

Problems  291  to  310 *v     489 


CONTENTS,  jj 

Expansion     .         •        k         •         •         •         •         •         •       »V        •  491 

(239.)  Coefficient  of  Expansion,  491.  —  (240.)  Relation  of  Cubic  to  Linear 
Expansion,  493.  —  (241.)  Volume  of  a  Vessel,  493. 

Expansion  of  Solids    .         .         .         .         .         .         .         .         .494 

(242.)  Measurement  of  Linear  Expansion,  494.  — (243.)  Determination  of 
Coefficient  of  Cubic  Expansion,  495. —  (244.)  General  Results,  496.— (245.) 
Expansion  of  Crystals,  498.  —  (246.)  Force  of  Expansion,  499.  —  (247.)  Illus- 
trations of  Expansion  of  Solids,  500.  —  (248.)  Applications  of  Expansion  of 
Solids,  504. 

Expansion  of  Liquids    .........  507 

(249.)  Absolute  and  Apparent  Expansion,  507.  —  (250.)  Absolute  Expan- 
sion of  Mercury,  508.  —  (251.)  Correction  of  Barometer  for  Temperature,  511. 

—  (252)  and  (253)  Apparent  Expansion  of  Mercury,  513.  —  (254.)    Relation 
between  Apparent  and  Absolute  Expansion,  515.  —  (255.)  Laws  of  the  Expan- 
sion of  Liquids,  516.  —  (256.)  Expansion  of  Liquids  above  the  Boiling-Poiqt, 
519  —  (257.)  Expansion  of  Water,  520.  —  (259.)  Point  of  Maximum  Density, 
520.  —  (259.)  Volume  of  Water  at  different  Temperatures,  526.  —  (260.)  Co^ 
efficient  of  Expansion  of  Water,  527. 

Expansion  of  Gases  f         .         ,         ,  528 

(261.)  Experiments  of  Regnault,  528.  —  (262.)  General  Results,  532.  —  (263.) 
Air-Thermometer,  533.  —  (264)  and  (265.)  Regnault's  Air-Thermometer,  534. 

—  (266.)  Air- Pyrometer,  539.  — (267.)  The  True  Temperature,  539.  —  (268.) 
Effects  and  Applications  of  the  Expansion  of  Air,  540. 

Problems  311  to  351 544 

Change  of  State  of  Bodies.  —  1.  Solids  to  Liquids        .         .         .       548 

(269.)  Melting-Point,  548.  —  (270.)  Vitreous  Fusion,  548.  —  (271.)  Freezing- 
Point,  548.  —  (272.)  Effect  of  Salts  on  the  Freezing-Point  of  Water,  549. — 
(273. )  Effect  of  Pressure  on  the  Melting-Point,  550.  —  (274.)  Change  of  Volume 
attending  Fusion,  551.  —  (275.)  General  Results,  553.  —  (276.)  Determination 
of  the  Melting-Point,  554.  —  (277  )  Heat  of  Fusion,  555.  —  (278)  and  (279.) 
Person's  Law,  560.—  (280.)  Absolute  Zero,  564. 

Change  of  State.  —  2.  Liquids  to  Gases  .         .         .         .         .565 

(281.)  Boiling-Point,  565.  —  (282.)  Variations  of  the  Boiling-Point,  568.— 
(283  )  Determination  of  the  Boiling-Point,  569.  —  (284.)  Formation  of  Aque- 
ous Vapor  of  Low  or  High  Tension,  570.  —  (285  )  Dalton's  Apparatus,  572. 

—  (286.)    Marcet's    Globe,    574. —  (287.)    Apparatus   of  Gay-Lussac,   574.— 
(288.)    Apparatus  of  Regnault,   575. — (289)    Discussion  of  Results,  580.— 
(290.)  Formauon  of  Vapors  of  different  Liquids,  582  —  (291.)  Maximum  Ten- 
sion of  Vapors,   584.  — (292.)  Gases  and    Vapors,  585.— (293.)   Distillation, 
588.  — (294.)  Steam-Bath,  591.  — (295.)  Papin's  Digester,  591.  — (296.)  Con- 
densation of  Gases,  592.  —  (297.)  Greatest  Density  of  Vapor,  600.  —  (298.) 
Smallest  Density  of  Vapor,  602. 

Heat  of  Vaporization 603 

(299  )  Latent  Heat  of  Vapor,  603.  —  (300.)  Latent  Heat  of  Steam,  606.— 
(301.)  Illustrations  of  Laws  of  Latent  Heat,  608.  —  (302.)  Applications  of  the 
Latent  Heat  of  Steam,  611.  —  (303.)  Spheroidal  Condition  of  Liquids,  611. 

Steam-Engine          .  615 

(305.)  The  Boiler,  615.—  (306  )  Dimensions  of  Steam-Boilers,  620.  — (307.) 
Watt's  Condensing-Engine,  621.— (308.)  Single-acting  Engine,  626.  —  (309.) 
Non-condensing  Engine,  628.  —  (310.)  Mechanical  Power  of  Steam,  631. — 
(311.)  Low  and  High  Pressure  Engines,  633. 

Problems  352  to  377 634 

JJygrometry    .         ,         .         .          .         .         .         .        -•  V       .         .  636 

(312.)  Formation  of  Vapor  in  an  Atmosphere  of  Gas,  636. —  (313.)  Hy- 
grometers, 639. —  (314.)  Drying  Apparatus,  646. 


Xii  CONTENTS. 


\gin  of  Heat 647 

(315.)  Sources  of  Heat,  647.  —  (316.)  Physical  Sources,  648.  — (317.)  Chem- 
ical Sources,  649. 

Propagation  of  Heat  .         .         .         .         .         .         .  .      .       650 

(318.)  Divisions  of  the  Subject,  650. —  (319.)  Laws  of  Radiation,  651.— 
(320.)  Laws  of  Conduction,  654.  —  (321.)  Illustrations  of  the  Laws  of  Conduc- 
tion, 657.  —  (322.)  Coefficient  of  Conduction,  659. 


CHAPTER    V. 
WEIGHING  AND  MEASURING. 

Solids    .     %•' -'."'•' 661 

(324.)  'Weight,  661.  —  (325.)  Specific  Gravity,  662.  —  (326.)  Volume,  664. 

Liquids     . .         .       665 

(327.)  Weight  and  Specific  Gravity,  665.  —  (328.)  Volume,  666. 

Gases  and  Vapors  .........  667 

(329.)  Weight,  667.— (330.)  Specific  Gravity  of  Gases,  670.  — (331.)  Spe- 
cific Gravity  of  Vapors,  674.  —  (332.)  Volumes  of  Gases,  679. 

Problems  378  to  420  .  682 


TABLES     gjjrcj     .        .      ;v';r:'':V'     .     .;>/      .        .        .         -  687 
INDEX  729 


ELEMENTS    OF    CHEMISTRY 


PART   I. 

CHEMICAL   PHYSICS 


PART    I. 

CHEMICAL   PHYSICS 


CHAPTER    I . 

INTRODUCTION. 

(1.)  Matter,  Body,  Substance.  —  That  of  which  the  universe 
consists,  which  occupies  space,  and  which  is  the  object  of  our 
senses,  is  named  matter.  Any  limited  portion  of  matter,  whether 
it  be  a  grain  of  sand  or  the  terrestrial  globe,  is  called  a  body  ; 
and  the  different  kinds  of  matter,  such  as  iron,  water,  or  air,  are 
termed  substances.  The  number  of  distinct  substances  already 
described  is  exceedingly  large  ;  but  they  are  all  formed  by  the 
combination  of  a  few  simple  substances,  called  Elements,  or  else 
consist  of  one  element  alone.  The  tendency  of  science  for  the 
last  fifty  years  has  been  to  increase  the  number  of  the  elements  ; 
at  present  sixty-two  are  admitted.  But  those  recently  discovered 
exist  only  in  minute  quantities  on  the  surface  of  the  globe,  and 
appear  to  play  a  very  subordinate  part  in  the  economy  of  na- 
ture. In  regard  to  the  essential  nature  of  matter,  or  of  the 
elements  of  which  it  consists,  we  have  no  knowledge ;  but  we 
have  observed  the  properties  of  almost  all  known  substances, 
as  well  elements  as  compounds,  have  studied  their  mutual  rela- 
tions and  their  action  on  each  other,  and  have  discovered  many 
of  the  laws  which  they  obey. 

(2.)  General  and  Specific  Properties.  —  If  we  study  the 
properties  of  iron,  we  shall  find  that  they  may  be  divided  into 
two  classes ;  —  one  class,  which  iron  possesses  in  common  with 
all  substances  ;  the  other,  which  are  peculiar  to  iron,  and  dis- 
tinguish it  from  other  kinds  of  matter.  A  mass  of  iron  occupies 
space,  —  or,  in  the  language  of  geometry,  possesses  extension ; 


4  CHEMICAL   PHYSICS. 

it  gravitates  towards  the  earth,  that  is,  it  has  weight.  But  ev- 
ery other  substance  as  well  as  iron,  gases  and  liquids  as  well  as 
solids,  possess  both  extension  and  weight.  Such  properties  as 
these,  which  are  common  to  all  kinds  of  matter,  are  called 
General  Properties.  Besides  these  general  properties,  iron  is 
endowed  with  other  qualities,  which  are  peculiar  to  itself.  Thus 
iron  not  only  possesses  extension,  but  it  has  a  peculiar  crystal- 
line form.  It  not  only  possesses  weight,  but  every  piece  of  iron 
weighs  7.8  times  as  much  as  the  same  bulk  of  water.  It  has 
also  a  certain  hardness  and  a  familiar  lustre.  Properties  like 
the  last,  which  are  peculiar  to  a  given  substance,  and  serve  to 
distinguish  it  from  other  kinds  of  matter,  are  called  Specific 
Properties. 

(3.)  Physical  and  Chemical  Changes. — If,  next,  we  study  the 
various  changes  to  which  all  substances  are  liable,  we  shall  find 
that  they  also  may  be  divided  into  two  classes ;  —  first,  those 
changes  by  which  the  specific  properties  are  not  altered ;  and,  sec- 
ondly, those  by  which  the  specific  properties  are  essentially  modi- 
fied, and  the  identity  of  the  substance  lost.  Thus  a  mass  of  copper 
may  be  transported  to  a  distant  part  of  the  globe,  it  may  be  di- 
vided into  exceedingly  small  particle's,  it  may  be  melted  and  cast 
into  nails,  it  may  be  coined ;  but  yet,  although  the  position,  the 
size,  or  the  external  shape  is  thus  entirely  changed,  those  quali- 
ties which  distinguish  copper,  which  make  it  to  be  copper,  are 
not  altered.  Water  may  be  frozen  by  cold  or  converted  into 
steam  by  heat,  yet  the  water  is  not  destroyed  ;  for  if  the  ice  be 
melted,  or  the  steam  condensed,  fluid  water  reappears,  with  all 
its  characteristic  properties.  A  bar  of  iron,  when  in  contact 
with  a  magnet,  becomes  itself  magnetic,  and  acquires  the  power 
of  attracting  small  particles  of  iron.  So  also  a  stick  of  sealing- 
wax,  if  rubbed  with  a  silk  handkerchief,  becomes  electrified,  and 
endowed  with  the  power  of  attracting  light  pieces  of  paper  ;  but 
the  peculiar  properties  of  iron  and  sealing-wax  are  not  essentially 
modified  by  these  changes.  Such  changes,  which  do  not  destroy 
the  identity  of  substance,  are  called  Physical  Changes. 

On  the  other  hand,  if  copper  filings  are  heated  for  some  time 
in  contact  with  the  air,  they  fall  into  a  black  powder  (oxide  of 
copper)  ;  if  heated  with  sulphuric  acid,  they  are  converted  into 
a  blue  crystalline  solid  (sulphate  of  copper)  ;  and  in  either  case 
the  properties  of  copper  entirely  disappear.  If  steam  is  passed 


INTRODUCTION.  5 

over  metallic  iron  heated  to  a  red  heat,  it  yields  a  combustible 
gas  (hydrogen) .  If  an  iron  bar  is  exposed  to  moist  air,  it  slowly 
crumbles  to  a  red  powder  (iron-rust).  If  sealing-wax  is  heated 
to  a  red  heat,  it  burns,  and  is  apparently  annihilated  ;  but,  as  we 
shall  hereafter  see,  it  changes  by  burning  into  invisible  gases 
(vapor  of  water  and  carbonic  acid).  Changes  like  these,  by 
which  the  distinguishing  properties  of  a  substance  are  altered, 
and  the  substance  itself  converted  into  a  different  substance,  are 
called  Chemical  Changes. 

(4.)  Physical  and  Chemical  Properties.  —  Corresponding  to 
the  two  classes  of  changes  above  described  are  two  classes  of 
properties,  into  which  we  may  divide  the  specific  properties  of  a 
substance.  Those  properties  which  a  substance  may  manifest 
without  undergoing  any  essential  change  itself,  or  causing  any 
essential  changes  in  other  substances,  are  generally  called  Phys- 
ical Properties.  On  the  other  hand,  those  properties  which  "  re- 
late essentially  to  its  action  on  other  substances,  and  to  the 
permanent  changes  which  it  either  experiences  in  itself,  or  which 
it  effects  upon  them,"  *  are  called  Chemical  Properties.  Thus, 
among  the  physical  properties  of  iron  we  should  include  its  great 
tenacity  and  malleability,  its  specific  gravity,  its  peculiar  lustre, 
its  great  infusibility,  the  facility  with  which  it  may  be  forged  at 
a  high  temperature,  its  power  of  transmitting  electricity  and  of 
assuming  magnetic  polarity.  Among  its  chemical  properties,  on 
the  other  hand,  we  should  enumerate  the  ease  with  which  it  rusts 
in  the  air,  the  readiness  with  which  it  dissolves  in  dilute  acids, 
its  combustibility  in  oxygen  gas,  and  many  others.  This  last 
class  of  properties  evidently  cannot  be  manifested  by  iron  with- 
out its  losing  its  essential  properties  and  ceasing  to  be  iron. 
The  first  class,  on  the  other  hand,  do  not  involve  any  such  radi- 
cal changes. 

(5.)  Chemistry  and  Physics.  —  It  is  the  province  of  Chemistry 
to  observe  the  chemical  properties  of  substances,  and  to  study  the 
chemical  changes  to  which  they  are  liable.  Physics,  on  the 
other  hand,  deals  with  the  physical  properties  and  the  physical 
changes  of  matter.  The  study  of  Chemistry  involves  the  discus- 
sion of  at  least  three  questions  in  regard  to  each  substance.  The 
chemist  asks,  in  the  first  place,  What  are  the  specific  properties 

*  Miller's  Elements  of  Chemistry,  Part  I.,  page  2. 
1* 


6  CHEMICAL   PHYSICS. 

of  the  substance  ?  in  the  second  place,  What  are  the  chemical 
changes  to  which  it  is  liable,  or  which  it  is  capable  of  producing' 
in  other  substances  ?  and,  in  the  third  place,  What  are  the 
causes  of  these  changes,  and  according-  to  what  laws  do  they 
take  place  ?  An  answer  to  the  first  of  these  questions  must  ob- 
viously be  obtained  before  the  chemist  can  approach  the  other 
two,  and  indeed  the  whole  of  Chemistry  is  based  upon  the  accu- 
rate observation  of  the  specific  or  distinguishing  properties  of 
substances.  These  properties,  as  we  have  seen,  are  physical  as 
well  as  chemical,  and  when  the  substances  can  only  be  observed 
in  a  state  of  chemical  rest,  the  chemist  is  obliged  to  depend  on 
the  physical  characteristics  alone  in  distinguishing  between  them ; 
and  under  all  circumstances  he  relies  upon  these  characters  to  a 
greater  or  less  degree.  Hence  the  study  of  Chemistry  necessa- 
rily implies  some  acquaintance  with  Physics,  and  a  thorough 
knowledge  of  Physics  will  always  be  found  useful  to  the  investi- 
gator of  chemical  phenomena.  There  are,  however,  some  portions 
of  the  subject  which  are  more  closely  connected  with  Chemistry 
than  the  rest,  and  which,  therefore,  it  is  particularly  convenient 
to  study  in  connection  with  this  science.  This  portion  of  Phys- 
ics, which  is  frequently  called  Chemical  Physics,  is  the  subject  of 
Part  I.  of  this  work.  Chemical  Physics  is  entirely  an  arbitrary 
division  of  the  science,  including  a  variety  of  subjects  which  are 
only  grouped  together  because  they  are  closely  connected  with 
Chemistry  in  its  present  condition.  It  treats  more  especially  of 
those  physical  properties  of  matter  which  are  used  by  chemists 
in  defining  and  distinguishing  substances,  and  which,  therefore, 
it  is  exceedingly  important  for  the  student  of  Chemistry  thor- 
oughly to  understand.  It .  treats  also  of  the  action  of  heat  on 
matter,  and  of  the  various  methods  by  which  the  weight  and 
volumes  of  bodies,  whether  solids,  liquids,  or  gases,  are  accu- 
rately measured. 

(6.)  Force  and  Law.  —  The  axiom,  that  every  change  must 
have  an  adequate  cause,  leads  us  to  refer  all  the  phenomena  of 
nature  to  what  we  term  forces ;  thus,  we  refer  the  falling  of 
bodies  towards  the  earth  to  the  force  of  gravitation,  the  motion 
of  a  steam-engine  to  the  expansive  force  of  heat,  and  the  burn- 
ing of  a  candle  to  the  force  of  chemical  affinity.  The  only  clear 
conception  of  the  origin  or  nature  of  force  to  which  man  can 
attain,  is  derived  from  studying  those  limited  phenomena  of 


INTRODUCTION.  7 

matter  which  can  be  traced  back  to  human  agency.  These  phe- 
nomena, as  we  are  conscious,  result  from  the  mysterious  action 
of  mind  on  matter ;  and  we  are  thus  led  to  infer  that  the  grand 
phenomena  of  nature  result  in  like  manner  from  the  action  of 
the  Infinite  Mind  on  matter.  In  this  view,  force  is  only  another 
name  for  the  volition  either  of  man  or  of  God,  and  the  varied 
phenomena  of  nature  are  only  the  manifestations  of  His  all- 
pervading  will. 

A  careful  study  of  material  phenomena  frequently  leads  us 
to  the  discovery  of  unexpected  analogies  between  those  which 
seemed  at  first  sight  entirely  disconnected.  No  two  phenomena 
are  apparently  less  related  than  the  motion  of  our  planet  through 
space  and  the  falling  of  a  stone  to  its  surface  ;  and  yet  it  has 
been  discovered  that  all  the  phases  of  both  phenomena  can  be  per- 
fectly explained,  by  assuming  that  every  particle  of  matter  in  the 
universe  attracts  every  other  particle  with  a  force  varying  directly 
as  the  mass  and  inversely  as  the  square  of  the  distance.  So  also 
the  ripples  on  the  surface  of  a  still  lake  have  no  apparent  resem- 
blance to  the  rays  of  light  which  play  upon  them  ;  but  neverthe- 
less it  has  been  found  that  all  the  phenomena  of  light  can  be 
fully  explained,  by  the  assumption  that  they  are  caused  by  a  sim- 
ilar undulatory  motion  in  an  ethereal  medium.  Such  generaliza- 
tions as  these,  by  which  the  phenomena  of  nature  are  linked 
together  and  in  a  measure  explained,  are  called  laws.  A  law  is 
the  mode  of  action  of  some  assumed  force  ;  thus,  the  law  of  gravi- 
tation is  the  mode  of  action  of  the  force  of  gravitation,  and  the  law 
of  undulations  is  the  mode  of  action  of  the  force  which  produces 
light.  But  if  force  is,  as  above  considered,  a  direct  emanation  of 
Divine  Power,  then  law  must  be  regarded  as  the  uniform  and 
unchanging  mode  of  action  of  the  Divine  Mind.  It  must  be  no- 
ticed, however,  that  what  we  call  a  natural  law  is  merely  our 
human  expression  of  the  Divine  mode  of  action  in  the  universe, 
and  that  this  is  accurate  in  proportion  to  the  extent  and  clear- 
ness of  our  knowledge  of  the  phenomena  and  of  their  relations. 
The  great  differences  which  exist  in  this  respect  are  implied  in 
the  very  language  of  science.  The  words  hypothesis,  theory, 
and  law  stand  for  the  same  thing,  that  is,  our  conception  of  the 
mode  in  which  God  acts  in  nature,  and  we  use  the  one  or  the 
other  according  to  our  own  conviction  of  the  accuracy  of  our 
conception.  If  we  suppose  that  it  is  merely  possibly  correct,  or 


8  CHEMICAL   PHYSICS. 

only  iii  part  true,  we  call  it  an  hypothesis  or  a  theory ;  but 
if  we  are  fully  convinced  of  its  truth,  we  say  that  it  is  a  law  of 
nature. 

One  criterion  by  which  we  judge  of  the  correctness  of  our 
ideas  of  the  Divine  mode  of  action  in  the  material  universe,  and 
by  which  we  determine  whether  a  proposed  explanation  of  mate- 
rial phenomena  should  be  regarded  as  an  hypothesis,  a  theory,  or 
a  law  of  nature,  is  the  completeness  with  which  it  explains  the 
class  of  phenomena  in  question.  A  law  of  nature  must  not  only 
cover  all  known  phenomena  of  the  class,  but  must  also  include  all 
those  which  may  hereafter  be  discovered,  and  even  predict  their 
existence  before  they  are  actually  observed.  This  has  been  the 
case  with  the  laws  of  nature  already  discovered,  and  with  none 
more  remarkably  than  with  the  law  of  gravitation,  which  may  be 
regarded  as  the  most  perfect  of  all.  This  law  was  first  advanced 
by  Newton  to  explain  the  phenomena  of  planetary  motion  then 
known,  by  connecting  them  with  those  of  falling  bodies  on  the 
surface  of  the  earth.  As  Astronomy  advanced,  this  law  was  not 
only  found  able  to  explain  all  the  complicated  perturbations  of 
lunar  and  planetary  motions  as  they  were  successively  discovered, 
but  it  even  went  before  the  observer,  and  enabled  the  astronomer 
to  calculate  with  absolute  exactness  the  extent  and  the  periods  of 
these  irregularities  of  motion,  although  it  will  require  centuries 
on  centuries  to  verify  his  results.  The  same  is  also  true  of  the  not 
less  remarkable  law  of  undulations  advanced  by  Huyghens  to  ex- 
plain the  comparatively  few  facts  of  optics  known  in  his  time.  As 
these  facts  have  been  rapidly  multiplied  by  the  wonderful  discov- 
eries of  Malus  and  of  Young,  the  law  has  not  only  been  found 
fully  adequate  to  explain  all,  but  it  has  also  predicted  the  existence 
of  phenomena,  which,  like  that  of  conical  refraction,  would  hardly 
have  been  noticed  had  they  not  been  thus  pointed  out.  To  hy- 
potheses and  theories  we  do  not  look  for  the  sam,e  full  explana- 
tion of  all  the  facts  which  we  require  of  a  law.  They  are  re- 
garded as  merely  provisional  expedients  in  science  until  the  law 
shall  be  discovered,  as  guesses  at  truth  before  the  truth  is  known. 
Laws  have  been  said  to  be  the  thoughts  of  God  manifested  in 
nature  and  expressed  in  human  language.  Hypotheses,  then, 
are  our  first  imperfect  comprehensions  of  these  thoughts.  They 
are  also  the  shadowing  forth  of  laws,  and  the  progress  of  science 
has  always  been  from  the  dim  glimmerings  of  truth  in  the 


INTRODUCTION.  9 

hypothesis  and  the  theory,  to  the  full  light  of  knowledge  in  the 
law. 

Another  criterion  of  the  validity  of  a  law,  no  less  important 
than  the  one  we  have  considered,  is  to  be  found  in  the  analogies 
of  nature.  The  force  of  analogy  is  the  great  directing  principle 
in  the  mind  of  the  successful  student.  It  is  this  which  leads 
him  to  pronounce  some  theories  unsound,  although  apparently 
sustained  by  facts,  and  to  accept  others,  which,  although  not  fully 
verified  by  experiment,  are  yet  in  harmony  with  the  general  plan 
and  order  of  creation,  and  with  those  convictions  of  the  truth 
which  are  based  on  an  enlarged  knowledge  and  an  extended  ob- 
servation of  natural  phenomena. 

In  thus  defining  law  as  the  thoughts  of  God  manifested  in  na- 
ture, and  force  as  the  constant  action  of  his  infinite  will,  we  must 
be  careful  to  remember  that  this  is  a  conclusion  of  metaphysical 
rather  than  of  physical  science.  The  demonstrations  of  physical 
science  unquestionably  point  to  the  same  result ;  but  it  is  the 
goal  towards  which  they  tend,  rather  than  one  which  they  have 
attained.  In  the  present  condition  of  science,  we  are  obliged  to 
use  language  which  implies  the  existence  of  separate  and  dis- 
tinct forces  ;  but  this  is  unimportant  so  long  as  we  keep  the  truth 
in  view,  and  do  not  allow  ourselves  to  be  led  into  materialism  by 
the  unavoidable  imperfections  of  scientific  language. 


CHAPTER    II. 

GENERAL  PROPERTIES   OF  MATTER. 

(7.)  Essential  and  Accidental  Properties.  —  Of  the  general 
properties  of  matter,  I  shall  consider  in  this  chapter  the  follow- 
ing, which  are  common  to  all  bodies,  solids,  fluids,  and  gases, 
and  which  it  is  important  for  us  to  study  early  in  our  course :  — 

Essential  Properties.  Accidental  Properties. 

1.  Extension,  implying,         4.  Weight. 

a.  Volume.  5.  Divisibility. 

b.  Density.  r    6.  Porosity. 

2.  Impenetrability.  7.  Compressibility  and  Expansibility. 

3.  Mobility.  8.  Elasticity. 

The  first  three  of  these  properties  are  evidently  more  essential 
than  the  rest.  We  cannot  conceive  of  a  kind  of  matter  which 
would  be  destitute  of  them.  Attempt  to  conceive  of  a  variety 
of  matter  which  would  not  occupy  space,  which  would  not  resist 
an  effort  to  condense  it  into  a  smaller  volume,  or  which  would  be 
incapable  of  motion,  and  it  will  be  seen  at  once  that  these  prop- 
erties form  an  essential  part  of  the  very  idea  of  matter.  The 
last  five  are  as  universal  properties  of  matter  as  the  first  three ; 
but  they  do  not  seem  to  our  minds  to  be  so  essential,  for  we  can 
conceive  of  matter  which  would  not  possess  them.  It  is  not 
difficult  to  conceive  of  matter  without  weight,  so  hard  as  to  be 
indivisible,  at  least  in  a  physical  sense,  without  pores,  incom- 
pressible, and  therefore  unelastic.  Indeed,  some  physicists  refer 
the  phenomena  of  light  and  heat  to  an  imponderable  variety  of 
matter,  and  the  Atomic  Theory  supposes  that  the  assumed  atoms 
are  indivisible,  incompressible,  and  without  pores. 

(8.)  Extension  and  Volume.  —  When  we  say  that  matter  has 
extension,  we  merely  mean  that  it  occupies  space,  and  the  amount 
of  space  which  a  given  body  occupies  we  call  its  volume.  We 
study  extension  without  any  reference  to  the  matter  of 


GENERAL  PROPERTIES  OF  MATTER.  11 

which  it  is  a  property,  and  we  shall  thus  arrive  at  the  principles 
of  Geometry.  —  This  science  distinguishes  three  degrees  of  ex- 
tension :  the  solid,  or  extension  in  three  dimensions  ;  the  surface, 
or  extension  in  two  dimensions ;  and  the  line,  or  extension  in 
one  dimension.  Only  the  first  of  these,  however,  can  be  said  to 
be  represented  in  matter,  for  a  surface  is  only  the  boundary  of  a^ 
solid,  and  a  line  the  boundary  of  a  surface. 

(9.)  The  Measure  of  Extension.  —  In  order  to  measure  the 
Volume  of  a  solid,  the  Area  of  a  surface,  or  the  Length  of  a  line, 
we  adopt  some  arbitrary  unit  of  extension  of  the  same  order,  and 
by  the  principles  of  Geometry  compare  all  other  extensions  with 
it.  The  unit  of  length  is  the  only  one  which  must  be  arbitrary, 
because  we  can  use  a  square  of  this  unit  in  measuring  surfaces, 
and  a  cube  of  this  unit  in  measuring  solids.  Various  units  both 
of  length  and  of  volume  have  been  adopted  in  different  countries. 
Of  the  numerous  systems  of  measure  there  are  two  which  it  is 
important  for  us  to  study. 

ENGLISH  SYSTEM  OF  MEASURES. 

(10.)  Units  of  Length.  —  The  unit  of  length  which  has  been 
adopted  in  this  country  is  the  same  as  that  of  England.  It  is 
called  a  yard^  and  is  said  to  have  been  introduced  by  King  Henry 
the  First,  "  who  ordered  that  the  ulna  or  ancient  ell,  which 
corresponds  to  the  modern  yard,  should  be  made  of  the  exact 
length  of  his  own  arm,  and  that  the  other  measures  of  length 
should  be  based  upon  it.  This  standard  has  been  maintained 
without  any  sensible  variation,  and  is  the  identical  yard  now  used 
in  the  United  States,  and  is  declared  by  an  act  of  Parliament, 
passed  in  June,  1824,  to  be  the  standard  of  linear  measure  in 
Great  Britain."  *  The  clause  in  the  act  is  as  follows  :  — 

"  From  and  after  the  first  day  of  May,  1825,  [subsequently 
extended  to  the  first  of  January,  1826,]  the  straight  line,  or  the 
distance  between  the  centres  of  the  two  points  in  the  gold  studs 
in  the  straight  brass  rod  now  in  the  custody  of  the  clerk  of  the 
House  of  Commons,  whereon  the  words  and  figures  '  Standard 
Yard,  1760,'  are  engraved,  shall  be  the  original  and  genuine 
standard  of  length  or  lineal  extension  called  a  yard ;  and  the 

*  Hunt's  Merchant's  Magazine,  Vol.  IV.  p.  334. 


12  CHEMICAL   PHYSICS. 

same  straight  line,  or  distance  between  the  centres  of  the  said  two 
points  in  the  said  gold  studs  in  the  said  brass  rod,  the  brass  being 
at  the  temperature  of  sixty-two  degrees  by  Fahrenheit's  ther- 
mometer, shall  be  and  is  hereby  denominated  the  i  Imperial 
Yard,'  and  shall  be  and  is  hereby  declared  to  be  the  unit  and 
only  standard  measure  of  extension,  wherefrom  or  whereby  all 
other  measures  of  extension  whatsoever,  whether  the  same  be 
lineal,  superficial,  or  solid,  shall  be  derived,  computed,  and  ascer- 
tained ;  and  that  all  measures  of  length  shall  be  taken  in  parts 
or  multiples  or  certain  proportions  of  the  said  standard  yard ; 
and  that  one  third  part  of  the  said  standard  shall  be  a  foot,  and 
the  twelfth  part  of  such  foot  shall  be  an  inch  ;  and  that  the  pole 
or  perch  in  length  shall  contain  five  and  a  half  such  yards,  the 
furlong  two  hundred  and  twenty  such  yards,  and  the  mile  one 
thousand  seven  hundred  and  sixty  such  yards." 

And  the  act  further  declares,  that  "if  at  any  time  hereafter 
the  said  imperial  standard  yard  shall  be  lost,  or  shall  be  in  any 
manner  destroyed,  defaced,  or  otherwise  injured,  it  shall  be  re- 
stored by  making,  under  the  direction  of  the  Lords  of  the  Treas- 
ury, a  new  standard  yard,  bearing  the  proportion  to  a  pendulum 
vibrating  seconds  of  mean  time  in  the  latitude  of  London  in  a 
vacuum  and  at  the  level  of  the  sea,  as  36  inches  to  39.1393 
inches." 

The  event  contemplated  by  the  last  clause  of  the  act  actu- 
ally happened  in  less  than  ten  years  after  its  passage,  for  the 
standard  was  destroyed  by  the  fire  which  consumed  the  Par- 
liament House  in  1834.  It  was  then  found  that  this  clause 
was  entirely  nugatory,  and  that  the  country  was  left  without  a 
legal  standard ;  for  the  restoration  of  the  lost  yard  could  not  be 
effected  with  any  tolerable  certainty  in  the  manner  prescribed  by 
the  act.  The  measurement  of  the  seconds  pendulum,  which  was 
made  the  basis  of  the  peremptory  enactment,  was  executed  with 
extraordinary  precaution  and  skill  by  Captain  Kater ;  but  this 
measurement  was  subsequently  found  to  be  incorrect,  owing  to 
the  neglect  of  certain  precautions  in  the  determination  of  the 
length  of  the  pendulum,  which  more  recent  experiments  have 
shown  to  be  indispensable.  On  account  of  these  sources  of  error, 
the  yard  could  not  be  restored  with  certainty  in  the  prescribed 
manner  within  one  five-hundredth  of  an  inch,  an  amount  which, 
although  inappreciable  in  all  ordinary  measurements,  is  a  large 


GENERAL  PROPERTIES  OP  MATTER.  18 

error  in  a  scientific  standard.  The  commissioners  appointed,  in 
1838,  "  to  consider  the  steps  to  be  taken  to  restore  the  lost 
standard,"  recommended  the  construction  of  a  standard  yard,  and 
four  "  Parliamentary  copies"  from  the  best  authenticated  copies 
of  the  imperial  standard  yard  which  then  existed.  They  also 
prescribed  the  manner  in  which  the  standard  and  the  four  Par- 
liamentary copies  should  be  preserved,  and  recommended  further 
that  authenticated  copies,  prepared  with  all  the  refinements  of 
modern  art,  should  be  distributed  throughout  the  realm,  and 
placed  in  the  custody  of  certain  government  officers.  The  recom- 
mendations of  this  commission  have  in  general  been  followed,* 
and  by  an  act  of  Parliament,  which  received  the  royal  assent 
July  30,  1855,  the  restored  standard  yard  was  legalized. 

The  actual  standard  of  length  of  the  United  States  is  a  brass 
scale  eighty-two  inches  in  length,  prepared  for  the  survey  of 
the  coast  of  the  United  States,  by  Troughton  of  London,  in  1813, 
and  deposited  in  the  Office  of  Weights  and  Measures  at  Wash- 
ington. The  temperature  at  which  this  scale  is  a  standard  is 
62°  Fahrenheit,  and  the  yard  measure  is  between  the  27th  and 
63d  inches  of  the  scale. f  From  recent  comparisons  of  this  scale 
with  a  bronze  copy  of  the  new  British  standard,  presented  to  the 
United  States  by  the  British  government,  it  appears  that  the  Brit- 
ish standard  is  shorter  than  the  American  yard  by  0.00087  of  an 
inch,  —  a  quantity  by  no  means  inappreciable.  Carefully  adjusts 
ed  copies  of  the  United  States  standard  yard  have  been  prepared, 
by  the  order  of  Congress,  under  the  direction  of  Professor  A.  D. 
Bache,  Superintendent  of  Weights  and  Measures,  and  distributed 
to  the  different  States  of  the  Union  ;  but  up  to  1859  the  standard 
had  not  been  denned  by  any  act  of  Congress.  The  subdivisions 
and  multiples  of  the  yard  are  given  in  Table  I.  at  the  end  of 
this  volume,  with  their  respective  numerical  relations. 

(11.)  Units  of  Surface  and  of  Volume.  —  All  the  English 
units  of  surface  are  squares  whose  sides  are  equal  to  the  units  of 
length,  with  the  exception  of  a  few,  which,  like  the  perch  or  the 
acre,  are  used  in  the  measurement  of  land,  and  in  other  coarse 
measurements.  The  square  inch  is  the  most  convenient  unit  of 

*  Account  of  the  Construction  of  the  New  National  Standard  of  Length  and  of  its 
principal  Copies.  By  G.  B.  Airy,  Esq.,  Astronomer  Royal.  Philosophical  Transac- 
tion<  of  the  Royal  Society  of  London,  Vol.  CXLVII.  p.  621. 

t  Report  of  the  Secretary  of  the  Treasury  on  Weights  and  Measures,  34th  Congress, 
3d  Session.     Ex.  Doc.  No.  27,  1857. 
2 


14  CHEMICAL   PHYSICS. 

surface  for  scientific  purposes.     The  circular  inch  is  also  some- 
times used  by  engineers. 

When  volume  can  be  calculated  from  linear  measurements  by 
the  principles  of  Geometry,  it  is  usual  to  estimate  it  in  cubic 
yards,  cubic  feet,  or  cubic  inches,  and  it  is  in  this  way  that  earth- 
work and  masonry  are  measured.  In  measuring  the  volume 
of  gases,  liquids,  and  of  many  varieties  of  solids,  however,  an 
arbitrary  unit  is  more  frequently  employed.  Several  such  units, 
entirely  independent  of  each  other,  were  formerly  used  in  dif- 
ferent trades ;  but  the  Imperial  Gallon,  established  by  an  act 
of  Parliament,  has  been  substituted  for  all  other  arbitrary  meas- 
ures of  volume.  It  is  equal  to  277.274  cubic  inches,  and  con- 
tains ten  avoirdupois  pounds  of  water  at  62°  of  the  Fahrenheit 
thermometer.  A  table  showing  the  relations  of  the  units  both 
of  surface  and  of  volume,  will  be  found  in  connection  with  the 
table  of  linear  measure. 

FRENCH  SYSTEM  OF  MEASURES. 

(12.)  History. — The  decimal  metrical  system  of  France  origi- 
nated with  her  Revolution.  "It  is  one  of  those  attempts  to 
improve  the  condition  of  human  kind,  which,  should  it  ever  be 
destined  ultimately  to  fail,  would  in  its  failure  deserve  little  less 
admiration  than  in  its  success."  *  Previous  to  the  Revolution, 
he  metrical  system  of  France  was  even  more  complex  than  that 
of  England,  almost  every  province  having  distinct  standards  of 
weight  and  measure  of  its  own,  —  a  condition  of  things  which 
was  productive  of  the  most  serious  inconveniences  in  trade  and 
commerce.  The  first  effective  movement  to  reform  this  extreme 
diversity  was  made  by  Talleyrand  in  the  Constituent  Assembly 
of  1790,  and  the  new  system  was  developed  by  a  commission 
of  members  of  the  Academy  of  Sciences,  consisting  of  Borda, 
Lagrange,  Laplace,  Monge,  and  Condorcet.  In  their  report, 
which  appeared  in  the  following  year,  they  proposed  that  the 
ten-millionth  part  of  the  quadrant  of  a  meridian  of  the  globe 
should  be  adopted  as  the  basis  of  a  new  metrical  system,  and 
called  a  Metre  ;  that  the  subdivisions  and  multiples  of  all 
measures  should  be  made  on  the  decimal  system  ;  that,  in 

*  Report  upon  Weights  and  Measures,  by  John  Quincy  Adams,  which  may  be  con- 
sulted for  a  full  history  of  this  subject. 


GENERAL   PROPERTIES   OP   MATTER.  15 

order  to  determine  the  metre,  an  arc  of  the  meridian,  extend- 
ing from  Dunkirk  to  Barcelona,  six  and  a  half  degrees  to  the 
north  and  three  degrees  to  the  south  of  the  mean  parallel  of  45°, 
should  be  measured,  and  that  the  weight  of  a  cubic  decimetre  of 
distilled  water  at  the  temperature  of  melting  ice  should  be  deter- 
mined and  adopted  as  the  unit  of  weight.  They  also  proposed 
a  new  subdivision  of  the  quadrant  into  one  hundred  degrees, 
the  degree  into  one  hundred  minutes,  and  the  minute  into  one 
hundred  seconds.  This  report  was  accepted,  and  the  execution 
of  the  great  work  was  intrusted  to  four  separate  commissions, 
including  the  names  of  the  most  celebrated  men  of  science  of 
France.  The  measurement  of  the  arc  was  assigned  to  De- 
lambre  and  Me'chain,  and  the  determination  of  the  weight  of 
water  to  Lefevre-Gineau  and  Fabbroni. 

Delambre  met  with  great  difficulties  in  the  measurement  of  the 
French  portion  of  the  arc.  The  work  was  commenced  at  the 
most  violent  period  of  the  Revolution,  and  was  repeatedly  ar- 
rested by  the  suspicions  of  the  people  and  the  fickleness  of  the 
government.  But,  after  repeated  interruptions,  the  work  was 
completed  in  1796,  when  the  whole  of  the  records  of  the  survey 
were  submitted  to  a  special  commission,  consisting  of  Delambre, 
Me'chain,  Laplace,  and  Legendre,  of  France,  Von  Swinden,  of 
Holland,  and  Trails,  of  Switzerland,  who  found  the  length  of 
the  metre  to  be  443.259936  lignes.* 

The  determining  of  the  unit  of  weight  led  to  a  most  impor- 
tant discovery.  The  commission  discovered  that  water  was  most 
dense,  not,  as  had  been  previously  supposed,  at  the  temperature 
of  melting  ice,  but  at  a  temperature  nearly  five  degrees  of  the 
centigrade  scale  higher.  They  therefore  determined  the  weight 
of  a  cubic  decimetre  of  distilled  water  at  its  greatest  density,  and 
not,  as  had  been  first  proposed,  at  0°  ;  and  to  this  weight  was 
given  the  name  of  Kilogramme.  On  the  19th  of  August,  1798, 
the  original  metre  and  kilogramme  were  presented,  with  an  ad- 
dress, to  the  two  councils  of  the  legislative  body. 

In  order  to  avoid  sources  of  error  which  might  arise  from  the 
ellipticity  of  the  earth,  the  measurement  of  the  arc  from  Dunkirk 
to  Montjouy  (Monjuich),  near  Barcelona,  was  subsequently  ex- 
tended by  Biot  and  Arago,  in  accordance  with  the  original  design 

*  The  French  standard  then  in  use. 


16  CHEMICAL  PHYSICS. 

of  Me*chain,  to  Formentera,  one  of  the  Balearic  Isles,  so  as  to  com- 
prehend an  arc  of  more  than  twelve  degrees  between  the  extreme 
stations,  which  would  be  almost  exactly  bisected  by  the  parallel  of 
45°  ;  it  being  well  known  that  from  the  length  of  any  given  arc 
which  is  bisected  by  the  parallel  of  45°  may  be  deduced  a  length 
of  a  quadrant  of  a  meridian,  and  therefore  of  the  metre,  which 
would  be  independent  of  the  earth's  ellipticity.  The  observations 
of  Biot  and  Arago  were  calculated  by  the  same  methods  prescribed 
by  Delambre  in  the  previous  survey,  and  the  result  appeared  to 
verify  the  accuracy  both  of  the  method  and  of  the  original  work, 
since  the  length  of  the  metre,  which  was  the  result  of  the  entire 
arc  between  Dunkirk  and  Formentera,  was  found  to  be  almost 
identical  with  that  which  had  been  previously  determined.  The 
perfect  accuracy  of  the  base  of  the  French  metrical  system 
seemed  thus  to  be  established  ;  but,  unfortunately,  later  exam- 
inations have  not  verified  this  conclusion. 

In  the  year  1838,  Puissant,  who  was  then  engaged  in  con- 
structing the  Carte  Geographique  de  la  France,  announced  that 
there  existed  an  important  error  in  the  calculated  length  of  the 
arc  of  the  meridian  on  which  the  length  of  the  metre  was  based, 
and  that  the  calculated  metre  differed  from  the  one  ten-millionth 
part  of  the  quadrant  —  the  metre  by  definition  —  by  -5  ^Vu  of  *ne 
whole  ;  and  that  the  provisional  metre  hastily  adopted  on  the  1st 
of  August,  1793,  during  the  heat  of  the  Revolution,  and  based 
on  an  old  measurement  of  an  arc  of  the  meridian  by  Lacaille, 
was  in  reality  more  accurate  than  that  which  was  established  by 
the  labors  of  the  great  commission.  Puissant's  results  were  sub- 
sequently verified  by  a  careful  re-examination  of  the  calculations 
of  the  commission,  when  it  appeared  that  the  error  he  had  de- 
tected, great  as  it  was,  resulted  from  two  greater  errors,  which 
had  in  part  balanced  each  other  in  the  final  result.  It  was  not, 
however,  thought  best  to  correct  the  length  of  the  actual  metre, 
and  it  still  remains  the  same  as  that  adopted  by  the  commission. 
Thus,  then,  it  appears  that  the  metre  of  France  is  no  less  an  ar- 
bitrary standard  of  measure  than  the  English  yard,  and  that,  like 
the  last,  if  destroyed,  it  cannot  be  restored  in  conformity  to  its 
definition.  Like  all  other  results  of  human  labor,  it  bears  the 
mark  of  imperfection  and  fallibility ;  and  the  singular  history  * 

*  See  the  Edinburgh  Review,  Vol.  LXXVII.  page  228,  for  a  full  account  of  this 
subject. 


GENERAL  PROPERTIES  OF  MATTER.  17 

of  the  work  teaches  most  impressively  the  limitation  and  uncer- 
tainty of  the  best  human  powers  of  observation  and  reasoning. 

(13.)  Subdivisions  and  Multiples  of  the  Metre.  —  The  subdi- 
visions and  multiples  of  the  metre  are  all  decimal.  The  names 
of  the  multiples  are  derived  from  the  Greek  numerals,  and 
those  of  the  subdivisions  from  the  Latin.  They  are  as  fol- 
lows :  — 

Measures  of  Length. 

Kilometre    =  1000  metres.  Metre  (m.)  =  1.000  metre. 

Hectometre  =    100      "  Decimetre  (d.  m.)  =  0.100      " 

Decametre  =      10      "  Centimetre  (c.  m.)  =  0.010      " 

Metre  1      "  Millimetre  (m.in.)  =  0.001      " 

In  this  work,  the  abbreviations  in  the  table  will  be  used  to  desig- 
nate these  units  of  length. 

(14.)  Units  of  Surface  and  of  Volume.  —  The  French  units  of 
surface  are  squares  whose  sides  are  equal  to  the  units  of  length. 
They  are  named  squares  of  these  units,  and  will  be  designated  by 
the  abbreviations  as  above  with  an  exponent  2  ;  thus,  5  m?  stands 
for  five  square  metres,  and  3  cTni?  for  three  square  centimetres. 
The  common  French  measure  of  land  is  the  square  decametre, 
which  is  called  an  are,  and  the  names  of  its  decimal  multiples 
and  subdivisions  are  formed  like  those  of  the  metre. 

The  units  of  volume  are  in  like  manner  cubes  of  the  units 
of  length,  and  are  named  cubic  metres,  cubic  centimetres,  etc. 
They  will  be  designated  as  before,  using  the  exponent  3 ;  thus, 
5  cTm.3  stands  for  five  cubic  centimetres.  The  cubic  decimetre  is 
the  common  measure  of  liquids,  and  is  called  a  litre  =  0.001  m:3. 
So  also  the  cubic  metre,  which  is  the  measure  for  bulky  materials, 
such  as  fire-wood,  has  received  the  separate  name  stere.  Both  the 
litre  and  the  st£re  have  decimal  multiples  and  subdivisions  named 
like  those  of  the  metre.  The  very  simple  decimal  relations  of 
the  French  system  render  it  exceedingly  valuable  in  all  scientific 
calculations,  and  it  will  therefore  be  exclusively  used  in  this 
book.  The  relation  between  the  French  and  English  units  is 
given  in  Table  L,  and  with  the  aid  of  the  annexed  logarithms  the 
reduction  from  one  to  the  other  can  easily  be  made.  A  similar 
table  has  also  been  added,  which  gives  the  means  of  reducing 
the  metre  to  several  of  the  most  important  standards  in  use  on 
the  continent  of  Europe. 
2* 


18  CHEMICAL   PHYSICS. 

The  methods  of  determining  approximately  length,  surface,  and 
solidity,  by  means  of  the  units  of  measure  just  described,  are 
known  to  all  who  have  studied  Geometry,  and  need  not  there- 
fore be  described.  When  great  accuracy,  however,  is  required, 
as  in  most  scientific  investigations,  these  methods  become  less 
simple,  and  cannot  be  fully  understood  until  the  student  is  famil- 
iar with  the  action  of  heat  on  matter.  This  will  be  described  in 
the  chapter  on  Weighing  and  Measuring. 

(15.)  Density  and  Mass.  —  The  idea  of  volume  involves  that 
of  density,  since  a  given  volume  may  be  filled  with  a  greater  or 
a  less  amount  of  matter.  The  amount  of  matter  contained  in  a 
cubic  centimetre  of  hydrogen  gas,  for  example,  is  many  thousand 
times  less  than  that  which  fills  a  cubic  centimetre  of  gold.  As 
used  in  Physics,  the  word  density  means  the  amount  of  matter 
contained  in  the  unit  of  volume.  This  quantity  will  always  be 
represented  by  D. 

The  amount  of  matter  which  a  body  contains  is  termed  its  mass, 
and  is  represented  by  M.  For  example,  the  amount  of  matter 
which  the  sun,  the  earth,  a  locomotive,  a  cannon-ball,  or  a  grain 
of  sand  contains,  is  called  the  mass  of  that  body.  When  the 
body  is  homogeneous,  there  is  a  very  simple  relation  between  its 
mass  and  its  density.  Its  density,  as  we  have  seen,  is  the  amount 
of  matter  which  one  cubic  centimetre  of  the  body  contains.  Its 
mass  is  the  amount  of  matter  which  the  whole  body  contains. 
If,  then,  we  represent  by  Fthe  volume  of  the  body,  that  is,  the 
number  of  cubic  centimetres  which  it  occupies,  it  follows  that 

M=DV.  [l.J 

This,  translated  into  ordinary  language,  means  that  the  amount 
of  matter  which  a  body  contains  is  equal  to  the  amount  of  matter 
which  one  cubic  centimetre  of  the  body  contains,  multiplied  by 
the  number  of  cubic  centimetres  which  the  body  occupies.  The 
mass  of  a  body  is  determined  from  its  weight  ;  for  it  will  *be 
hereafter  proved  that  the  weight  of  a  body  is  proportional  to  the 
amount  of  matter  it  contains.  It  must,  however,  be  carefully 
kept  in  mind,  that  weight,  although  proportional  to  mass,  is  not 
the  mass,  just  as  the  arc  of  a  circle  is  an  entirely  different  quan- 
tity from  the  angle  which  it  measures. 

From  equation  [1]  we  obtain  D  =  =  ;  that  is,  the  density 
is  the  mass  of  the  unit  of  volume,  or,  as  above,  the  amount  of 


GENERAL  PROPERTIES  OF  MATTER.  19 

matter  in  the  unit  of  volume.  In  order  to  estimate  mass  and 
density,  we  assume  a  certain  amount  of  matter  as  a  unit  of  mass 
and  compare  all  other  amounts  with  it.  When  we  say  that  the 
mass  of  a  given  volume  of  iron  is  10,  we  mean  that  the  amount 
of  matter  it  contains  is  ten  times  as  great  as  the  amount  of  matter 
contained  in  this  assumed  unit  of  mass.  In  like  manner,  when 
we  say  that  the  density  of  mercury  is  equal  to  1.386,  we  mean 
that  one  cubic  centimetre  of  mercury  contains  1.386  times  as  much 
matter  as  the  unit  of  mass.  In  every  case,  the  numbers  express- 
ing mass  and  density  stand  for  units  of  mass.  The  unit  of  mass 
is  derived  from  the  unit  of  weight,  as  will  be  explained  in  the 
section  on  Gravitation. 

The  terms  Mass  and  Density  will  be  constantly  used  through- 
out this  work,  and  their  meaning  should,  therefore,  be  clearly 
impressed  upon  the  mind. 

(16.)  Impenetrability.  —  Matter  not  only  occupies  space,  but  it 
also  resists,  with  differing  degrees  of  force,  any  attempt  to  reduce 
it  into  a  smaller  volume.'  Thus,  one  litre  of  air  can  be  made  to 
occupy  a  volume,  so  far  as  we  can  see,  indefinitely  smaller,  but 
only  by  great  mechanical  force.  This  resistance  which  all  bodies 
offer  to  any  attempt  to  condense  them,  is  termed  Impenetrability. 

PROBLEMS. 

1.  What  is  the  length  of  one  degree  on  the  meridian  at  the  latitude  of 
45°  in  French  linear  measure  ? 

2.  The  latitude  of  Dunkirk  was  found  by  Delambre  to  be  51°  2'  9"; 
that  of  Formentera,  as  determined  by  Biot,  is  38°  39'  56".     What  is  the 
distance  between  these  parallels  in  metres  ? 

3.  The  distance  between  the  parallels  of  Dunkirk  and  Formentera,  as 
determined  by  triangulation,  is  730,430  toises  of  864  lignes  each.     What 
is  the  length  of  a  metre  in  fractions  of  a  toise,  and  in  lignes  ? 

4.  The  equatorial  and  polar  diameters  of  the  globe  are  to  each  other  in 
the  proportion  of  299.15  to  298.15.    What  is  the  length  of  each  in  metres  ? 

5.  Had  the  decimal  division  of  the  circle  mentioned  on  page  15  been 
adopted,  what  would  have  been  the  length  of  one  degree,  one  minute,  and 
one  second  in  metres  ? 

6.  To  how  many  cubic  centimetres  do  five  litres  correspond  ?     To  how 
many  do  3.456  litres,  0.0034  litre,  and  5.674  litres  correspond? 

7.  To  how  many  cubic  metres  do  564.82  litres,  3240.85>  litres,  0.675 
litre,  and  0.032  litre  correspond  ? 

8.  A  box,  measuring  ten  centimetres  in  each  direction,  will'  hold  how 
many  litres,  and  what  portion  of  a  cubic  metre? 


20  CHEMICAL   PHYSICS. 

9.  Reduce,  by  means  of  the  table  at  the  end  of  the  book,  — 

a.  30  inches  to  fractions  of  a  metre. 

b.  76  centimetres  to  English  inches. 

c.  36  feet  to  metres. 

d.  10  metres  to  feet  and  inches. 

10.  Reduce,  by  means  of  the  table  at  the  end  of  the  book, — 

a.  8  Ibs.  6  oz.  to  grammes. 

b.  7640  grammes  to  English  apothecaries'  weight. 

c.  45  grains  to  grammes. 

11.  Reduce,  by  means  of  the  table  at  the  end  of  the  book, — 

a.  4  pints  to  litres  and  cubic  centimetres. 

b.  5  gallons  to  litres  and  cubic  centimetres. 

c.  5  litres  to  English  measure. 

d.  4  cubic  centimetres  to  English  measure. 


MOTION. 

(17.)  Position.  — We  conceive  of  a  body,  not  only  as  occupying 
a  certain  portion  of  space,  but  also  as  existing  in  space,  and  there- 
fore as  being  in  a  determinate  Position  with  reference  to  other 
bodies.  A  book,  for  example,  not  only  fills  a  certain  amount 
of  space,  but  also  holds  a  certain  position  with  reference  to  the 
surface  of  the  table  on  which  it  lies,  or  with  reference  to  the 
walls  of  the  room  in  which  the  table  stands.  If  we  select  a 
point  of  that  book,  its  position  on  the  table  can  easily  be  de- 
fined by  measuring  its  distance  from  each  of  two  adjacent 
edges  of  the  table  along  a  line  parallel  to  the  other  of  the 
two  edges,  and  its  position  in  the  room  can,  in  like  manner, 
be  defined  by  measuring  its  distance  from  two  adjacent  walls 
and  the  ceiling  along  lines  parallel  to  the  three  edges  formed 
by  the  meeting  of  these  three  surfaces.  This  is  the  method 
most  commonly  used  in  Geometry  of  defining  the  position 

of  a  point.  The  distances 
which  determine  the  position 
of  a  point  are  called  co-ordi- 
nates, and  the  edges  and  sur- 
faces to  which  the  position  is 
referred  are  called  co-ordinate 
axes  and  co-ordinate  planes. 
In  Fig.  1,  the  position  of  the 
point  p  is  determined  by  the 


GENERAL  PROPERTIES  OP  MATTER.  21 

distances  p  b  =  b  and  p  a  =  a  from  the  two  co-ordinate  axes  o  x 
and  o  y ;  and  in  Fig.  2,  the  position  of  the  same  point  is  determined 
by  the  distances  p  c  =  c,  p  b  =  b,  and  pa  =  a  from  the  planes  xy, 
x  z,  and  y  z.    In  Part  II.  of 
this  work,  the  use  of  co-ordi- 
nates will  be  fully  illustrated 
in  their  application  to  the 
study  of  crystallography. 

The  position  of  points  on 
the  surface  of  the  globe  is 
referred  to  the  equator  and 
the  meridian  of  Greenwich. 
In  this  case,  however,  the 
position  is  not  defined  by 

the  distance  from  these  planes,  as  in  the  example  just  taken,  but 
by  the  latitude  and  longitude ;  the  first  being  the  angular  dis- 
tance of  the  place  from  the  equator  measured  on  its  own  merid- 
ian, and  the  second  the  angle  made  by  its  meridian  with  that  of 
Greenwich.  In  like  manner,  the  position  of  a  body  in  the  solar 
system  is  defined  by  stating  its  distance  from  the  sun  and  its  angu- 
lar position  with  reference  to  the  ecliptic  and  the  vernal  equinox, 
to  which  its  heliocentric  latitude  and  longitude  are  referred. 

(18.)  Mobility.  —  The  idea  of  position  necessarily  involves 
that  of  change  of  position,  which  we  call  motion.  We  cannot, 
for  example,  conceive  of  the  book  as  having  a  definite  position  on 
the  table,  without  also  connecting  with  it  the  idea  that  its  posi- 
tion could  be  changed,  or,  in  other  words,  that  it  could  move. 
A  body  is  said  to  be  moving  when  it  is  constantly  changing  its 
position  with  reference  to  the  co-ordinate  lines  to  which  its  posi- 
tion is  referred  ;  and  when  no  such  change  is  taking  place,  it  is 
said  to  be  at  rest.  Rest  and  motion  are  relative  terms ;  for  abso- 
lute rest  is  not  known  in  nature.  Every  body  on  the  surface  of 
the  globe  partakes,  not  only  in  a  motion  of  revolution  round  the 
axis  of  the  earth,  but  is  also  moving  round  the  sun,  and  per- 
haps accompanying  the  sun  in  its  revolution  round  a  more  dis- 
tant centre.  All  known  matter  is  in  motion,  and  when,  in  any 
case,  we  say  that  it  is  at  rest,  we  merely  mean  to  assert  that  it  is 
at  rest  with  reference  to  certain  lines  or  planes,  which  were  arbitra- 
rily assumed  for  co-ordinates.  A  body  on  the  deck  of  a  steamboat 
may  be  at  rest  with  reference  to  the  boat,  but  in  rapid  motion  with 


22  CHEMICAL   PHYSICS. 

reference  to  the  earth.  In  like  manner,  a  body  on  the  surface  of 
the  globe,  which  is  said  to  be  at  rest  because  it  is  not  changing 
its  position  with  reference  to  the  equator  and  first  meridian,  is  yet 
in.  very  rapid  motion  with  reference  to  the  ecliptic  and  the  vernal 
equinox.  So,  on  the  other  hand,  a  body  may  appear  to  be  in 
rapid  motion,  and  yet  at  rest  with  'reference  to  the  earth  or  the 
sun.  For  example,  a  ship,  which  is  sailing  through  the  ocean  at 
the  rate  of  ten  kilometres  an  hour,  while  the  ocean  current  is 
flowing  at  the  same  rate  in  the  opposite  direction,  is  at  rest  with 
reference  to  the  earth,  although  it  would  appear  to  be  in  motion  to 
persons  on  board  the  ship.  Again,  any  point  on  the  surface  of  the 
globe  at  the  latitude  of  50°  is  moving  from  west  to  east,  in  con- 
sequence of  the  rotation  of  the  globe  on  its  axis,  about  289  metres 
each  second,  but  is,  relatively  to  the  surface  of  the  globe,  at  rest. 
If  a  cannon-ball  is,  at  the  same  latitude,  moving  289  metres  each 
second  from  east  to  west,  it  will  appear  to  be  in  rapid  motion 
to  an  observer  at  this  point,  while  it  is  at  rest  with  reference 
to  the  sun. 

Experience  teaches  us  that  a  body  may  move  on  the  surface 
of  the  globe  with  equal  readiness  in  any  direction,  and  therefore 
that  this  motion  is  not  influenced  by  the  motion  of  the  earth  itself. 
The  same \amount  of  gunpowder  which  would  drive  the  cannon- 
ball  289  metres  each  second  from  west  to  east,  would  drive  it  with 
the  same  velocity  from  east  to  west,  or  in  any  other  direction. 
It  is  evident,  from  these  and  similar  considerations,  that  a  body 
may  partake  of  several  motions  at  once,  and  yet  that  each  may 
be  entirely  independent  of  the  rest. 

(19.)  Time  and  Velocity.  —  All  the  phenomena  of  nature 
may  be  referred  to  motion ;  and  the  succession  of  natural  phe- 
nomena gives  us  the  idea  of  duration,  or  time.  In  order  to 
measure  the  duration  of  phenomena,  we  select  the  duration  of 
some  one  as  our  unit,  and  compare  the  duration  of  others  with  it. 
It  is  essential  that  our  unit  should  be  invariable,  and  such  inva- 
riable units  of  time  we  find  in  the  motions  of  the  heavenly  bodies 
and  in  that  of  the  pendulum.  The  duration  of  a  single  oscilla- 
tion of  a  pendulum  0.99394  m.  long,  at  the  latitude  of  Paris,  is  a 
second,  the  smallest  unit  in  use,  and  the  one  which  we  shall 
have  most  occasion  to  use  in  this  book.  Therefore,  when  the 
unit  of  time  is  spoken  of,  it  is  always  to  be  understood  to  mean 
one  second.  The  duration* of  the  revolution  of  the  earth  on  its 


GENERAL  PROPERTIES  OP  MATTER.  23 

axis  is  the  next  larger  unit,  which  we  call  a  day,  and  that  of  the 
revolution  of  the  earth  round  the  sun,  the  largest  unit  in  com- 
mon use,  is  called  a  year. 

The  distance  passed  over  by  a  moving  body  in  the  unit  of  time 
measures  its  Velocity,  which  we  will  represent  by  t).  When, 
then,  a  body  is  said*  to  have  a  velocity  of  ten  metres,  we  merely 
mean  that,  if  it  continue  to  move  at  the  same  rate,  it  will  pass 
over  ten  metres  in  each  second  of  time. 

(20.)  Uniform  and  Varying'  Motions.  —  The  motion  of  a  body 
is  said  to  be  uniform  when  its  velocity  does  not  change.  In  such 
motion  the  body  will  pass  over  the  same  distance  in  each  second, 
or,  in  other  words,  the  distance  passed  over  in  uniform  motion  is 
proportional  to  the  time.  Denoting,  then,  by  d  the  distance 
passed  over,  and  by  T  the  number  of  seconds,  we  have 

d=bT,    or     1)  =  ^,    and    T=~.  [2.] 

We  have  an  example  of  uniform  motion  in  a  railroad  train 
moving  with  a  constant  speed. 

In  varying  motions,  the  distances  passed  over  in  successive 
seconds  are  unequal.  The  body  has  no  longer  a  constant  ve- 
locity, and  its  velocity  at  any  moment  is  the  distance  it  would 
pass  ov^r  in  each  second,  if,  with  the  velocity  then  acquired,  its 
motion  suddenly  became  uniform.  The  motion  of  a  body  may 
vary  according  to  different  laws.  There  are  two  kinds  of  varying 
motion  which  it  is  important  to  study.  They  are  called  uniform- 
ly accelerated  motion  and  uniformly  retarded  motion. 

(21.)  Uniformly  Accelerated  Motion. — The  motion  of  a  body 
is  said  to  be  uniformly  accelerated,  when  its  velocity  increases 
by  an  equal  amount  each  second.  This  amount  is  called  the  ac- 
celeration, and  will  be  represented  by  u.  The  most  familiar  ex- 
ample of  such  a  motion  is  that  of  the  fall  of  a  stone  to  the  earth. 
Starting  from  the  state  of  repose,  its  velocity  at  the  end  of  the  first 
second  is  9.8088  m.,  which  we  may  call  in  round  numbers  10  m. ; 
at  the  end  of  the  second  second,  its  velocity  is  20  m. ;  at  the  end 
of  the  third,  30  m. ;  at  the  end  of  T  seconds,  its  velocity  is 
10  X  T  metres.  To  make  the  case  general,  if,  starting  from  a 
state  of  rest,  the  body  acquires  a  velocity  each  second  represented 
by  t),  then  its  velocity r\),  after  T  seconds  will  be, 

[3.] 


24  CHEMICAL  PHYSICS. 

In  order  to  find  the  distance  passed  over  at  the  end  of  T 
seconds,  we  make  use  of  the  principle  proved  by  Galileo,  that 
this  distance  is  the  same  as  if  the  body  had  moved  at  a  uniform 
rate  with  a  mean  velocity.  In  the  case  of  a  falling  stone,  the 
velocities  at  the  end  of  successive  seconds  are,  — 

0"  I"         2"         3"         4"         5"         6"         7"  n" 

Om.      10m.    20m.    30m.    40m.    50m.    60m.    70m  .....  (10w)m. 

At  the  end  of  five  seconds,  the  velocity  is  50  m.  ;  at  the  com- 
mencement, the  velocity  is  0  m.  According  to  the  principle  just 
stated,  the  distance  passed  over  is  the  same  as  if  the  body  had 
moved  uniformly  during  the  five  seconds  with  the  mean  velocity 
of  25  m.  In  like  manner,  the  distance  passed  over  between  the 
end  of  the  third  and  the  end  of  the  seventh  second  will  be 
J  (30  +  TO)  4  =  200  metres.  Representing,  then,  the  accelera- 
tion of  velocity  during  each  second  by  u,  as  above,  we  shall  have, 
for  the  distance  passed  over  during  T  seconds  by  a  body  moving 
with  a  uniformly  accelerated  motion,  and  starting  from  a  state 
of  rest, 

T=|t)  T2.  [4.] 


The  truth  of  this  principle  can  be  proved  in  the  following  way  . 
Let  us  suppose  the  time  T  divided  into  a  large  number  (n)  of  very 

•          T 
small  intervals.    Each  of  these  intervals  will  be  represented  by  —  . 

These  intervals  we  will  take  so  small,  that  the  motion  during  this 
minute  fraction  of  a  second  may  be  regarded  as  uniform,  and  as 
having  the  same  velocity  which  it  really  has  only  at  the  end  of 
the  interval.  Representing  the  velocity  at  the  end  of  one  second 

T  T 

by  a,  the  velocity  at  the  end  of  —  seconds  will  be,  by  [3],    —  t)  ; 

T  T 

the  velocity  at  the  end  of  2  —  seconds  will  be   2  —  t>  ;     at   the 

n  n 

T  T 

end  of  3  —   seconds,    3  —  tJ,  etc. 
n  n 

Regarding  this  velocity  as  uniform  during  the  interval,  we  have, 
by  equation  [2]  ,  for  the  distance  passed  over  during  the  first  in- 

rpz 

terval,  the  value  dt  =  -^  t).    In  the  same  way,  we  shall  find, 

yr2  /yr2 

for  the  second  interval,  dt  =  2  -^  t)  ;  for  the  third,  c?3  =  3  -^-t)  ; 

rpl 

and  for  the  last,  dn  =  w  —  t).  The  space  passed  over  during  the 
whole  time  T  will  be  equal  to  the  sum  of  these  values. 


GENERAL   PROPERTIES    OF   MATTER.  25 

7*2  7*2  7^2 


+  3  +  4+  .....  +n). 

The  quantity  within  the  parenthesis,  being  the  sum  of  the 
terms  of  an  arithmetical  progression,  is  equal  to  \  (n  -f-  1)  n  ; 
and  substituting  this  value,  we  obtain, 


This  value  of  d  will  be  the  more  accurate  the  smaller  are  the 
intervals  of  time,  or  the  larger  the  number  into  which  T  is 
divided  ;  and  it  will  be  absolutely  accurate  when  the  number  is 
infinitely  large.  In  this  case  n  =  cc,  and  the  last  equation  be- 
comes the  same  as  [4], 

c/=|t)T2.  [5.] 

For  another  time  T',  we  should  have  d'  =  \  t)  T'2,  and,  com- 
paring the  two  equations, 

d:  d'  =  %  t)  T2  :  J  t)  T'z  =  T2  :  T'2  ; 

that  is,  in  a  uniformly  accelerated  motion,  the  distances  passed 
over  by  a  moving  body  starting  from  a  state  of  rest  are  propor- 
tional to  the  squares  of  the  times  employed.  By  substituting 
in  [5]  the  value  of  T  obtained  from  [3]  ,  it  gives, 


i  i)'2 

for  another  velocity  t)',  we  should  have  d'  =  ~,  and  comparing 

this  equation  with  the  last, 


which  shows  that,  in  a  uniformly  accelerated  motion  starting- 
from  a  state  of  rest,  the  distances  passed  over  by  a  moving  body 
are  proportional  to  the  squares  of  the  final  velocities.  By  trans- 
position we  obtain  from  [6], 


which  is  an  expression  for  the  final  velocity  in  terms  of  the  dis- 
tance passed  over,  and  the  constant  increment  of  velocity  for 
each  second. 

3 


26  CHEMICAL   PHYSICS. 

Returning  to  the  previous  illustration,  if  we  represent  by  a 
the  distance  through  which  a  stone  falls  in  the  first  second,  we 
can  easily  find  the  following  values  for  the  distances  it  will  fall 
through  during  each  succeeding  second,  and  also  for  the  whole 
distance  it  will  have  fallen  through  at  the  end  of  each  second. 

I"    2"      3"      4"      5"       6"       7"  n" 

Successive  distances,  a  3  a  5  a  7  a  9  a  II  a  13a....(2?i — 1)  a. 
Whole  distances,  a  4  a  9  a  16  a  25  a  36  a  49  a n2  a. 

The  co-efficients  in  the  last  series  are  to  each  other  as  the  squares 
of  the  times  ;  —  which  has  already  been  proved.  Those  in  the 
first  series  are  as  the  series  of  odd  numbers,  and  can  be  deduced 
from  the  last  series,  by  subtracting  from  each  of  its  terms  the 
one  next  preceding  it. 

(22.)  Uniformly  Retarded  Motion.  —  When  a  stone  is  thrown 
vertically  from  the  earth,  its  velocity  diminishes  by  an  equal 
amount  each  second,  and  such  a  motion  may  be  said  to  be  uni- 
formly retarded.  The  velocity  of  the  stone  rapidly  diminishes 
until  it  becomes  zero,  when  for  a  moment  it  is  at  rest,  and  then 
it  falls  back  to  the  point  where  it  started.  The  law  which  gov- 
erns the  upward  motion  will  be  most  readily  discovered  if  we 
regard  the  stone  as  moving,  at  the  same  time,  in  two  opposite 
directions ;  rising  in  the  air  in  virtue  of  the  initial  velocity  it 
has  received,  and  at  the  same  time  falling  to  the  earth  in  con- 
sequence of  the  force  of  gravitation  (compare  next  section). 
The  first  is  a  uniform  motion,  and  obeys  the  law  expressed  by 
[2]  ;  the  second  is  a  uniformly  accelerated  motion,  and  obeys 
the  laws  expressed  by  [3]  and  [4] .  Since,  now,  all  uniformly 
retarded  motions  may  be  resolved  in  a  similar  way,  it  is  evident 
that  the  velocity  of  the  motion  and  the  distance  passed  over  by 
the  moving  body  after  a  given  number  of  seconds  may  be  found 
by  subtracting  from  the  velocity  and  distance  which  would  be 
due  to  the  forward  motion  alone,  the  loss  caused  by  the  uniformly 
accelerated  motion  in  the  opposite  direction.  If,  then,  we  use 
v  to  denote  the  initial  velocity,  it  is  evident  that  the  residual 
velocity  at  the  end  of  T  seconds  will  be  expressed  by  the  equa- 
tion (compare  [2]  and  [3]) 

b  =  tV— nZl  [8.] 

The  body  will  evidently  come  to  rest  when  t)  T  equals  {)' ;  when 

T=$L  [9.] 


.GENERAL  PROPERTIES  OF  MATTER.  27 

In  the  case  of  the  stone,  t)  is  equal,  as  before,  to  about  ten  metres ; 
so  that  a  stone  thrown  upwards  with  a  velocity  of  one  hundred 
metres  a  second  would  come  to  rest  in  ten  seconds.  At  the  end 
of  five  seconds  its  velocity  would  be  100  —  10  X  5  =  50  metres. 
In  like  manner,  the  distance  passed  over  at  the  end  of  ^seconds 
will  be  the  difference  between  the  values  of  d  in  [2]  and  [4] ,  or 

d=b>  T—  JtjT2.  [10.] 

The  height  to  which  the  stone  of  the  previous  example  would 
rise  in  five  seconds  is,  then,  100  X  5  —  J 10  X  25  =  375  metres. 
To  find  how  far  the  uniformly  retarded  body  will  move  before 
coming  to  rest,  substitute  in  [10]  the  value  of  T  given  in  [9], 
which  gives 

,    b" 

d=jv- 

The  stone  .will  then  rise  to  -^-  =  500  metres,  before   it  begins 

to  fall. 

(23.)  Compound  Motion.  —  It  has  already  been  stated,  that  a 
body  may  be  moving  in  several  directions  at  once,  and  moving 
with  perfect  freedom  in  each.  The  movements  of  the  passengers 
on  the  deck  of  a  vessel  sailing  over  a  calm  sea  preserve  the  same 
relations  of  direction  and  velocity,  relatively  to  the  different  parts 
of  the  vessel,  as  if  it  were  at  rest.  So  also,  the  motions  on  the 
surface  of  the  globe  are  not  influenced  by  its  rotation  on  its  axis, 
or  its  motions  through  space.  A  point  on  the  rim  of  a  wagon- 
wheel  partakes  of  the  forward  motion  of  the  wagon,  while  it  is 
also  revolving  round  the  axle.  The  actual  motion  of  a  body 
which  is  the  result  of  two  or  more  motions,  is  termed  a  com- 
pound motion ;  and  we  will  now  inquire  what  must  be  the  path 
and  velocity  of  such  motions,  commencing  with  the  simplest  case, 
where  there  are  but  two  motions,  and  where  both  are  uniform. 

(24.)  Parallelogram  of 
Motions.  —  Let  us  then  sup- 
pose that  a  body,  starting 
from  a,  is  moving  towards 
m  with  a  uniform  motion, 
and  that  at  the  same  time 
the  line  a  f  is  moving  par- 
allel to  itself,  and  also  with  K= 


28  CHEMICAL   PHYSICS. 

a  uniform  motion,  towards  e  s,  the  point  a  always  keeping  on  the 
line  a  e.  Let  us  also  suppose  that  the  velocities  are  so  adjusted, 
that,  when  the  body  reaches  the  point  £ ,  the  line  will  have  reached 
the  position  e  s.  It  is  easy  to  show  that  the  path  described  by 
the  body  is  the  diagonal  a  s  of  the  parallelogram,  of  which  a  e  and 
e  s  are  two  sides. 

Lay  off,  in  the  direction  am,  a  line,  a  s ,  equal  to  the  velocity 
of  the  moving  body,  and  on  the  line  a  n  a  distance,  a  e,  equal  to 
the  velocity  of  the  moving  line.  Divide  both  of  these  lines  into 
the  same  number  of  equal  parts.  Each  of  these  will  be  equal  to 
the  space  passed  over  by  the  moving  body  or  line  in  a  small  frac- 
tion of  a  second,  which  we  may  take  as  small  as  we  choose.  At 
the  end  of  the  first  of  these  intervals,  the  body  will  evidently 
reach  the  point  p  ;  at  the  end  of  the  next,  the  point  q ;  at  the 
end  of  the  third,  r ;  and  so  on,  until  the  end  of  the  second,  when 
it  will  reach  the  point  s.  By  making  the  number  of  intervals 
larger  and  larger,  we  can  prove  that  the  body  will  pass  succes- 
sively a  larger  and  larger  number  of  points  on  the  line  a  s  ;  and 
by  making  the  number  of  intervals  infinite,  that  it  will  pass 
every  point  on  the  line,  or,  in  other  words,  that  it  will  move  on 
the  line  itself. 

It  will  be  noticed,  that  the  proof  is  general  for  any  velocities 
when  the  two  motions  are  uniform  ;  and  moreover,  that  the  line 
a  s  represents,  not  only  the  direction,  but  also  the  velocity  of  the 
moving  body.  Hence  follows  the  well-known  proposition,  first 
enunciated  by  Galileo,  and  generally  termed  the  Composition  of 
Velocities  :  —  The  velocity  resulting1  from  two  simultaneous  ve- 
locities is  represented,  both  in  direction  and  in  amount,  by  the 
diagonal  of  a  parallelogram  constructed  on  two  straight  lines, 
which  represent  the  direction  and  amount  of  these  velocities. 
The  reverse  of  this  must  also  be  true ;  and  any  given  motion 
may  be  considered  as  resulting  from  two  others  which  stand  in 
the  same  relations  to  it,  both  as  regards  direction  and  velocity, 
that  the  sides  of  a  parallelogram  do  to  its  diagonal.  Hence  the 
converse  proposition :  —  A  velocity  in  any  given  direction  may 
be  resolved  into  two  others,  represented  both  in  direction  and 
amount  by*  the  two  sides  of  a  parallelogram,  of  which  the  first 
velocity  is  the  diagonal. 

As  the  same  line  may  be  the  diagonal  of  an  infinite  number  of 
different  parallelograms,  it  follows  that  a  given  motion  may  be 


GENERAL  PROPERTIES  OF  MATTER.  29 

composed  of,  or  may  be  resolved  into,  an  infinite  number  of  dif- 
ferent pairs  of  uniform  motions. 

We  have  considered,  above,  a  motion  as  resulting  from  two 
other  uniform  motions  ;  but  a  motion  may  result  from  three  or 
more  motions.  As  these  motions  are  entirely  independent  of 
each  other,  we  can  obviously  find,  by  the  above  method,  what 
would  be  the  result  of  two  alone  ;  and  then,  by  combining  this 
resultant  with  the  third  motion,  we  shall  obtain  a  second  result- 
ant, which  would  be  the  result  of  three  alone  ;  and  by  combining 
the  second  resultant  with  the  fourth  motion,  we  should  obtain  a 
third  resultant  ;  —  and  so  we  can  proceed  until  we  obtain  the 
final  resultant  of  all  the  motions. 

What  has  been  proved  to  be  true  in  regard  to  the  resultant  of 
two  or  more  uniform  motions,  is  also  true  in  regard  to  two  or  more 
uniformly  varying  motions,  provided  the  variations  of  both  follow 
the  same  law.  This  truth  can  easily  be  proved  in  the  case  of  two 
uniformly  accelerated  or  uniformly  retarded  motions,  by  laying 
off,  on  two  lines  representing  the  directions  of  the  motions,  the 
spaces  passed  over  during  successive  intervals  of  time,  taken  so 
small  that  the  motion  during  each  interval  may  be  considered 
uniform.  We  can  thus  find  the  points  at  which  the  moving  body 
will  be  at  the  end  of  these  successive  intervals,  as  above ;  and  it 
will  then  be  easy  to  prove  that  the  resulting  motion  may  be  rep- 
resented, both  in  direction  and  velocity,  by  the  diagonal  of  a 
parallelogram,  of  which  the  two  sides  represent  the  velocities  at 
the  end  of  one  second. 

In  the  case  where  the  original  motion  is  uniform,  it  is  easy  to 
prove  that  the  resulting  motion  is  also  uniform  ;  and  where  it  is 
varying,  that  the  resulting  motion  varies  according  to  the  same 
law  as  its  two  components.  Thus,  in  the  last  example,  the  result- 
ing motion  will  be  uniformly  accelerated  or  retarded,  as  the  case 
may  be. 

(25.)  Curvilinear  Motion.  —  In  the  cases  above  considered, 
the  resulting  motion  is  rectilinear ;  if,  however,  any  one  of  the 
motions  of  which  a  compound  motion  is  composed  obeys  a  differ- 
ent law  from  the  rest,  the  resulting  motion  is  curvilinear.  As 
the  velocity  of  a  moving  body  may  vary  according  to  many  dif- 
ferent laws,  and  as  an  infinite  number  of  combinations  of  such 
varying  motions  may  be  made,  an  infinite  variety  of  curvi- 
linear motions  may  result.  We  can  only  consider  here  one,  and 
3* 


80  CHEMICAL  PHYSICS. 

that  one  of  the  simplest  cases,  which  will  serve  as  an  example 
of  the  rest.  Let  us,  then,  suppose  a  body  moving  from  a  to  m  (Fig. 
4)  with  a  uniform  motion,  and  at  the  same  time  moving  in  the 

direction  a  n  with  a  uniformly 
accelerated  motion.  An  ex- 
ample of  such  a  motion  would 
be  that  of  a  cannon-ball,  fired 
horizontally  from  the  embra- 
sure of  a  fort,  at  some  height 
above  the  general  surface  of 
the  ground.  In  virtue  of  the 
projectile  force,  it  would  move 
horizontally  along  the  line  a  m 
with  a  uniform  motion,  while 
in  obedience  to  the  force  of 
gravity  it  would  rapidly  fall  to 
?t  *'  the  earth,  in  the  direction  a  n, 

with  a  uniformly  accelerated  motion.  To  find  the  path  of  the  re- 
sulting motion,  let  fa  be  the  velocity  of  the  uniform  motion,  and 
t)  the  acceleration  of  velocity  of  the  falling  body  for  each  second. 
Lay  off  on  the  line  a  m  the  distances  a  ft,  ft  /,  7  #,  etc.,  each  equal 
to  t).  Lay  off  on  the  line  a  n  the  distances  ab,bc,cd,  etc.,  equal 
to  J  t),  J  t),  f  D,  etc.,  the  distances  through  which  the  ball  will  fall  in 
successive  seconds.  Draw  through  each  of  the  points  j3>  y>  #?  etc., 
lines  parallel  to  a  n,  and  through  6,  c,  d,  etc.,  lines  parallel  to 
am.  The  points  P,  Q,  R,  etc.,  where  the  first  set  of  lines  inter- 
sect the  second,  are  evidently  points  through  which  the  ball  must 
pass.  Join  these  points  by  a  curved  line,  and  this  line  will  repre- 
sent the  path  of  the  ball.  It  is  easy  to  show  that  this  path  is  a 
parabola.  For  this  purpose,  let  the  lines  a  m  and  a  n  be  the  aies 
of  co-ordinates.  The  co-ordinates  of  any  point,  as  s,  are  s  e  =  x 
and  s  £  =  y  ;  and  we  know  that  x  =  s  a  =  t)  T,  and  also  y  =  e  a 
=  £  t)  T2.  Equating  the  values  of  T  obtained  from  these  equa- 
tions, we  have,  by  reduction, 


2   )2 

Since     -  is  a  constant  quantity,  this  is  the  equation  of  a 

2  to2 

parabola,  in  which  4  p  =  -  . 


GENERAL  PROPERTIES  OF  MATTER.  .;          81 

PROBLEMS. 

Velocity  and  Uniform  Motion. 

12.  A  locomotive  runs  36  kilometres  in  lht  20'.     What  is  the  velocity 
of  the  locomotive  ? 

13.  A  horse  trots  11  kilometres  in  one  hour.     What  is  his  velocity? 

14.  A  man  walks  5.6  kilometres  in  lh'  10'.     What  is  his  velocity? 

15.  From  the  extremities,  A  and  B,  of  a  straight  line  24,000  m.  long, 
two  bodies  start  at  the  same  time.     The  one  from  A  moves  in  the  direc- 
tion A  B  with  a  velocity  of  2m.;   the  other  from  B,  in  the  direction 
B  A,  with  a  velocity  of  3m.    'At  what  distance  from  A,  and  after  what 
time,  will  they  meet  ? 

1 6.  From  the  extremities,  A  and  B,  of  a  straight  line  a  m.  long,  two 
bodies  start ;  the  one  from  A,  t"  after  the  one  from  B.     The  one  from  A 
moves  with  a  velocity  of  c  m.,  the  one  from  B  with  a  velocity  of  ct  m.    At 
what  distance  from  A  will  they  meet  ? 

Uniformly  Accelerated  or  Retarded  Motion. 

17.  Find  the  space  through  which  a  body  falls  in  7",  and  the  velocity 
acquired.     The  increment  of  velocity  each  second  is  t)  =  9.8  m. 

18.  A  stone  falls  from  the  top  of  a  tower  to  the  earth  in  2.5".     How 
high  is  the  tower  when  JJ  =  9.8  m.  ? 

19.  On  the  surface  of  the  moon,  the  increment  of  velocity  of  a  falling 
body  is  t)  =  1.654;  on  the  surface  of  the  planet  Jupiter,  tJ  =  26.243. 
Find  the  answers  to  the  last  two  problems  with  these  values. 

20.  A  stone  is  let  fall  into  a  pit  100m.  deep.     With  what  velocity  will 
it  strike  the  bottom  of  the  pit  ?     With  what  velocity  would  it  strike  the 
bottom  of  a  similar  pit  on  the  moon,  and  on  Jupiter  ? 

21.  A  stone  is  projected  vertically  with  a  velocity  of  50m.     How 
high  will   it   rise   from  the  earth  ?     How  high  would  it  rise  from  the 
moon,  and  from  Jupiter  ?     After  how  many  seconds  will  it  again  reach 
the  ground  in  the  three  cases  ? 

22.  A  body  is  projected  vertically  from  the  bottom  of  a  tower  80  m. 
high,  with  a  velocity  of  48  m.     In  what  time  will  it  reach  the  top,  and 
what  will  be  its  velocity  at  that  time  ?     Also,  to  what  height  above  the 
top  of  the  tower  will  it  rise,  and  after  what  time  will  it  again  reach  the 
bottom  ? 

23.  A  body  is  projected  vertically  with  30  m.  velocity.    A  second  later, 
another  body,  with  40  m.  velocity,  is  projected  vertically  from  the  same 
point.    At  what  point  of  elevation  will  the  two  meet  ? 

24.  A  cannon-ball,  being   projected  vertically  upwards,  returned  in 
20"  to  the  place  from  which  it  was  fired.     How  high  did  it  ascend,  and 
what  was  the  velocity  of  its  projection  ?     Solve  the  problem  also  for  t)  = 
1.654,  and  t)  =  26.243. 


32  CHEMICAL  PHYSICS. 


FORCE. 

(26.)  Force.  —  Matter,  of  itself,  is  incapable  of  changing  its 
state,  either  of  rest  or  of  motion.  If  a  body  be  at  rest,  it  cannot 
put  itself  in  motion ;  if  a  body  be  in  motion,  it  can  neither 
change  that  motion  nor  reduce  itself  to  rest.  Any  such  change 
must  be  produced  by  some  external  cause  independent  of  the 
body.  This  quality  of  matter  we  term  Inertia  ;  and  the  external 
cause  we  term  Force.  In  discussing  the  origin  and  nature  of 
force  in  the  introductory  chapter,  we  used  this  word  for  the  cause 
of  all  the  phenomena  of  nature.  We  shall  use  it,  in  this  section, 
in  a  more  limited  sense,  as  meaning  "  any  agency  which,  applied 
to  a  body,  imparts  motion  to  it,  or  produces  pressure  upon  it,  or 
causes  both  of  these  effects  together."  In  studying  the  action  of 
a  force  upon  a  body,  we  must  consider  three  tilings.  First,  the 
point  of  the  body  to  which  it  is  applied,  its  point  of  application ; 
secondly,  its  intensity;  thirdly,  its  direction.  The  action  of 
forces  on  bodies  is  the  subject-matter  of  Mechanics.  We  shall 
only  be  able  to  consider  here  those  elementary  principles  of 
this  science  which  we  shall  have  occasion  to  use  in  this  book, 
referring  the  student  to  works  on  Mechanics  for  a  full  exposition 
of  the  subject. 

(27.)  Direction  of  Force.  —  When  a  force  applied  to  any 
point  of  a  body  causes  it  to  move,  the  direction  of  the  motion  is 
the  direction  of  the  force.  If  the  point  cannot  move,  the  direc- 
tion of  the  force  is  the  direction  of  the  pressure  exerted  by  it,  or 
the  direction  in  which  the  point  would  move  if  it  were  free. 
When  two  or  more  forces  are  applied  to  any  point  of  a  body, 
each  of  these  produces  the  same  effect  as  if  it  were  acting  alone. 
This  is  a  necessary  consequence  of  what  has  already  been  stated, 
in  regard  to  the  perfect  freedom  with  which  a  body  may  move  in 
several  directions  at  once.  Each  of  these  motions  may  be  the 
result  of  a  separate  force,  which  thus  acts  in  producing  motion  as 
if  it  were  acting  alone.  Hence,  also,  the  action  of  a  force  upon 
a  body  is  not  aifected  by  its  condition  of  rest  or  motion,  because 
the  result  which  it  produces  is  by  the  above  principle  entirely  in- 
dependent of  the  motions  which  other  forces  have  impressed  upon 
it.  For  example,  if  a  body  moving  with  a  given  velocity,  under 
the  influence  of  a  given  force,  is  suddenly  acted  upon  by  another 
and  equal  force,  in  a  direction  at  right  angles  to  the  first,  it  will 


GENERAL  PROPERTIES  OF  MATTER.  33 

move  in  the  new  direction  with  the  same  velocity  as  if  it  had 
been  previously  at  rest.  The  path  it  describes  can  be  found  by 
combining  the  two  motions  according  to  the  principles  already 
described. 

It  follows  from  this  principle,  that  a  body  under  the  in- 
fluence of  a  force  which  is  constant,  both  in  direction  and 
intensity,  moves  with  a  uniformly  accelerated  velocity.  That 
this  must  be  the  case  can  be  seen  by  reflecting  that,  if  this 
force  imparts  to  the  body  a  velocity  t)  during  the  first  second, 
it  will,  from  the  principle  just  stated,  impart  the  same  velocity 
during  each  succeeding  second.  At  the  end  of  the  second 
second,  the  body  will  then  have  the  velocity  gained  during  two 
seconds,  or  2  t) ;  at  the  end  of  the  third  second,  it  will  have 
the  velocity  gained  during  three  seconds,  or  3  t) ;  and  so  on. 
In  other  words,  the  velocity  will  be  proportional  to  the  time, 
which  is  the  characteristic  of  uniformly  accelerated  motions. 
The  reverse  of  this  also  must  be  true  ;  that  is,  a  body  moving 
with  a  uniformly  accelerated  velocity  in  a  straight  line,  must  be 
under  the  influence  of  a  force  of  constant  intensity  acting  in  the 
direction  of  its  motion. 

If,  when  a  body  has  acquired  a  given  velocity,  the  force  ceases 
to  act,  the  body  will  continue  to  move  with  the  same  velocity  and 
ill  the  same  direction  which  it  had  when  the  action  of  the  force 
ceased  ;  in  other  words,  it  will  have  a  uniform  motion,  and  the 
motion  will  continue  until  it  is  arrested  by  an  equivalent  force, 
acting  for  an  equal  time  in  the  opposite  direction.  This,  which 
is  a  necessary  consequence  of  the  principle  of  inertia,  is  illus- 
trated by  many  familiar  facts.  A  train  of  cars  continues  to 
move  after  the  action  of  the  steam  has  ceased,  and  until  the  fric- 
tion of  the  wheels  and  the  resistance  of  the  atmosphere  destroys 
the  motion.  Were  it  not  for  these  opposing  forces,  a  body  once 
set  in  motion  on  the  earth  would  continue  to  move  indefinitely 
with  the  same  velocity,  and  in  the  same  direction,  which  it  had 
when  the  force  which  produced  the  motion  ceased  to  act.  This 
does  not  admit  of  direct  experimental  illustration  ;  because,  on 
the  surface  of  the  earth,  we  can  never  entirely  remove  a  body  from 
the  influence  of  the  resistance  of  the  air  or  of  friction.  But 
even  here,  the  more  completely  these  influences  are  removed,  the 
longer  motion  continues  ;  and  in  the  heavenly  bodies,  where  they 
do  not  exist,  at  least  to  any  sensible  degree,  the.  motion,  is  per- 


34  CHEMICAL  PHYSICS. 

petual.  A  uniform  motion  in  a  straight  line  does  not,  therefore, 
necessarily  imply  the  existence  of  a  force  still  acting  ;  it  only 
shows  that  a  force  has  acted  at  some  previous  time.* 

(28.)  Equilibrium.  —  When  two  or  more  forces  arc  acting  on 
a  body,  or  on  a  system  of  bodies,  in  such  a  way  that  they  exactly 
balance  each  other's  effects,  they  are  said  to  be  in  equilibrium. 
Forces  so  adjusted  will  not  communicate  motion  to  a  body  at  rest, 
or  alter  its  motion,  if  already  in  motion.  That  portion  of  the 
science  of  Mechanics  which  treats  of  the  conditions  of  equilibri- 
um, is  termed  Statics  ;  that  part,  of  which  the  object  is  to  deter- 
mine the  motion  which  a  body  assumes  when  the  forces  which 
are  applied  do  not  constitute  an  equilibrium,  is  called  Dynamics. 

(29.)  Measure  of  Forces.  —  We  conceive  of  forces  as  having 
different  intensities,  and  hence  as  quantities,  which  can  be  ex- 
pressed in  numbers,  selecting  one  of  them  as  the  unit.  As, 
however,  we  only  know  forces  through  their  effects,  we  can  only 
compare  them  together  by  comparing  their  effects  ;  that  is,  by 
comparing  together  the  amounts  of  motion  they  cause,  or  the 
amounts  of  pressure  they  exert.  Let  us  then  seek  for  a  measure 
of  force  in  the  amount  of  motion  which  it  causes.  In  discussing 
this  subject  we  can  assume  as  axioms,  —  first,  that  two  forces 
are  equal  which  will  give  equal  velocities  to  equal  amounts  of 
matter  in  the  unit,  of  time ;  secondly,  that  two  forces  are  equal 
which,  when  applied  in  opposite  directions  to  any  point  of  the 
same  body,  or  to  any  two  points  situated  in  the  line  of  the  forces 
and  inseparably  united,  leave  it  at  rest.  The  following  proposi- 
tions can  now  be  easily  proved. 

Proposition  1.  Two  constant  forces,  which  in  the  unit  of  time 
impart  to  unequal  masses  of  matter  equal  velocities,  must  be  to 
each  other  as  these  masses.  Let  us  suppose  that  we  have  n 
equal  masses  of  matter,  each  represented  by  m,  on  which  are 
acting  n  equal  forces  in  directions  parallel  to  each  other,  each 
represented  by  /.  By  the  axiom  above,  each  of  these  masses 

*  This  statement  does  not  apparently  agree  with  the  principle  of  the  introductory 
chapter,  in  which  it  is  maintained  that  all  phenomena  imply  a  continuously  acting 
cause ;  but  it  must  be  remembered  that  rest  and  motion  are  merely  relative  terms, 
and  that  the  last  is  as  much  a  state  or  condition  of  matter  as  the  first.  Any  change 
of  condition,  whether  from  rest  to  motion,  from  motion  to  rest,  or  from  one  mode  of 
motion  to  another,  implies  the  intervention  of  some  force ;  but  the  mere  continuance 
in  a  given  condition  implies  a  continuously  acting  cause  only  so  far  as  such  a  cause 
is  implied  by  the  continued  existence  of  all  created  things. 


GENERAL   PROPERTIES   OP   MATTER.  35 

will  receive  the  same  velocity  in  the  unit  of  time  ;  they  will,  there- 
fore, all  move  in  the  same  direction  and  with  the  same  velocity, 
and  must  preserve  the  same  relative  position.  We  may  then 
regard  them  as  united  in  a  single  body,  whose  mass  is  equal  to 
n  X  m,  on  which  is  acting  a  force  equal  to  n  X  /.  Hence  it 
follows,  that  the  force  n  X  /  will  give  to  the  mass  n  X  m  the 
same  velocity  that  the  force  /  will  give  to  the  mass  m.  It  is  evi- 
dent that 

n  X  /  :  /  =  n  X  m  :  m. 

To  make  this  proof  more  general.  Let  M  and  M '  represent  the 
two  masses  of  matter,  which  we  will  suppose  to  be  commensu- 
rable, and  let  m  be  their  common  measure  ;  so  that 

M—nm,     and     M'  =  n'm. 

Represent  by  /  the  value  of  the  force  which  will  impart  to  m  the 
given  velocity  in  the  unit  of  time  ;  then,  by  what  precedes, 

nf  will  give  the  same  velocity  to  n  m,  or  M,  and 
rif  "  "  "  n1  m,  or  M'. 

Represent  nf  by  F,  and  n'f  by  F',  and  we  have 

nf:n'f=nm:n'm,     or     F :  F'  =  M :  M1,      [11.] 

which  was  to  be  proved.  If  the  masses  are  not  commensurable, 
we  can  take  m  infinitely  small. 

Proposition  2.  Two  constant  forces,  which  in  the  unit  of  time 
impart  to  equal  masses  of  matter  unequal  velocities,  must  be 
to  each  other  as  these  velocities.  Represent  the  two  forces  by 
F  and  F',  which  we  will  suppose  to  be  commensurable,  and  let 
/  be  their  common  measure  ;  so  that  F=nf,  and  F'  =  n'f. 
Represent  also  by  o  and  u'  the  velocities  which  these  forces  re- 
spectively impart  to  the  common  mass,  M,  in  the  unit  of  time. 
The  force  /  will  be  capable  of  imparting  to  M  a  velocity,  which 
we  will  represent  by  t)".  It  follows  now,  from  the  last  proof, 

that  jP  =  ft /will  impart  to  M  a  velocity  n  v"  =  t),  and 
that  F'=  n'f         "  "  «         n1  v"  =  D'  ; 

hence, 

nf:n'f=nv":n'v",    or    F :  F'  =  t)  :  V.         [12.] 

Proposition  3.  Two  constant  forces  are  to  each  other  as  the 
products  of  the  masses  by  the  velocities  which  they  impart  to 
these  masses  in  the  unit  of  time.  Let  F  and  F1  be  the  two  forces 


36  CHEMICAL   PHYSICS. 

acting  on  the  masses  M  and  M',  and  imparting  to  them  the 
velocities  u  and  t)'  in  the  unit  of  time.  Represent  by  /  a  force 
which  imparts  to  the  mass  M  the  velocity  t)'  in  the  unit  of  time. 
F  and  /  are,  then,  two  forces  which,  in  the  unit  of  time,  impress 
on  equal  masses,  Mand  M,  unequal  velocities,  t)  and  t)' ;  hence, 
from  Proposition  2, 

F:f=v  :  *'. 

Moreover,  f  and  F'  are  two  forces  which  impress  on  unequal 
masses,  M  and  M',  equal  velocities,  D'andn';  hence,  from  Prop- 
osition 1, 

/:  F'  =  M:  M'. 

Multiplying  the  two  proportions,  term  by  term,  we  obtain 

F:  F'  =  Mv:  M '  D',  [13.] 

which  was  to  be  proved. 

In  order  to  measure  a  force,  we  have  then  only  to  select  some 
one  force  for  our  unit,  and,  by  the  principles  of  the  above  propo- 
sitions, compare  all  other  forces  with  it.  We  will  then  assume, 
as  the  unit  of  force,  that  force  which,  acting  on  the  unit  of  mass 
during  one  second,  will  impress  upon  it  a  velocity  of  one  metre, 
or  that  force  which  causes  an  acceleration  of  one  metre  in  the 
velocity  of  the  unit  of  mass  each  second.  If  then  a  given  force, 
F,  acting  during  one  second,  impresses  on  a  given  mass  of  mat- 
ter, M9  a  velocity,  t),  we  can  easily  find  the  relation  it  bears  to 
the  unit  of  force  by  the  above  proportion, 

F:  F'  =  Mv:  M' V. 

If  F1  is  the  unit  of  force,  then,  by  definition,  Mf  and  t)'  are  both 
equal  to  unity ;  and  the  proportion  gives 

F=Mv.  [14.] 

It  will  be  remembered  (21),  that  the  quantity  fl  is  termed 
technically  the  acceleration.  Hence,  the  measure  of  a  force  is 
the  product  of  the  mass  moved  by  the  acceleration.  For  example, 
if  the  mass  moved  is  equal  to  four  units  of  mass,  and  the  accel- 
eration is  equal  to  six  metres,  the  intensity  of  the  force  is  equal 
to  twenty-four  ;  that  is,  the  intensity  of  the  force  is  twenty-four 
times  as  great  as  the  unit  of  force. 

If  a  constant  force  continues  to  act  upon  a  body  during  a  given 
time,  it  imparts  to  it  each  second,  as  we  have  seen,  as  much  ve- 
locity as  it  gave  to  it  the  first.  This  velocity  we  have  called  the 


GENERAL   PROPERTIES   OF   MATTER.  37 

acceleration,  and  represented  by  u.  At  the  end  of  T  seconds  the 
velocity  is  Tt),  which  has  been  represented  by  t).  If  now  the 
force  ceases  to  act,  the  motion  becomes  uniform,  and  the  body 
continues  to  move  with  the  velocity  t)  =  Tu.  In  order  to  stop 
this  motion,  it  would  be  necessary  to  apply  to  the  body,  in  an  op- 
posite direction,  a  force  of  the  same  intensity,  for  an  equal  time. 
If  M  represents  the  mass  of  the  body,  M  v  represents  the  inten- 
sity of  the  original  force  ;  and  hence  it  would  require  a  force  of 
the  intensity  M  v  acting  during  T  seconds  to  destroy  the  mo- 
tion. Evidently,  however,  the  same  effect  could  be  produced  by 
a  force  of  T  times  the  intensity,  acting  for  one  second.  The 
intensity  of  this  force  would  be 


[15.] 

Hence  the  product  of  the  mass  of  a  body  by  its  velocity  repre- 
sents the  intensity  of  a  force  which,  acting  during  one  second, 
will  bring  the  body  to  rest.  This  product  is  usually  called  the 
momentum  of  a  moving  body.  We  say,  for  example,  that  a  body 
whose  mass  is  equal  to  five  units,  and  which  is  moving  with 
a  velocity  of  four  metres,  has  a  momentum  equal  to  20  ;  and 
we  mean  by  this,  that  it  would  require  a  force  twenty  times  as 
intense  as  the  unit  of  force,  and  acting  for  one  second  in  a  direc- 
tion opposite  to  that  of  the  motion,  to  bring  the  body  to  rest. 
The  momentum  is  also  frequently  called  the  moving'  force  of  the 
body,  because  it  not  only  represents  the  intensity  of  the  force  re- 
quired to  overcome  its  motion,  but  also  because  the  body  itself 
would  exert  a  force  of  this  intensity  against  any  obstacle  tending 
to  resist  its  motion.  In  this  view,  momentum  may  be  regarded 
as  representing  the  accumulated  intensity  of  force  in  a  body  ;  the 
product  M  v  representing  the  intensity  of  force  in  a  body  after 
one  second  ;  the  product  M  t)  representing  the  accumulated  in- 
tensity after  T  seconds. 

It  must  be  carefully  noticed,  that  we  have  considered  in  this 
section  solely  the  measure  of  the  intensities  of  forces,  and  not 
the  measure  of  their  quantities.  The  quantity  of  a  force,  or,  as 
this  is  frequently  called,  its  power,  is  measured  in  a  different 
way,  as  will  be  shown  in  (42).  In  this  woik,  we  shall  have  to 
deal  almost  solely  with  the  intensities  of  forces,  and  when  the 
measure  of  force  is  referred  to,  it  must  be  always  understood 
to  mean  the  measure  of  its  intensity,  unless  the  reverse  is  ex- 
pressly stated. 

4 


38  CHEMICAL   PHYSICS. 


COMPOSITION    OF   FORCES. 

(30.)  Components  and  Resultant.  —  In  mechanical  problems 
we  frequently  have  two  or  more  forces  acting  at  once  on  the  same 
point  of  a  body,  or  on  several  points  which  are  immovably  united 
together  ;  and  it  becomes  important  to  consider  what  will  be  their 
combined  effect.  This  problem,  which  is  termed  the  composition 
of  forces,  reduces  itself  to  that  of  finding  the  direction  and 
amount  of  a  single  force  which  would  produce  the  same  motion 
as  that  resulting  from  the  action  of  all  the  forces  combined. 
This  single  force  is  called  the  resultant,  and  the  forces  to  which 
it  is  equivalent  in  effect  are  called  its  components.  It  follows, 
from  this  definition,  that  a  force  is  mechanically  equivalent  to 
the  sum  of  its  components,  and,  on  the  other  hand,  that  any 
number  of  forces  are  mechanically  equivalent  to  their  resultant ; 
because,  as  we  only  know  forces  through  their  effects  in  pro- 
ducing motion,  any  forces  which  produce  the  same  motions  are 
to  us  equivalent. 

(31.)  Forces  may  be  represented  by  Lines.  —  The  unit  of 
force  has  been  defined  as  that  force  which  causes  an  acceleration 
of  one  metre  in  the  motion  of  the  unit  of  mass  each  second  ;  and, 
further,  it  has  been  shown  that  the  product  of  the  mass  moved, 
by  the  acceleration,  is  the  number  of  units  of  force  to  which  any 
given  force  is  equivalent.  If,  then,  we  represent  the  unit  of 
force  by  a  line  one  centimetre  long,  any  other  force  will  be  repre- 
sented by  a  line  as  many  centimetres  long  as  the  number  which 
is  obtained  by  multiplying  the  mass  it  moves  by  the  acceleration 
it  imparts  each  second.  Moreover,  since  these  lines  may  be 
made  to  represent  the  directions  as  well  as  the  amounts  of  the 
forces,  the  problems  of  resolution  of  forces  may  be  reduced  to 
problems  of  geometry. 

(32.)  The  point  of  application  of  a  force  may  be  changed  to 
any  other  point  of  the  body  on  the  line  of  the  direction  of  the 
force,  ivithout  altering-  in  any  respect  the  action  of  the  force  on 
the  body,  provided  only  that  the  two  points  are  immovably  united 

together.  The  truth  of  this  proposition 
seems  almost  self-evident ;  for  it  amounts 
only  to  this,  —  that  a  given  force  acting 
in  the  direction  A  B  (Fig.  5)  will  pro- 
Flg' 5*  duce  the  same  effect,  whether  it  is  applied 


GENERAL  PROPERTIES  OF  MATTER.  39 

in  pushing  the  body  forward  at  A,  or  in  pulling  it  forward  from 
B.  The  following  illustration  may  make  the  matter  still  clearer. 
We  will  assume  that  the  force  applied  at  A  is  equal  to  five  units 
of  force,  and  is  in  the  direction  A  B.  We  will  now  apply  two 
forces,  each  of  the  same  value  as  the  last,  to  the  point  B ;  one  in 
the  direction  A  B,  and  the  other  in  the  direction  B  A,  as  we  can 
obviously  do,  without  changing  the  condition  of  the  body.  The 
second  of  these  forces  will,  by  the  axiom  of  (29),  exactly  counter- 
balance the  force  applied  at  A,  and  we  shall  then  have  left  a 
force  of  five  units  applied  at  B,  and  acting  in  the  direction  A  B, 
producing  an  equivalent  effect  to  that  of  the  first  force. 

(33.)  Resultant  of  Forces  in  the  same  Straight  Line. — The 
resultant  of  a  number  of  forces  acting  in  the  same  straight  line 
on  a  point  of  a  body,  is  obviously  equal  to  the  sum  of  the  forces 
acting  in  one  direction  less  the  sum  of  the  forces  acting  in  the 
opposite  direction ;  and  this  resultant  is  in  the  direction  of  the 
largest  sum.  If,  for  example,  we  have  three  forces  applied  to 
the  point  A  (Fig.  5)  in  the  direction  A  B,  equal  respectively  to 
4,  6,  and  7  units,  and  two  forces  in  the  opposite  direction  equal 
to  18  and  10  units,  then  the  resultant  force  will  be  equal  to 
(4  +  6  +  7)  —  (18  +  10)  =  —11  units,  and,  as  the  nega- 
tive sign  indicates,  will  act  in  the  direction  B  A.  The  validity 
of  this  principle  follows  from  the  fact,  that  eacli  force  acts  as  if 
it  were  the  only  force  acting  (27).  As  was  shown  in  the  last 
section,  it  is  unimportant  whether  all  the  forces  are  applied 
at  A^  or  whether  they  are  applied  at  different  points  along  the 
line  A  B. 

(34.)  Resultant  of  Forces  acting-  in  differ- 
ent Directions ,  but  applied  at  the  same  Point) 
or  Parallelogram  of  Forces.  —  Let  us  sup- 
pose that  we  have  two  forces,  F'  and  F", 
applied  to  the  point  A  (Fig.  6),  in  the  di- 
rections A  b  and  A  b'  respectively,  and  let  us 
inquire  what  will  be  their  resultant.  It  has 
already  been  proved,  that  two  forces  acting 
on  the  same  or  equal  masses  of  matter  are 
to  each  other  as  the  accelerations  ;  or, 

F'  :  F"  =  t>'  :  t)". 
What  therefore  is  true  in  regard  to  the  two 


40  CHEMICAL   PHYSICS. 

velocities  must  be  true  relatively  in  regard  to  the  two  forces, 
so  that  if  we  can,  by  any  method,  find  the  resultant  of  the  two 
velocities,  this  same  method  will  give  us  the  resultant  of  the  two 
forces.  -Now  it  has  been  proved  (24),  that  the  resultant  of  two 
velocities  is  represented,  both  in  direction  and  amount,  by  the 
diagonal  of  a  parallelogram  whose  sides  represent  the  directions 
and  velocities  of  the  two  motions  ;  and  hence  it  follows,  that  the 
resultant  of  tivo  forces  is  represented,  both  in  direction  and  in- 
tensity, by  the  diagonal  of  a  parallelogram  whose  sides  represent 
the  directions  and  intensities  of  the  component  forces.  The  re- 
sultant of  two  forces  can,  therefore,  always  be  found  by  a  very 
easy  geometrical  construction.  It  can  also  be  calculated  ;  for  we 
have,  by  a  well-known  principle  of  trigonometry,  from  Fig.  6, 

JTC2  =  AB2  +  BCZ  —  2  AB  .  B~C  .  cos  A B  C ; 

or,  since  B  A  B'  =  180°  —ABC,  and  therefore  cos  A  B  C  = 
—  cos  B  A  B',  we  have 

AC*  =  ABZ  +  BC2  +  2  AB  .  B~C  cos  B  A  B'. 

Representing  the  two  component  forces  by  F1  and  F",  their  re- 
sultant by  F,  and  the  angle  between  the  components  by  en,  the 
last  equation  becomes 

Fz  =  F'*  +  F"2  +  2  F'  F"  cos  a.  [16.] 

In  many  cases  with  which  we  meet  in  nature,  the  directions  of  the 
two  components  make  a  right  angle  ;  then  the  last  term  of  [14] 
disappears,  and  the  equation  becomes 

F2  =  F/Z  +  F"2.  [17.] 

(85.)  Decomposition  of  Forces.  — As  any  given  motion  may 
be  the  result  of  an  infinite  number  of  pairs  of  motions  (24),  so 
any  given  force  is  the  equivalent  of  an  infinite  number  of  pairs 
of  forces.  It  follows  from  what  has  been  proved  above,  that 
we  can  replace  a  given  force  acting  on  the  point  A  (Fig.  7),  and 
represented  in  direction  and  intensity  by  A  P,  by  the  two  forces 
represented  by  either  of  the  pairs  of  lines  A  B  and  A  B',  A  C 
and  AC',  AD  and  AD,  A  E  and  A  E,  or  indeed  by  any  other 
pair  of  forces  which  can  be  represented  by  the  sides  of  a  par- 
allelogram, of  which  the  line  representing  the  given  force  is 
the  diagonal.  As  the  sides  of  a  parallelogram  may  have  any 


GENERAL  PROPERTIES  OP  MATTER.  41 

angular  position  whatsoever  with  reference  to  the  diagonal,  it 

follows  that  a  given  force  may  be  decomposed  into  two  others  in 

any  required  directions.     If,  then,  the  value  of  a  force  in  units, 

and  two  directions,  are  given, 

the   value   in   units   of   two 

components   in   these    direc- 

tions can  always  be  found. 

The  problem  can  be   solved 

geometrically  thus.     Draw  a 

line,  A  C  (Fig.  6),  as  many 

centimetres    long    as    there 

are  units  in  the  given  force. 

Draw  two  indefinite  lines,  A  b 

and  A  b',  in  the  required  di- 

rections,  making  the    given 

angles  with  A  C.     Finally,  draw  through   C  lines   parallel   to 

A  b  and  A  b'.     These  lines  will  intersect  the  first  at  the  points 

B  and  B',  and  the  length  in  centimetres  of  A  B  and  A  B'  thus 

determined  will  be  the  values  in  units  of  the  reqiiired  forces. 

The  problem  can  also  be  solved  by  trigonometry.  Denote  the 
value  in  units  of  the  given  force  by  F,  and  those  of  the  required 
components  by  x  and  y.  Denote  also  the  angles  which  x  and  y 
are  required  to  make  with  F  by  a  and  ft  respectively.  In  the 
triangle  A  B  C,  we  have 

A  B  :  A  C  =  sin  A  C  B  :  sin  A  B  C  ; 
and  also,  since  A  B'  =  B  C, 

A  B1  :  A  C  =  sin  B  A  C  :  sin  A  B  C. 

Substituting  in  these  proportions  the  equivalent  values  A  B  =  .r, 
AB'=y,  BAC=a,  A  C  B  =  p,  A  B  C=  180°  —  (a 
they  become 


x  :  F=smp  :  sin  (a  +  /3),    and    y  :  .F=sin  a  :  sin 

Hence, 

T-»        sin  /?  j  T-»        sin  a  ri  &  -> 

x=F-  —  7  —  tt-—r,     and     y  =  F-  —  7—  —  ^.         [18.1 
sin  («-f-/?)'  sin  («-|-  /?) 

When  the  two  components  are  at  right  angles  to  each  other,  then 
a  +  ft  =  90°,  and 

x  =  F  sin  j3,     and    y  =  F  sin  a. 

4* 


42  CHEMICAL   PHYSICS. 

The  decomposition  of  a  force  into  two  others  is  very  frequently 
applied  in  mechanics,  in  order  to  determine  the  action  of  a  force 
when  it  does  not  act  in  the  direction  in  which  its  point  of  appli- 
cation moves.  The  case  of  a  canal-boat  affords  an  illustration  of 

its  application.  The  power  is 
applied  to  the  boat  at  the 
point  A  (Fig.  8),  through  the 
cord  A  C,  which  is  attached 
at  the  other  end  to  the  horses 
Fig  g  on  the  tow-path.  The  boat  is 

prevented    from   approaching 

the  bank  by  the  action  of  the  rudder,  and  can  only  move  in  the 
direction  A  a.  Knowing  the  force  exerted  in  the  direction  Af, 
and  the  angle  a,  it  is  required  to  find  the  effective  force  by  which 
the  boat  is  propelled.  Decompose  the  force  F  into  two  com- 
ponents, x  in  the  direction  A  a,  and  y  in  the  direction  A  b.  The 
last  force  is  balanced  by  the  resistance  of  the  water ;  but  the 
first,  acting  in  the  direction  of  least  resistance,  that  of  the  boat's 
length,  propels  it  through  the  water.  This  force,  or  x,  is  equal  to 
F  cos  a,  and  will  evidently  be  larger  as  the  value  of  a  is  smaller, 
or,  in  other  words,  as  the  towing-line  is  longer. 

It  follows,  from  what  has  been  said,  that  a  force  can  produce 
motion  in  any  direction  between  its  own  original  direction  and 
one  perpendicular  to  it.  It  cannot  produce  motion  in  a  direction 
perpendicular  to  itself,  because,  as  can  be  easily  deduced  from 
[18],  the  perpendicular  resultant  would  in  such  a  case  be  equal 
to  zero. 

In  general,  when  the  point  of  application  is  made  to  move  in 
a  different  direction  from  that  of  the  force  applied  to  it,  the  effect 
of  this  force  is  determined  by  resolving  the  force  into  two  others  : 
one  in  the  new  direction,  which  represents  the  effect  sought ;  the 
other  perpendicular  to  it,  which  is  destroyed  by  the  resistance  to 
the  motion  in  that  direction. 

(36.)  Composition  of  several  Forces  acting"  in  different  Di- 
rections. —  The  course  of  reasoning  used  above,  in  regard  to 
the  composition  of  two  forces,  applies  equally  to  the  composi- 
tion of  any  number  of  forces  acting  on  the  same  point.  Hence, 
the  resultant  of  several  forces  can  be  found  in  the  same  way  as 
the  resultant  of  several  motions  (24).  Let  us  suppose,  for  ex- 
ample, that  the  forces  acting  on  the  point  O  (Fig.  9)  are 


GENERAL  PROPERTIES  OF  MATTER. 


43 


represented  both  in  direction  and  amount  by  the  lines  O  A,  O  B, 
O  C,  and  O  D.     We  can  find  their  resultant  in  the  following 
manner.     We  first   seek  the  resultant,  Or,  of  O  A  and  O  B. 
The  force  represented  by  this  line 
being  in  all  respects  equivalent  to 
its   two   components,  we  can  com- 
bine it  with  O  C  and  obtain  a  sec- 
ond  resultant,   O  rf.     This   result- 
ant, combined  with  the  last  force, 
O  Dj  will  give  us  the  final  resultant 
of  all  the  forces. 

The  trigonometrical  formulae  of 
(35)  can  easily  be  applied  by  the 
student,  in  solving  problems  on  the 
composition  of  several  forces. 

(37.)  Composition  of  Parallel  Forces.  —  We  will  consider,  in 
the  first  place,  the  case  where  there  are  but  two  parallel  forces, 
F'  and  F".  Let  A  and  B  (Figs.  10,  11)  be  the  points  of  appli- 
cation of  these  forces,  which  are  immovably  united.  Join  these 
points  by  the  line  A  B.  Draw  the  parallel  lines  A  P  and  B  Q, 
so  as  to  represent  the  direction  and  intensities  of  the  two  forces 
F'  and  F1-,  respectively.  In  Fig.  10,  the  forces  are  supposed  to 
act  in  the  same  direction,  and  in  Fig.  11  in  opposite  directions. 
The  figures  have  been  so  lettered,  that  the  following  demonstra- 
tion applies  equally  to  both  cases.  We  wish  to  find  the  direc- 
tion, the  intensity,  and  the  point  of  application  of  a  single  force, 
F,  which  would  be  equivalent  to  the  two  forces  F'  and  F". 


Fig.  9. 


Fig.  10.  Fig.  11. 

Apply  to  the  points  A  and  B,  and  in  the  direction  of  the  line 
uniting  them,  two  equal  and  opposite  forces,/'  and/",  which  we 
will  represent  by  drawing  A  £=/',  and  B  S=f".  As  these 
forces  exactly  balance  each  other,  they  cannot  change  the  ve- 


44  CHEMICAL  PHYSICS. 

locity  or  the  direction  of  the  motion  resulting  from  the  parallel 
forces  F'  and  F",  and  hence  will  not  affect  our  demonstration. 
The  line  A  r,  found  by  completing  the  parallelogram  A  S  r  P, 


Fig.  10.  Fig.  11. 

evidently  represents  the  direction  and  intensity  of  the  resultant 
of  the  two  forces  F'  and  /',  and  the  line  B  I  the  direction  and 
intensity  of  the  resultant  of  the  two  forces  F"  and/".  Produce 
these  lines  until  they  cross,  at  a  point  m.  By  (32)  it  follows 
that  the  effect  of  these  resultants  is  the  same  as  if  they  were  both 
applied  directly  to  the  point  m,  in  the  directions  m  A  and  m  B. 
We  can  now  decompose  each  of  these  resultants,  at  the  point  m, 
into  two  components  parallel,  and  hence  also  equal,  to  the  origi- 
nal forces  F'  and/',  F"  and/".  The  two  components  parallel 
and  equal  to  A  S  and  B  S  will  be  applied  to  the  point  m  in  op- 
posite directions ;  and  since,  by  construction,  A  S  is  equal  to 
B  S,  these  two  components  must  also  be  equal,  and  will  therefore 
neutralize  each  other.  The  two  components  parallel  and  equal 
to  A  P  and  B  Q  will  also  both  be  applied  at  the  point  m.  In 
Fig.  10,  where  the  original  forces  were  in  the  same  direction,  the 
two  components  will  be  in  the  same  direction,  and  will  conspire 
to  move  the  point  m  in  the  direction  m  C.  In  Fig.  11,  where 
the  original  forces  were  in  opposite  directions,  the  two  compo- 
nents will  be  in  opposite  directions,  and  will  tend  to  move  the 
point  m  in  the  direction  of  the  greater  component  with  a  force 
equal  to  their  difference.  Hence,  the  final  resultant  will  be  a 
force  in  the  direction  m  C,  parallel  to  the  original  forces,  in  the 
one  case  equal  to  their  sum,  and  in  the  other  to  their  difference. 
The  point  of  application  of  this  force  may  obviously  be  transferred 
to  the  point  C,  without  altering  the  conditions  of  its  action. 

To  find  the  position  of  the  -point  C.  By  construction,  the  sides 
of  the  triangle  A  Pr  are  parallel  to  those  of  the  triangle  m  C  A, 
and  likewise  the  sides  of  the  triangle  B  Q  t  are  parallel  to  those 


GENERAL  PROPERTIES  OP  MATTER.  45 

of  the  triangle  m  C  B,  and  hence  their  homologous  sides  are  pro- 
portional ;  so  that  we  have  the  proportions, 

A  C  :  m  C  =  r  P  :  A  P,     and     B  C :  m  C  =  t  Q  :  B  Q. 
We  have,  by  construction, 

rP=A  S  =  t  Q  =  BS=f,  AP  =  F',  and  BQ=F'", 
hence,  by  substitution, 

A  C  :  m  C=f  :  F',     and     B  C  :  m  C=f"  :  F" ; 
or, 

m  C=A  Cj,  =  BC^,    or     A  C X  F>=  B  C  X  F" ; 

or, 

AC:BC  =  F":F'.  [20.] 

Hence  it  appears  that,  when  the  two  forces  have  the  same  direc- 
tion, as  in  Fig.  10,  the  point  of  application,  C,  of  the  resultaht 
force  divides  the  straight  line  A  B,  which  joins  the  points  of  ap- 
plication of  the  components,  into  two  parts,  which  are  inversely 
proportional  to  the  amounts  of  the  given  forces.  When,  on  the 
other  hand,  the  forces  are  in  opposite  directions,  as  in  Fig.  11, 
the  point  of  application  of  the  resultant  is  still  on  the  same  line, 
but  -beyond  the  point  of  application  of  the  larger  of  the  compo- 
nents, and  at  distances  from  the  points  A  and  B,  which  are,  as 
before,  inversely  proportional  to  the  intensities  of  the  two  forces. 
Our  general  result,  then,  is  the  following :  — 

I.  In  regard  to  the  resultant  of  two  parallel  forces  acting  in 
the  same  direction.     1.   The  intensity  of  this  resultant  is  equal 
to  the  sum  of  the  intensities  of  its  components.     2.   The  direc- 
tion is  the  same  as  the  common  direction  of  the  components. 
3.   The  point  of  application  divides  the  line  joining-  the  points  of 
application  of  the  components  into  two  parts,  which  are  inversely 
proportional  to  the  intensities  of  the  forces. 

II.  In  regard  to  the  resultant  of  two  parallel  forces  acting  in 
opposite  directions.     1.   The  intensity  of  this  resultant  is  equal 
to  the  difference  of  the  intensities  of  its  components.     2.   The 
direction  is  the  same  as  that  of  the  larger  component.     3.    The 
point  of  application  is  on  the  line  joining-  the  points  of  applica- 
tion of  the  components,  produced  beyond  the  point  of  application 
of  the  larger  of  the  two,  and  is  at  distances  from  these  points 
which  are  inversely  proportional  to  the  intensities  of  the  given 
forces. 


46 


CHEMICAL   PHYSICS. 


Fig.  12. 


It  follows,  from  the  nature  of  a  resultant  force,  that  a  force 
applied  at  C,  Figs.  10,  11,  which  is  equal  and  opposite  to  the  re- 
sultant of  the  two  forces  F  and  F',  ought  exactly  to  balance  this 
resultant.  This  obvious  truth  will  enable  us  to  put  the  validity 
of  our  conclusions  to  the  test  of  experiment.  The  experiment 
may  be  arranged  as  in  Fig.  12.  P  and  P'  are  two  points  at 

the  ends,  for  example,  of 
a  wooden  rod.  To  these 
points  are  attached  cords, 
which,  passing  over  the  two 
pulleys  M  and  M'9  are  at- 
tached to  the  two  weights 
A  and  A'.  A  third  weight, 
R,  is  suspended  by  means 
of  a  looped  cord  to  the  rod, 
so  that  its  position  can  be 
easily  shifted.  In  this  ex- 
periment the  weights  cor- 
respond to  the  forces  F'  and 
F"  of  Fig.  10,  while  the  cords  indicate  the  directions  in  which 
the  forces  act.  By  varying  the  amount  of  the  weights,  and  also 
the  position  of  the  weight  R  on  the  rod,  it  will  be  found  that 
equilibrium  can  be  maintained  only  when  the  conditions  above 
stated  are  fulfilled.  Thus,  if  the  weight  R  be  20. grammes, 
the  sum  of  the  weights  A  and  A1  must  also  be  20  grammes.  If 
A'  is  equal  to  12  grammes,  then  A  must  equal  8,  and  the  position 
of  the  loop  on  the  rod  must  be  such,  that  O  P'  shall  be  to  O  P 
as  8  is  to  12.  If,  then,  the  distance  P  P'  is  equal  to  20  c.  m., 
the  distance  P  O  will  be  12  c.  m.,  and  P'  O  will  be  8  c.m. 

This  same  experiment  also  illustrates  the  case  represented  in 
Fig.  11,  where  the  two  components  are  acting  in  opposite  direc- 
tions ;  for,  as  the  system  of  weights  is  in  equilibrium,  it  follows 
that  the  force  exerted  by  any  one  may  be  regarded  as  equal  in 
intensity  to  the  resultant  of  the  other  two ;  this  resultant,  how- 
ever, acting  in  the  opposite  direction  to  the  force  exerted  by  the 
weight.  Hence,  we  may  consider  the  forces  exerted  at  the  points 
O  and  P'  to  be  the  components  of  a  force  equal  to  that  exerted 
by  the  weight  at  P,  but  in  a  direction  opposite  to  P  M.  Taking 
the  values  of  the  weights  when  the  system  is  in  equilibrium,  as 
given  above,  it  is  evident  that  the  amount  of  the  resultant,  and 


GENERAL   PROPERTIES    OF   MATTER. 


47 


the  position  of  its  point  of  application,  $,  are  the  same  as  would 
be  found  by  the  rule  ;  for,  in  the  first  place,  the  weight  A  is 
equal  to  the  difference  of  the  two  weights  R  and  A,  and,  in  the 
second  place,  the  distances  P  O  and  P  P  are  inversely  propor- 
tional to  the  values  of  the  two  weights  R  and  A'. 

(38.)  Couples.  —  When  the  two  parallel  forces  are  exerted  in 
opposite  directions,  there  is  one  set  of  conditions  which  presents 
a  case  of  peculiar  interest ;  and  that  is,  when  the  two  compo- 
nents are  equal.  In  this  case,  the  value  of  the  resultant  is  evi- 
dently equal  to  zero ;  and,  moreover,  the  point  of  application  is 
at  an  infinite  distance  from  the  points  of  application  of  the  two 
equal  components.  The  last  fact  follows  from  the  proportion 
[20] ,  A  C  :  B  C  =  F"  :  F'.  This,  by  the  theory  of  proportions, 
may  be  written, 

A  C—  B  C  :  F"  —  F'  =  A  C :  F"  =  B  C  :  F' ; 
or,  substituting  (see  Fig.  11)  A  B  =  A  C—  B  C,  and  F= F"—  F', 

AB:  F=AC:  F"  =  BC:  F1. 
Hence, 

ABX  I 


AC  = 


and     B  C  = 


F 


[21.] 


When  the  two  components  are  equal,  the  resultant  F  =  0, 
and  both  the  distances  A  C  and  B  C  become  equal  to  infin- 
ity. In  this  case,  therefore,  there  is  no  single  resultant,  and 
therefore  no  tendency  to  produce  in  a  body  any  progressive  mo- 
tion. Such  a  system  of  forces  is  termed  a  couple,  and  its  ten- 
dency is  to  make  the  body  rotate.  The  theory  of  couples  is  of 
great  importance  in  mechanics  ;  but  as  we  shall  not  have  occasion 
to  apply  it  in  this  work,  we  shall  not  dwell  upon  it. 

(39.)  Composition  of  several  Parallel  Forces.  —  We  can  evi- 
dently find  the  resultant  of  several  parallel  forces,  by  combining 
them  two  by  two,  as  in  the  case  of  forces 
acting  in  different  directions.  In  Fig. 
13,  the  points  m,  ra',  ra",  and  m'"  are  the 
points  of  application  of  the  parallel 
forces  F,  F1,  F",  and  F'",  all  acting 
in  the  same  direction.  In  order  to  find 
a  common  resultant,  we  first  combine 
F  with  F' ;  let  o  be  the  point  of  appli- 
cation of  the  first  resultant.  We  next 


43 


CHEMICAL   PHYSICS. 


combine  the  first  resultant  with  F"9  and  let  o'  be  the  point  of 
application  of  the  second  resultant.  Lastly,  we  combine  the 
second  resultant  with  F'"9  and  we  shall  then  find  a  final  result- 
ant of  all  the  forces.  This  is  evidently  equal  in  amount  to  the 
sum  of  all  the  components,  and  its  point  of  application  will  be 
on  the  line  o1  m'"9  at  an  intermediate  position  between  the  two 
points,  which  may  be  determined  by  means  of  the  proportions 
given  above. 

Where  all  the  parallel  components  are  not  in  the  same  direc- 
tion, we  combine  each  set  separately,  and  thus  obtain  two  partial 
resultants,  acting  in  opposite  directions.  If  these  are  equal,  we 
shall  have  a  couple ,  and  no  final  resultant.  If  they  are  not 
equal,  we  can  find  a  resultant  by  the  method  already  described. 

(40.)  Centre  of  Parallel  Forces.  —  By  referring  to  Figs.  10, 
11,  and  the  demonstration  following,  it  will  be  seen  that  the 
position  of  the  point  C  does  not  depend  on  the  common. direction 
of  the  forces  represented  by  A  P  and  B  Q,  but  only  on  their  rel- 
ative intensities.  If  we  suppose  these  components  to  revolve 
round  their  points  of  application,  A  and  B,  the  resultant  will 
still  pass  through  C  in  any  position  they  may  assume,  provided 
only  that  they  remain  parallel.  Moreover,  it  will  be  seen  that 
the  point  of  application  of  the  resultant,  which  we  transferred  for 
convenience  from  m  to  (7,  may  be  at  any  point  on  the  line  of  its 
direction.  In  other  words,  it  is  not  fixed  by  the  conditions  of  the 
problem,  except  so  far  as  this,  that  it  must  be  on  the  line  m  C  R. 
It  follows,  then,  that  if,  in  the  system  of  parallel  forces  of  Fig.  13, 
we  suppose  the  components  to  revolve  about  their  points  of  ap- 
plication, their  resultants  will  always  pass  through  the  point  G, 
provided  only  that  they  remain  parallel.  In  Fig.  14,  all  the 
components  have  been  revolved  through  an  angle  equal  to 
P1  G  P.  The  direction  of  the  resultant 
has  changed  from  P'GtoP  G,  but  it  still 
passes  through  the  point  G.  In  the  posi- 
tion of  the  components  represented  by 
Fig.  13,  the  point  of  application  may  be 
at  any  point  of  the  body  on  the  line  G  P 
which  corresponds  to  the  line  G  P1  of 
Fig.  14.  In  the  second  position  of  the 
components  in  Fig.  14,  it  may  be  at  any 
point  on  the  line  G  P.  The  point  G,  in 


GENERAL  PROPERTIES  OF  MATTER.  49 

which  all  the  successive  directions  of  the  resultant  intersect  when 
its  components  revolve  about  their  points  of  application,  is  called 
the  centre  of  parallel  forces.  It  follows,  from  this  definition, 
that  if  the  forces  remain  parallel,  and  their  points  of  appli- 
cation invariable,  this  system  of  points  may  be  turned  round 
the  centre  of  parallel  forces  without  changing  the  point  of  appli- 
cation of  the  resultant ;  so  that,  if  this  point  were  supported,  the 
system  would  remain  in  equilibrium  in  any  position  we  could 
give  it  in  turning  it  round  this  point. 

(41.)  Action  and  Reaction.  —  The  simplest  case  of  the  action 
of  one  body  upon  another,  is  when  a  body  in  motion,  which  we 
may  call  M,  strikes  upon  another  at  rest,  which  may  be  termed 
M'.  If  M1  is  free  to  move,  it  will  be  put  in  motion  by  the  action 
of  Mj  and  in  any  case  the  reaction  of  M',  in  retarding  M"1  s  mo- 
tion, will  be  precisely  equal  to  the  action  of  M  in  communicating 
motion  to  M'.  This  principle,  which  is  a  necessary  result  of  the 
inertia  of  matter,  is  generally  expressed  thus  :  —  Action  and  re- 
action are  always  equal  and  opposite. 

The  changes  in  the  motion  and  in  the  moving  force  of  both 
bodies,  which  result  from  collision,  are  in  general  of  a  complicated 
kind,  and  depend  on  the  degree  of  elasticity  of  the  bodies,  their 
form,  mass,  and  other  circumstances.  To  simplify  the  question, 
we  shall  consider  the  bodies  as  completely  devoid  of  elasticity, 
and  so  constituted  that  after  the  collision  they  shall  move  as  one 
body.  Let  us  then  inquire  what  will  be  the  direction  and  velocity 
of  the  united  mass  after  the  impact. 

The  mass  M ',  being  previously  at  rest,  can  have  no  motion 
save  what  it  may  receive  from  the  mass  M9  and  consequently 
must  move  in  the  same  direction  as  the  mass  M  moved  in  before 
the  collision.  Again,  since  bodies  cannot  generate  or  destroy 
motion  in  themselves,  it  follows  that  whatever  motion  the  mass 
M'  may  acquire  must  be  lost  by  the  mass  M ;  and  also,  that  the 
total  momentum  of  the  united  masses  after  the  collision  must  be 
exactly  equal  to  the  momentum  of  the  mass  M  before  it.  If  b 
and  t)'  represent  the  velocities  before  and  after  impact,  then,  by 
(29),  M\)  and  (Jf  +  -M"')  t)'  represent  the  momentum  before 
and  after  impact ;  and  since  these  are  equal,  we  have 

Jlfb  =  (Jtf+Jf/)b/,    whence     fr  =  b  M  ^  „,.      [22.] 

I 

Let  us  next  suppose  that  the  two  bodies  are  both  moving,  and 

6 


50  CHEMICAL  PHYSICS. 

in  the  same  direction  ;  the  mass  M  with  a  velocity  fo,  and  the 
mass  M'  with  a  velocity  Jb',  less  than  t).  What  will  be  the  com- 
mon velocity  after  impact  ?  The  momenta  of  the  two  bodies  are 
M  b  and  M1  b.  Since  these  motions  are  in  the  same  direction, 
they  cannot  be  either  diminished  or  increased  by  the  collis- 
ion, and  hence  the  momentum  of  the  united  bodies  will  be 
Mb  +  M'  b'.  If,  then,  b"  be  the  unknown  velocity  of  the 
united  masses,  we  have 

"    and  b" 


Let  us  now  suppose  that  the  two  bodies  are  both  moving,  but 
in  opposite  directions,  and  that  the  momentum  of  M  is  greater 
than  that  of  M'.  On  their  collision,  the  momentum  of  M'  will 
destroy  just  so  much  of  that  of  M  as  is  equal  to  its  own  amount  ; 
for  it  is  evident  that  equal  and  opposite  momenta  must  destroy 
each  other.  The  momentum  left  after  collision  must,  therefore, 
equal  M  b  —  M'  fa',  and,  using  b"  as  before,  we  shall  have 


')",   and      '/  =        -.    [24.] 


In  the  last  case,  as  in  the  first,  the  reaction  of  the  mass  M'  is 
equal  to  the  action  of  the  mass  M.  The  action  of  the  mass  M 
has  consisted,  first,  in  destroying  the  momentum  of  M',  equal  to 
M'  b  ;  second,  in  giving  to  it  the  momentum  M'  b".  The  total 
action  is  therefore  expressed  by  M'  b  +  M'  b".  The  reaction  of 
M'  has  consisted,  first,  in  destroying  a  portion  of  the  momentum 
of  M,  equal  to  M'  b  ;  and  second,  in  subtracting  from  the  re- 
mainder of  the  momentum  of  M  the  amount  which  it  has  after 
the  collision,  or  M1  b".  The  total  reaction  is  therefore,  as  before, 

M'  b  +  M'  b'. 

We  will  now  suppose  that  the  two  masses  are  moving  in  differ- 

ent directions  ;  M  in  the  direc- 
tion A  B,  Fig.  15,  with  a  velocity 
t),  and  M1  in  the  direction  A1  B1, 
with  a  velocity  b'>  The  direc- 
tion of  the  motion  after  collision, 
and  the  momentum  of  the  united 
masses,  can  be  easily  ascertained 
by  the  application  of  the  prin- 
ciple of  the  parallelogram  of 
Kg.  15.  forces  already  explained  (33). 


GENERAL  PROPERTIES  OP  MATTER.  51 

Let  the  distance  CD  represent  the  momentum  M  fa,  and  the  dis- 
tance C  D'  the  momentum  M '  t)',  and  complete  the  parallelogram 
&DED'.  Draw  its  diagonal  C E.  This  diagonal  will  then 
represent  the  direction  of  the  common  motion  and  the  momen- 
tum of  the  combined  masses,  which  is  equal  to  (-M"+  M')  t)". 
To  find  the  velocity,  it  will  be  necessary  to  divide  the  number 
expressed  by  this  diagonal  by  the  sum  of  M  and  M '. 

If,  in  the  first  case,  we  suppose  the  body  M'^  at  rest,  to  be  in- 
finitely large,  as  compared  with  the  moving  mass  M,  then  the 
value  of  t)'  [22]  becomes  0,  which  shows  that  the  whole  momen- 
tum is  destroyed.  This  is  practically  the  case  when  the  moving 
mass  impinges  against  a  fixed  obstacle,  which  is  either  very  much 
larger  than  itself,  or  which  is  firmly  fastened  to  the  earth.  The 
body  must,  however,  be  supposed  to  strike  the  surface  of  the  ob- 
stacle from  a  direction  at  right  angles  to  this  surface.  Should  it 
strike  the  surface  at  an  oblique  angle,  we  may  have  a  different 
result.  Let  us  suppose  an  unelastic  sphere  impinges  against  an 
unyielding  surface,  D  B  C,  in  the 
direction  A  B,  with  a  velocity  t) 
and  a  momentum  M  t)  ;  what 
would  be  the  result  ?  By  the 
principle  of  the  parallelogram  of 
force,  the  momentum  M  t)  is  equiv- 
alent to  two  others,  one  in  the  di- 
rection A  Z),  and  the  other  in  the  Fig  16 
direction  D  B.  The  first  will  be 
destroyed  at  the  impact ;  but  the  second,  which  is  equal  to 
M  t)  cos  a,  will  give  the  sphere  a  motion  with  the  velocity  t)  cos  a 
in  the  direction  B  C.  In  the  figure  the  surface  is  a  plane,  but 
the  demonstration  is  true  for  any  curved  surface  ;  in  such  cases, 
however,  the  plane  D  B  C  of  the  figure  is  the  tangent  plane  to 
the  surface  at  the  point  of  contact. 

It  follows  from  the  above  discussion,  that  the  loss  of  mo- 
mentum in  a  mass,  M,  impinging  on  another  mass,  M',  when  at 
rest,  is  always  proportional  to  its  velocity.  This  loss,  as  can 
easily  be  deduced  from  [22] ,  is  equal  to 


VM+M>' 

a  quantity  whose  value  is  evidently  proportional  to  that  of  t). 
In  all  the  above  cases,  it  can  easily  be  shown  that  the  re- 


52  CHEMICAL  PHYSICS. 

action  of  the  body  M '  is  always  exactly  equal  and  opposite  to  the 
action  of  the  body  M.  The  same  is  also  true,  when  the  body  M 
acts  on  the  body  M'  through  the  forces  of  gravitation,  electri- 
city, magnetism,  etc.,  and  not  by  direct  impact.  A  needle,  for 
example,  attracts  a  magnet  with  exactly  the  same  force  with 
which  the  magnet  attracts  the  needle  ;  and  were  both  free  to 
move,  the  magnet  would  move  towards  the  needle  as  well  as  the 
needle  towards  the  magnet.  It  is  also  true,  when  a  body  does  not 
strike,  but  merely  presses  against,  an  obstacle,  —  as,  for  example, 
when  a  weight  rests  on  a  table,  —  that  the  reaction  of  the  obstacle 
is  exactly  equal  to  the  pressure. 

(42.)  Power,  or  Living  Force. — It  has  been  shown  (14),  that 
the  intensity  of  a  force  is  measured  by  M  t).  ,In  the  case  of  a  loco- 
motive, for  example,  M  represents  the  whole  mass  of  the  locomo- 
tive and  train,  and  t)  the  acceleration  of  velocity  imparted  by  the 
moving  force  each  second.  Were  the  motion  not  retarded  by 
friction  and  other  causes,  its  velocity  would  increase  indefinitely, 
according  to  the  laws  of  uniformly  accelerated  motion  already  de- 
scribed. In  fact,  however,  with  a  given  force,  .F,  this  velocity  soon 
comes  to  a  maximum,  which  it  does  not  exceed ;  and  so  long  as  the 
force  and  the  resistance  do  not  vary,  the  train  moves  with  a  uni- 
form motion.  During  this  time  the  action  of  the  force  is  exactly 
balanced  by  the  resistance  arising  from  friction  and  other  causes, 
and  the  train  moves  in  virtue  of  the  momentum,  -M"t),  previously 
acquired.  In  the  space  passed  over  by  the  train  each  second,  the 
counteracting  forces  just  neutralize  the  force  jP,  exerted  by  the 
moving  agent  during  the  same  period.  It  might  now  be  supposed, 
that,  if  this  force  were  suddenly  quadrupled,  so  as  to  equal  4  F, 
the  velocity  would  again  increase  until  it  attained  to  four  times  its 
present  amount.  In  fact,  however,  its  velocity  rapidly  increases, 
but  only  to  twice  its  present  amount ;  and  then  it  is  found  that  the 
resistance  is  again  just  balanced  by  the  greater  force.  That  this 
must  be  the  case  can  be  seen  by  reflecting,  that,  with  a  double 
velocity,  the  moving  train  passes  over  double  the  space  each  sec- 
ond, and  therefore  encounters  twice  as  many  points  of  resistance. 
Moreover,  it  strikes  each  of  these  points  with  double  the  velocity, 
and  hence  meets  at  each  point  twice  the  resistance.  It  there- 
fore meets,  during  a  second,  twice  as  many  points  of  resist- 
ance, and  suffers  at  each  point  twice  as  much  resistance.  The 
resistance  during  a  second  is  thus  four  times  as  great  as  before, 


GENERAL   PROPERTIES    OP   MATTER.  53 

and  must  require  four  times  as  much  force  to  overcome  it.  In 
order  to  obtain  three  times  the  velocity,  it  would  be  necessary  to 
increase  by  nine  times  the  force  ;  and  in  general  the  force  re- 
quired will  be  proportional  to  the  square  of  the  velocity  to  be 
attained.  What  is  true  of  the  motion  of  a  train  of  cars  is  true 
also  of  the  motion  of  a  steamboat,  and  indeed  of  all  motion 
whatsoever  by  which  work  is  or  may  be  accomplished.  Hence 
the  ability  of  a  force  to  do  work  is  proportional,  not  to  the 
velocity,  but  to  the  square  of  the  velocity  which  it  imparts  to 
the  moving  body. 

The  space  passed  over  during  a  second  by  a  body  starting  from 
a  state  of  rest,  is  equal  to  £  t)  [5].  The  intensity  of  the  force 
which  has  moved  it  over  this  space  is  equal  to  M  u  The  product 
of  the  intensity  of  the  force  by  the  space  passed  (the  number  of 
points  at  which  it  has  acted),  represents  the  work  accomplished 
by  the  force.  This  product,  equal  to  J  M  o2,  was  named  by 
Leibnitz  vis  viva,  or  living  force,  to  distinguish  it  from  force 
which  does  not  produce  motion,  but  only  pressure  ;  and  which  he 
named  dead  force.  A  discussion  was  excited  by  Leibnitz  on  this 
subject,  in  which  all  the  mathematicians  of  the  eighteenth  cen- 
tury took  part,  and  which  continued  for  more  than  forty  years;  — 
one  party  claiming,  with  Leibnitz,  that  force  was  proportional  to 
the  square  of  the  velocity  ;  and  the  other,  that  it  was  propor- 
tional to  the  simple  velocity,  —  the  first  party  measuring  force 
by  the  vis  viva,  and  the  other  by  the  momentum.  As  not  unfre- 
quently  happens  in  such  cases,  both  parties  were  right  ;  and  their 
two  opinions  were  harmonized  by  introducing  the  element  of 
time.  For,  as  we  have  seen,  the  living  force  represents,  not 
the  intensity  of  the  force  at  any  instant,  which  is  always  meas- 
ured by  M  D,  but  the  work  which  the  force  will  accomplish  dur- 
ing a  second  of  time. 

It  represents,  in  other  words,  the  power  or  quantity  of  the  force, 
in  distinction  from  the  intensity  of  the  force.  The  intensity  of  a 
force  has  been  represented  by  F.  The  power  or  quantity  of  a 
force  may  be  denoted  by  P.  Hence, 


and     P  =  J  M  u2.  [25.] 

The  word  /ore  e  is  generally  used  in  a  restricted  sense,  as  in  (29), 
to  denote  only  the  intensity  of  any  effort,  the  quantity  of  the  force 
exerted  being  called  power.     These  terms  will  be  adopted  with 
their  usual  sense  in  this  volume. 
5* 


54  CHEMICAL  PHYSICS. 

PROBLEMS. 

NOTE.    The  following  problems  should  be  solved  both  by  geometrical  construction 
and  by  trigonometry,  whenever  both  methods  are  applicable. 

Measure  of  Force. 

25.  A  mass  of  matter  equal  to  10  units  of  mass  receives  an  acceleration 
from  a  given  force  of  5  metres.     What  is  the  intensity  of  the  force  ? 

26.  A  mass  of  matter  equal  to  7  units  of  mass  receives  an  accelera- 
tion  from  a  given  force  of  9.8  metres.     What  is  the  intensity  of  the 
force  ? 

27.  A  mass  of  matter  equal  to  15  units  of  mass  receives  an  accelera- 
tion from  a  given  force  of  1.654  metres.     What  is  the  intensity  of  the 
force  ? 

28.  A  mass  of  matter  equal  to  20  units  of  mass  receives  an  accelera- 
tion from  a  given  force  of  26.243  metres.     What  is  the  intensity  of  the 

force? 

Momentum. 

29.  A  railroad  train  whose  mass  equals  1000  units  is  travelling  with 
a  velocity  of  50  kilometres  an  hour.     What  is  its  momentum  ?     How 
many  units  of  force  would  be  required  to  stop  the  train  in  ten  minutes, 
supposing  the  moving  power  to  cease  acting  ? 

30.  A  vessel  whose  mass  equals  120,000  units  is  moving  with  a  ve- 
locity of  2.25  metres.     What  is  its  momentum  ?     How  many  units  of 
force  would  be  required  to  stop  it  in  five  minutes,  supposing  the  moving 
power  to  cease  acting  ?     If  the  resistance  of  the  water  and  other  causes 
of  retardation  are  equivalent,  on  an  average,  to  a  force  of  900  units,  how 
soon  would  the  vessel  come  to  rest  after  the  moving  power  ceased  ? 

Composition  of  Forces. 

31.  Three  forces  are  acting  on  a  point  in  the  direction  A  B,  equal  re- 
spectively to  20,  35,  and  70  units.     In  the  opposite  direction,  B  A,  are 
acting  four  forces,  equal  respectively  to  10,  45,  15,  and  30  units.     What 
is  the  intensity,  and  what  the  direction,  of  the  resultant  ? 

32.  A  force  equal  to  1000  units  is  acting  on  a  point  in  the  direction 
B  A.     What  is  the  intensity  of  each  of  two  components,  which  are  to 
each  other  as  3  :  5,  and  both  of  which  are  acting  in  the  same  direction  as 
the  resultant  ?     What  is  the  intensity  of  each  of  two  components,  one  of 
which  acts  in  the  direction  of  the  resultant  and  the  other  in  an  opposite 
direction,  and  which  are  to  each  other  in  the  relation  of  3  :  5  ? 

33.  It  is  required  to  resolve  a  force  equal  to  441  units  into  six  compo- 
nents, in  the  same  direction  as  the  resultant,  whose  intensities  shall  be  to 
each  other  as  1  :  2  :  22  :  23  :  24  :  25. 

34.  It  is  required  to  resolve  a  force  equal  to  44  units  into  six  compo- 


GENERAL  PROPERTIES  OP  MATTER.  55 

nents.  Three  of  these,  which  have  the  same  direction  as  the  resultant, 
are  to  each  other  as  1  :  3  :  5  ;  while  the  three  others,  which  have  an  op- 
posite direction,  are  to  each  other  as  1  :  2  :  3.  Moreover,  the  sum  of  the 
first  is  5.4  times  greater  than  the  sum  of  the  last 

35.  Two  forces  are  acting  at  right  angles  to  each  other  on  one  point. 
The  force  F1  =  5  units,  and  the  force  F"  =  5  \/~3    units.     What  is 
the  intensity  of  the  resultant  ?  and  what  is  the  angle  which  its  direction 
makes  with  the  direction  of  F1  ? 

36.  Two  forces  acting  at  right  angles  on  one  point  are  equal,  F1  to  3 
units,  and  F"  to  4  units.     What  is  the  intensity  of  the  resultant  ?  and 
wrhat  is  the  angle  which  its  direction  makes  with  the  direction  of  F'  ? 

37.  It  is  required  to  resolve  a  force,  F  =  100  units,  into  two  compo- 
nents, F1  and  F",  making  with  F  the  angles  65°  and  25°  respectively. 
What  must  be  their  intensities  ? 

38.  It  is  required  to  resolve  a  force,  F  =  100  units,  into  two  compo- 
nents at  right  angles  to  each  other,  one  of  which  which  shall  be  equal  to 
30  units.     What  must  be  the  value  of  the  second  component  ?  and  what 
the  values  of  the  angles  which  both  components  make  with  the  resultant  ? 

39.  Two  forces,  each  equal  to  100  units,  act  on  one  point.     The  angle 
made  by  the  directions  of  the  two  forces  equals  45°.     What  is  the  value 
of  the  resultant  ? 

40.  The  directions  of  two  forces,  F'  =  100  and  F"  =  50,  acting  on 
one  point,  make  an  angle  of  145°.     What  is  the  value  of  the  resultant 
F?  and  what  are  the  angles  which  F  makes  with  F'  and  F"? 

41.  It  is  required  to  decompose  a  force,  F  =  125,  into  two  compo- 
nents, the  direction  of  each  of  which  shall  make,  with  the  direction  of  F, 
an  angle  of  25°.     What  will  be  the  value  of  each  component  ? 

42.  It  is  required  to  resolve  a  force,  F  =  100,  into  two  components, 
F'  and  F",  whose  direction  shall  make,  with  the  direction  of  F,  the  an- 
gles of  10°  and  20°  respectively.     What  will  be  the  value  of  each  com- 
ponent ? 

43.  Five  forces,  whose  directions  are  in  the  same  plane,  act  on  one 
point     The  intensities  of  the  forces,  and  the  angles  which  their  directions 
make  with  a  fixed  direction  passing  through  the  point  of  application  in 
the  same  plane,  are  given  in  the  following  table :  — 

Intensity  of  the  Forces.  Inclination  to  the  fixed  Direction. 

90  50° 

100  120° 

120  170° 

50  250° 

40  290° 

What  is  the  intensity  of  the  resultant  ?  and  what  is  the  angle  which  its 
direction  makes  with  the  fixed  direction  ? 


56  CHEMICAL  PHYSICS. 

44.  The  force  F  =  100  is  resolved  into  two  components,  F1  =100 
and  F"  =  150.     What  are  the  angles  which  the  directions  of  these  com- 
ponents make  with  the  direction  of  F  ? 

45.  At  the  extremities  of  a  straight  line  44  c.  m.  long,  two  parallel 
forces,  F1  =  15  and  F"  ===  7,  are  acting  in  the  same  direction.     What 
is  the  intensity  of  the  resultant  ?  and  what  is  the  position  of  the  centre  of 
the  two  forces  ? 

46.  At  the  extremities  of  a  straight  line  12  c.  m.  long,  two  parallel 
forces,  F1  —  19  and  F"  =13,  are  acting  in  opposite  directions.    What 
is  the  intensity  of  the  resultant  ?  and  what  is  the  position  of  the  centre  of 
the  two  forces  ? 

Action  and  Reaction. 

47.  A  mass  M  =  20  units,  moving  with  a  velocity  of  5  m.,  meets 
a  second  mass  M1  =15  units,  which  is  at  rest.     What  will  be  the  ve- 
locity of  the  combined  masses  after  collision  ?     In  this  and  in  the  few 
succeeding  problems  the  masses  are  supposed  to  be  unelastic,  and  so 
constituted  that  after  the  collision  they  will  move  on  together  as  one 
body. 

48.  A  mass  M  =  500  units,  moving  with  a  velocity  of  15  m.,  strikes 
another  mass  M1  =  50  units,  moving  with  a  velocity  of  10m.  in  the 
same   direction.     What  will  be   the  velocity  of  the    combined  masses 
after  the  collision  ? 

49.  A  mass  M=  250  units,  moving  with  a  velocity  of  20  m.,  meets 
another  mass  M1  =  300  units,  moving  with  a  velocity  of  2  m.  in  the  op- 
posite direction.     What  will  be  the  velocity  of  the  combined  masses  after 
the  collision  ? 

50.  A  mass  M  =  25  units,  moving  with  a  velocity  of  5m.,  meets  an- 
other mass  M '  =  30  units,  moving  with  a  velocity  of  2  m.     The  direc- 
tions  of   the   two  motions   before    collision  make  with   each   other  an 
angle   of  75°.      What   will   be   the  velocity   of  the   combined   masses 
after  the  collision  ?   and  what  will  be  the  angle  made  by  the  direction 
of  the  resulting  motion  with  the  directions  of  the  two  motions  before 
collision  ? 

GRAVITATION. 

(43.)  Definition.  — When  bodies  near  the  surface  of  the  earth 
are  left  unsupported,  they  fall  to  the  ground  ;  or,  if  supported, 
they  exert  a  downward  pressure,  which  we  term  their  weight. 
The  cause  of  these  phenomena  is  called  the  force  of  gravity. 
This  force  is  the  attraction  which  the  earth  exercises  upon  all 
bodies  on  or  near  its  surface,  and  is  only  a  particular  case  of  a 


GENERAL  PROPERTIES  OF  MATTER.  57 

general  force  of  nature,  in  virtue  of  which  all  bodies  in  the  uni- 
verse attract  each  other,  with  a  force  depending  on  their  masses 
and  their  mutual  distances.  Astronomy  exhibits  the  grandest 
examples  of  this  force,  in  the  motions  of  the  heavenly  bodies  ;  but 
it  can  also  be  shown  that  the  same  force  acts  upon  the  smallest 
masses  of  matter  with  which  we  experiment  on  the  surface  of  the 
globe.  The  existence  of  this  force  of  attraction  between  the  heav- 
enly bodies  was  first  recognized  by  Newton,  who  discovered  the 
law  which  it  obeys,  and  gave  to  it  the  name  of  Universal  Gravi- 
tation. In  this  work,  we  shall  only  have  occasion  to  study  those 
phenomena  of  gravitation  which  are  caused  by  the  attraction 
which  the  earth  exerts  for  bodies  on  or  near  its  surface.  Let  us 
then  inquire  what  is  the  direction,  what  the  point  of  application, 
and  what  the  intensity  of  this  force.  Compare  (26). 

(44.)  Direction  of  the  Earth's  Attraction.  —  It  has  been 
stated  (27),  that  the  direction  of  a  force  is  the  direction  of  the 
motion  which  it  causes,  or  the  direction  of  the  pressure  which  it 
exerts.  When  bodies  fall  freely,  they  move  on  a  line  which,  if 
extended,  would  pass  through  a  variable  point  near  the  centre 
of  the  globe,  called  its  centre  of  attraction.  Hence,  the  direction 
of  the  force  of  gravitation  is  that  of  a  line  joining  the  centre 
of  attraction  of  the  earth  to  the  point  of  application  of  the  body. 
This  direction  is  given  by  a.  plumb-line ,  which  is  merely  a  small 
weight,  generally  of  lead,  suspended  by  a  light 
and  flexible  thread  (Fig.  17).  When  the  weight 
thus  freely  suspended  is  at  rest,  it  is  easy  to  show 
that  the  pressure  exerted  by  the  force 
of  gravitation  is  in  the  direction  of 
the  line.  In  Fig.  18,  for  example, 
this  pressure  must  be  in  the  direc- 
tion A  C.  To  prove  this,  suppose  for 
a  moment  the  force  exerting  the  pres- 
sure were  in  any  other  direction,  as 
A  B  ;  then  the  force  in  the  direction 
A  B  could  be  decomposed  into  two 
components,  one  in  the  direction  A  C,  which  would 
be  neutralized  by  the  resistance  of  the  point  of 
suspension,  the  other  in  the  direction  A  D,  which 
would  cause  motion.  As  by  supposition  the  weight  rig.  is. 
is  at  rest,  it  follows  that  the  direction  of  the  pressure,  and  hence 


58  CHEMICAL   PHYSICS. 

also  the  direction  of  the  force  of  gravitation,  must  be  that  of  the 
plumb-line. 

If  several  plumb-lines  be  placed  near  each  other,  it  will  be 
found  that  the  lines  when  at  rest  will  all  be  sensibly  parallel  to 
each  other ;  because  their  distances  apart  are  inconsiderable  in 
comparison  with  the  length  of  the  radius  of  the  earth.  Hence 
the  directions  of  the  forces  of  gravity  exerted  by  the  earth  on 
neighboring  bodies  are  parallel.  The  direction  of  the  plumb- 
line  at  any  place  is  called  the  vertical  direction,  and  the  di- 
rection perpendicular  to  this  the  horizontal  direction.  The 
surface  of  a  liquid  at  rest,  as  will  be  proved  hereafter,  is  always 
horizontal,  and  therefore  perpendicular  to  the  plumb-line. 

(45.)  Point  of  Application  of  the  Earth's  Attraction.  —  As 
every  particle  of  a  body  is  similarly  situated  towards  the  earth,  it 
follows  that  every  particle  must  be  equally  attracted,  and  that 
there  must  be  as  many  points  of  application  as  there  are  parti- 
cles of  the  body.  The  action  of  the  earth's  attraction  may  there- 
fore be  regarded  as  the  action  of  an  infinite  number  of  parallel 
and  equal  forces  on  as  many  distinct  points  of  application.  The 
resultant  of  these  forces  can  be  easily  found  by  extending  the 
method,  discussed  in  (39),  of  finding  the  resultant  of  several 
parallel  forces,  to  the  case  where  the  number  of  forces  is  infinite. 
As  the  general  conclusions  of  (39)  are  independent  of  the  num- 
ber of  parallel  forces,  it  follows  that  the  direction  of  the  result- 
ant of  the  forces  of  gravity,  acting  on  the  particles  of  a  body,  is 
parallel  to  the  common  direction  of  the  forces,  and  also  that  the 
intensity  of  the  resultant  is  equal  to  the  sum  of  the  intensities  of 
the  components. 

If,  for  example,  A  B  (Fig.  19)  represents  a  mass  of  matter, 
and  the  small  arrows  pointing  vertically  downwards  represent 
the  directions  of  the  gravitating  forces  acting  on  the  particles  com- 
posing such  mass,  then  it  follows,  from  what  has  been  explained, 
that  the  resultant  of  all  these  forces  will  have  a  direction,  D  E, 
parallel  to  their  common  direction,  and  will  have  an  intensity 
equal  to  their  sum.  The  position  of  this  resultant  remains  yet  to 
be  determined.  The  principles  of  mathematics  enable  us,  in  many 
cases,  to  combine  together  the  forces  acting  on  all  the  particles 
of  a  body,  by  extending  the  method  used  in  (39),  Fig.  13,  and 
thus  to  calculate  the  exact  position  of  the  resultant ;  but  its  posi- 
tion can  in  most  cases  be  determined  more  readily  by  experi- 
ment. 


GENERAL  PROPERTIES  OF  MATTER. 


59 


If,  in  Fig.  19,  we  suppose  that  the  line  represented  by  the  large 
arrow  is  the  direction  of  the  resultant,  it  is  evident  that,  if  any 
point,  such  as  (7,  on  that  line,  is  supported,  the 
body  will  remain  at  rest ;  because  the  resultant 
of  all  the  forces  acting  upon  the  body  having  the 
direction  D  E,  will  be  expended  in  pressure  on 
the  fixed  point  C.  It  is  not  essential  that  the 
point  of  support  should  be  in  the  body,  for  the 
same  would  be  true  for  any  point  in  the  direc- 
tion of  the  arrow  D  E.  If,  for  example,  D  were 
a  pin,  from  which  the  body  was  suspended  by 
a  thread  attached  to  the  body  at  any  point  in  the 
line  D  C,  then  the  body  would  still  remain  at  Fi«-  19- 

rest ;  for,  as  before,  the  resultant  having  the  direction  D  E  would 
be  expended  in  pressure  on  the  pin  at  D.  It  would  be  different, 
however,  with  a  point  of  support  not  in  the  direction  of  the  arrow, 
such  as  P.  If  the  body  be  connected  with  this  point  by  a  string 
attached  at  C,  it  will  no  longer  remain  at  rest ;  for  the  resultant 
jD  .E,  acting  at  the  point  C,  can  be  decomposed  into  two  compo- 
nents,—  the  first  in  the  direction  of  C  H,  which  would  be  ex- 
pended in  pressure  on  the  point  P,  and  the  second  in  the  direction 
C  I,  which  would  move  the  body  towards  the  vertical  line.  It 
follows,  therefore,  that,  if  a  body  be  supported  by  a  fixed  point, 
it  cannot  remain  at  rest,  unless  the  resultant  of  all  the  parallel 
forces  which  gravity  exerts  upon  its  particles  passes  through  that 
point. 

This  fact  gives  us  the  means  of  ascertaining  experimentally 
the  position  of  the  resultant  of  the  parallel  forces  which  gravity 
exerts  upon  the  particles  of  a  body.  We  have 
only  to  suspend  it  by  a  string  attached  to  any 
point  of  the  body,  and  the  direction  which  the 
string  assumes  will  be  the  direction  of  the  re- 
sultant of  the  forces  of  gravity  when  the  body 
is  in  that  position.  In  Fig.  20,  for  example,  the 
resultant  of  the  forces  which  gravity  exerts  upon 
the  particles  of  the  chair  is  the  line  A  .£?,  when 
the  chair  is  in  the  position  represented  in  the 
figure.  If  we  attach  the  string  to  another 
point,  the  chair  will  take  another  position,  and 
the  resultant  will  also  change  its  position  to  the  2Q 


60  CHEMICAL   PHYSICS. 

line  CD,  Fig.  21.     We  should  find,  by  experiment,   that   for 
every  point  of  suspension  there  would  be  a  different  position  of 
the  chair,  and  also  a  different  position  of 
the  resultant. 

When,  in  any  given  position  of  a  body, 
we  have  determined  the  position  of  the 
resultant  of  the  forces  of  gravity,  we  have 
also  determined  a  line  on  which  the  point 
of  application  of  the  earth's  attraction  must 
be  ;  because,  by  (32),  this  point  may  be 
any  point  on  the  line  of  the  resultant.  The 
position  of  the  line,  however,  will  depend 
on  the  position  of  the  body  ;  and  there- 
pi  21  fore,  in  order  to  determine  it,  the  position 

of  the  body  must  be  given. 

(46.)  Centre  of  Gravity.  —  When  a  body  is  turned  round  in. 
any  direction,  it  is  easy  to  see  that  the  lines  of  direction  of  the  par- 
allel forces,  which  gravity  exerts  on  its  particles,  revolve  about 
their  points  of  application,  retaining  their  parallelism.  Hence  it 
follows,  from  (40),  that,  in  any  position  which  the  body  may  as- 
sume, the  resultant  of  these  forces  will  always  pass  through  the 
same  point.  This  common  point  of  intersection  of  the  resultants 
of  the  forces  of  gravity,  in  any  position  which  the  body  may  as- 
sume, is  termed  the  centre  of  gravity.  This  point  has  several 
important  relations,  which  we  will  now  consider. 

The  centre  of  gravity  may  always  be  regarded  as  the  point 
of  application  of  the  resultant  of  the  forces  which  gravity  exerts 
upon  the  particles  of  a  body,  because  it  has  been  proved,  first, 
that  the  point  of  application  may  be  any  point  on  the  line  of  the 
resultant ;  secondly,  that  the  centre  of  gravity  is  a  point  common 
to  all  the  resultants. 

When  the  centre  of  gravity  is  supported,  the  body  remains  at 
rest.  If  the  centre  of  gravity  be  supported  on  a  point  or  axis, 
and  the  body  is  free  to  turn  round  such  axis,  the  body  will  re- 
main at  rest  in  any  position  in  which  it  can  be  placed.  This 
result  follows  necessarily  from  the  last ;  for,  as  the  point  of  appli- 
cation of  the  resultant  is  fixed,  the  whole  intensity  of  the  forces 
of  gravity  must  be  expended  in  pressure  against  this  point. 

The  whole  attractive  force  exerted  by  a  mass  of  matter  may 
be  regarded  as  emanating  from  its  centre  of  gravity.  The  prin- 


GENERAL   PROPERTIES    OF   MATTER.  61 

ciple,  that  action  and  reaction  are  always  equal  and  opposite, 
applies  to  the  attraction  of  gravity  exerted  by  one  mass  of  matter 
over  another.  The  earth  is  attracted,  by  a  body  near  its  surface, 
with  a  force  exactly  equal  to  the  attraction  exerted  by  the  earth 
on  this  body.  Now,  since  the  attraction  of  the  body  must  be 
equal  and  opposite  to  that  of  the  earth,  it  follows  that  the  re- 
sultant of  the  force  must  be  on  the  same  line  with  the  centre  of 
gravity,  and  hence  may  always  be  regarded  as  emanating  from 
it.  Hence,  also,  the  attraction  of  the  earth  may  be  regarded  as 
emanating  from  some  one  point,  which  is  not,  however,  the 
same  as  the  centre  of  its  figure,  and,  moreover,  it  is  variable. 

A  singular  result  follows  from  the  principle  of  reaction  above 
stated,  since  it  must  be,  when  a  body  falls  to  the  ground,  that 
the  earth  must  rise  to  meet  the  body,  —  and  this  is  true  ;  but  the 
extent  of  the  motion  of  the  earth  is  as  much  less  than  that  of 
the  body,  as  the  mass  of  the  earth  is  greater  than  the  mass  of  the 
body.  Representing  by  m  the  mass  of  the  body,  we  have  for  the 
intensity  of  the  earth's  attraction  m  t) ;  and  representing  by  M 
the  mass  of  the  earth,  we  have  for  the  intensity  of  the  body's  at- 
traction for  the  earth  M  t)' ;  and  since  these  are  equal,  wo  have 

mv  =  Mv',    or    v':v  =  m:M; 

that  is,  the  velocity  acquired  by  the  earth  at  the  end  of  one  sec- 
ond is  as  much  less  than  that  acquired  by  the  body,  as  the  mass 
of  the  body  is  less  than  that  of  the  earth. 

(47.)  Position  of  the  Centre  of  Gravity.  —  For  tho  methods 
of  calculating  the  position  of  the  centre  of  gravity,  we  must  refer 
the  student  to  works  on  Mechanics,  since  these  methods  depend 
on  the  principles  of  the  higher  mathematics.  The  position  of 
the  centre  of  gravity  can  be  found  experimentally  by  suspending 
the  body  by  a  cord  from  two  points  successively,  as  represented 
in  Figs.  20,  21.  The  point  where  the  line  of  the  cord  produced 
in  one  position  intersects  the  line  of  the  cord  produced  in  the 
second,  is,  by  (46),  the  centre  of  gravity.  It  can  thus  be  proved, 
that,  when  a  homogeneous  body  has  a  regular  form,  the  centre  of 
gravity  is  at  the  centre  of  the  figure.  This  is  the  case  with  the 
sphere,  the  cube,  the  octahedron,  and  the  other  regular  solids  of 
geometry.  So  also,  when  a  homogeneous  body  has  a  symmetrical 
axis,  the  centre  of  gravity  will  be  a  point  of  this  axis.  Thus,  in 
a  cone,  the  centre  of  gravity  is  in  the  axis  of  tho  cone,  and  it  can 
6 


62  CHEMICAL   PHYSICS. 

easily  be  seen  that,  if  a  cone  be  suspended  by  a  string  from  its 
apex,  the  direction  of  the  line  of  suspension  would  coincide  with 
the  direction  of  the  axis  of  the  cone  ;  because,  as  the  matter  is 
uniformly  distributed  round  this  axis,  the  gravity  of  its  particles, 
acting  equally  on  every  side,  will  have  no  tendency  to  move  it 
when  in  this  position. 

The  centre  of  gravity  is  not  necessarily  in  the  body.  Thus, 
the  centre  of  gravity  of  a  hoop  is  at  its  centre,  and  the  cen- 
tre of  gravity  of  a  hollow  sphere,  an  empty  box,  or  a  cask,  is 
within  it. 

The  centre  of  gravity  of  two  separate  and  independent  bodies 
immovably  united  is  a  point  between  them.  This  point  can  be 
very  easily  determined  mathematically,  from  principles  already 
established. 

Let  A  and  B,  Fig.  22,  be  the  two  bodies,  and  let  a  and  b  be  their 
centres  of  gravity.  Connect  the  two  by  a  line.  From  what  has 

been  said,  it  follows  that  the 
attraction  of  the  earth  on  this 
system  may  be  regarded  as  the 
action  of  two  parallel  forces  at 
a  and  b.  Hence,  the  point  of 
application  of  the  resultant,  the 

centre  of  gravity  of  the  system,  must  be  on  the  line  a  b,  and 
must  divide  the  line  into  two  parts,  which  are  inversely  pro- 
portional to  the  intensities  of  the  forces.  It  will  be  shown  in 
(49)  that  the  two  forces  are  proportional  to  the  masses,  and 
hence  the  centre  of  gravity  must  divide  the  line  a  b  into  two 
parts  which  are  inversely  proportional  to  the  masses  of  the  two 
bodies  A  and  B. 

(48.)  Stable,  Unstable,  and  Neutral  Equilibrium. — It  is  a 
necessary  consequence  of  what  has  been  said,  that  the  centre  of 
gravity  of  a  body  has  always  a  tendency  to  move  into  the  lowest 
position  of  which  the  conditions  will  admit.  Hence,  if  the  body 
is  supported  at  only  one  point,  it  cannot  remain  at  rest,  unless 
this  point  of  support  is  either  at  the  centre  of  gravity  or  is  in  the 
same  vertical  with  it.  If  the  centre  of  gravity  is  below  the 
point  of  support,  the  body  is  in  a  stable  equilibrium ;  because, 
if  by  any  means  the  centre  is  displaced,  the  force  of  gravity  will 
tend  to  restore  it  to  its  original  position.  If,  however,  the  centre 
of  gravity  is  above  the  point  of  support,  the  body  will  be  in  an 


GENERAL   PROPERTIES    OF   MATTER.  63 

unstable  equilibrium  ;  for  the  slightest  displacement  will  remove 
the  centre  out  of  the  vertical,  and  it  will  then  move  to  the  lowest 
possible  position.  The  chair  suspended  by  a  string  in  Fig.  20  is 
in  a  stable  equilibrium,  because  the  centre  of  gravity  is  below 
the  point  of  support.  The  same  chair  could,  with  great  care,  be 
balanced  on  the  end  of  one  of  its  legs,  but  its  equilibrium  would 
then  be  unstable ;  because  the  centre  of  gravity  would  be  above 
the  point  of  support,  and  the  slightest  displacement  of  the  centre 
of  gravity  would  cause  the  chair  to  fall. 

When  a  body  rests  on  a  base,  it  is  stable,  when  the  vertical 
passing  through  the  centre  of  gravity  falls  within  the  base.  The 
stability  of  the  body  in  such  a  position  is  estimated  by  the  mag- 
nitude of  the  force  required  to  overturn  it.  If  its  position  can 
be  disturbed  or  deranged  without  raising  its  centre  of  gravity, 
the  slightest  force  will  be  sufficient  to  move  it ;  but  if  its  position 
cannot  be  changed  without  causing  its  centre  of  gravity  to  rise 
to  a  higher  position,  then  a  force  will  be  required  which  would  be 
sufficient  to  raise  the  entire  body  through  the  height  to  which  its 
centre  of  gravity  must  be  elevated.  This  is  illustrated  in  Figs. 
23,  24,  25.  To  turn  the  cylinder  over  the  edge  B,  it  would  bo 


Fig.  23.  Fig.  24.  Fig.  26. 

necessary  in  either  case  to  move  the  centre  of  gravity,  G9  over 
the  arc  G  E,  and  hence  to  raise  it  through  the  height  HE. 
This  distance  is  greater,  and  hence  the  force  required  to  over- 
turn the  cylinder  is  greater,  the  larger  the  base  of  the  cylinder 
relatively  to  its  height.  It  can  also  easily  be  seen  that  the  sta- 
bility is  greatest  when  the  vertical,  passing  through  the  centre  of 
gravity,  passes  also  through  the  centre  of  the  base.  If  it  passes 


64  CHEMICAL  PHYSICS. 

through  tho  edge  of  the  base,  as  in  Fig.  26,  the  slightest  force 
will  overturn  it.     If  it  passes  outside  of  the  base  (Fig.  27),  then 


Fig.  26.  Fig.  27. 

the  centre  will  be  unsupported,  and  the  cylinder  will  fall.  These 
principles,  which  have  been  illustrated  by  a  cylinder,  may  be 
readily  extended  to  other  bodies. 

When  a  body  rests  on  two  or  more  points,  it  is  not  necessary 
for  its  stability  that  its  centre  of  gravity  should  be  directly 
over  one  of  these  points ;  it  is  only  necessary  that  its  vertical 
should  fall  between  them.  If  a  body  rests  on  two  points,  it 
is  supported  as  effectually  as  if  it  rested  on  an  edge  coinciding 
with  the  straight  line  which  unites  the  two.  If  it  rests  on  three 
points,  it  is  supported  as  firmly  as  it  would  be  by  a  triangular 
base  coinciding  with  the  triangle  of  which  the  three  points  are 
vertices. 

A  familiar  condition  of  equilibrium  is  presented  by  a  sphere 
resting  on  a  level  plane.  Such  a  sphere  has  but  ,one  point  of 
support,  and  this  is  directly  under  the  centre  of  gravity.  If  the 
sphere  is  rolled  upon  the  plane,  the  centre  of  gravity  will  neither 
rise  nor  fall.  Hence  any  force,  however  slight,  will  cause  it  to 
move  ;  and,  on  the  other  hand,  the  body  will  have  no  tendency, 
of  itself,  to  change  its  position  when  it  is  disturbed.  This  condi- 
tion is  called  neutral  equilibrium.  A  cylinder  resting  with  its 
edge  on  a  plane  and  level  surface  is  another  example  of  neutral 
equilibrium. 

(49.)  Intensity  of  the  Earth's  Attraction.  —  The  falling  of  a 
stone  to  the  earth  is,  as  has  been  stated  (21),  an  example  of  a 
uniformly  accelerated  motion.  Hence,  the  force  of  gravitation 


GENERAL  PROPERTIES  OF  MATTER.  65 

must  be  a  force  of  constant  intensity  (27).  The  amount  of  ac- 
celeration, as  was  also  stated  (21),  at  the  latitude  of  Paris,  is 
$  =  9.8088  metres.  This  acceleration  is  the  same  for  all  masses 
of  matter,  whether  large  or  small.  The  apparent  contradiction 
to  this  statement  in  common  experience  arises  from  the  fact,  that 
the  fall  of  light  bodies  is  more  retarded  by  the  resistance  of  the 
air  than  that  of  heavy  bodies.  If,  however,  the  experiment  is 
made  in  a  vacuum,  it  will  be  found  that  a  gold  eagle  and  a  feather 
will  fall  with  equal  rapidity.  The  intensity  of  a  force  is,  as  we 
have  seen,  equal  to  M  V.  Representing  the  intensity  of  the  force 
of  gravity,  which  acts  on  a  given  mass  of  matter,  Jf,  by  Cr,  we 
shall  have,  for  the  latitude  of  Paris, 

G  =  M  9.8088  (units  of  force).  [26.] 

For  any  other  mass  of  matter,  M1 ,  we  shall  have,  in  the  same 
way, 

G1  =  M '  9.8088  (units  of  force). 
Hence, 

G:  G'  =  M:  M'.  [27.] 

The  intensity  of  the  earth's  attraction  is  therefore  proportional 
to  the  quantity  of  matter  on  which  it  acts.  In  other  words,  the 
force  increases  with  the  quantity  of  matter  to  which  it  is  applied. 
In  this  respect  gravity  differs  from  many  other  forces  with  which 
we  are  familiar,  from  muscular  force  and  the  force  of  a  steam- 
engine,  for  example,  since  these  have  a  constant  value,  and  do  not 
vary  with  the  amount  of  matter  to  which  they  are  applied. 

We  assumed  (45)  that  the  earth's  attraction  acts  equally  on 
every  particle  of  matter.  If  this  is  true,  it  follows  that  the  re- 
sultants of  all  the  forces  of  gravity  acting  on  the  separate  parti- 
cles of  two  bodies  must  be  proportional  to  the  number  of  par- 
ticles in  each ;  in  other  words,  to  the  masses  of  the  two  bodies. 
That  this  is  the  case,  is  proved  by  the  experiment  on  falling 
bodies  alluded  to  above,  arid  by  the  proportion  [27]  which  fol- 
lowed. Hence  the  assumption  of  (45)  was  correct. 

As  the  intensity  of  the  force  of  gravity  varies  with  the  amount 
of  matter  on  which  it  acts,  we  must,  in  estimating  the  strength 
of  this  force  in  different  places,  always  compare  the  intensities 
of  the  force  when  acting  on  equal  masses  of  matter.  It  simpli- 
fies the  subject,  to  take  a  quantity  of  matter  equal  to  the  unit  of 
mass  in  each  case.  Representing  then  by  #•  the  intensity  of  the 
6* 


66  CHEMICAL   PHYSICS. 

attraction  of  gravitation  for  the  unit  of  mass,  we  can  easily  de- 
duce from  [26], 

g  =  9.8088  (units  of  force)  ;  [28.] 

and  also 

G  =  Mg  (units  of  force).  [29.] 

In  this  book,  g  will  always  be  used  to  express  the  intensity  of  the 
force  of  gravity  acting  on  the  unit  of  mass,  or,  in  general,  the 
intensity  of  the  force  of  gravity ;  and  G  will  always  be  used  to 
express  the  intensity  of  the  force  of  gravity  acting  on  a  given 
mass,  M.  In  every  case  they  both  stand  for  a  certain  number  of 
units  of  force.  The  intensity  of  the  earth's  attraction  varies 
slightly  at  different  points  of  its  surface  ;  thus,  at  the  equator, 
g  =  9.7806  ;  at  the  latitude  of  Paris,  as  above,  g  =  9.8088  ; 
and  at  the  pole,  g  =  9.8314. 

In  order  to  determine  the  intensity  of  gravity  at  different 
places,  it  might  be  supposed  that  we  could  measure  the  dis- 
tance through  which  a  heavy  body  would  fall  the  first  second, 
and  then,  by  the  principles  of  uniformly  accelerated  motion  (21), 
twice  this  distance  would  be  equal  to  the  value  of  g  at  the  given 
place.  On  account  of  the  great  rapidity  with  which  bodies  fall, 
it  is  impossible  to  measure  this  distance  with  any  accuracy  ;  nor 
is  this  necessary,  since  we  have  in  the  pendulum  an  instrument 
by  which  we  can  determine  indirectly  the  value  of  g  with  great 
precision. 

(50.)  Pendulum.  —  A  pendulum  is  a  heavy  body,  suspended 
from  a  fixed  point  by  a  rod  or  cord.  If  the  centre  of  gravity  of 
the  body  is  directly  under  the  point  of  support,  the  body  remains 
at  rest ;  but  if  the  body  be  drawn  out  of  this  position,  so  that 
the  centre  of  gravity  will  be  on  either  side  of  the  vertical  line 
passing  through  the  point  of  support,  then  the  body,  when  disen- 
gaged, will  fall  towards  the  vertical  line,  and  in  consequence  of 
its  inertia  will  continue  its  motion  beyond  the  vertical  line  until 
it  comes  to  rest.  It  will  then  return  to  the  vertical,  and  thus 
oscillate  from  side  to  side.  In  order  to  investigate  the  phe- 
nomena of  this  kind  of  motion,  the  mathematicians  study  at  first 
an  ideal  pendulum,  which  they  call  a  simple  pendulum,  to  distin- 
guish it  from  the  actual  material  pendulum,  which  they  call  a 
compound  pendulum. 

(51.)  Simple  Pendulum.  —  A  simple  pendulum  consists  of  a 
material  point  suspended  to  a  fixed  point  by  means  of  a  thread 


GENERAL   PROPERTIES   OF   MATTER.  67 

without  mass  or  weight,  perfectly  flexible  and  inextensible. 
Such  a  pendulum  is  of  course  only  a  mathematical  abstrac- 
tion ;  but  we  can  approach  sufficiently  near  to  it,  for  purposes 
of  illustration,  by  suspending  a  small  lead  bullet  to  a  fixed  point 
by  means  of  a  fine  silk  thread. 

Let  O  A,  Fig.  28,  be  such  a  simple  pendulum,  in  a  vertical  po- 
sition, and' therefore  at  rest.  If  we  now  withdraw  it  to  the  posi- 
tion O  B,  the  force  of  gravity  act- 
ing on  the  point  B  in  the  direction 
B  g-  may  be  decomposed  into  two 
components;  one,  B  a,  which  will  be 
destroyed  by  the  resistance  of  the 
thread  and  of  the  fixed  point  O ;  the 
other,  B  6,  perpendicular  to  O  B, 
which,  being  unresisted,  will  move 
the  point  B  towards  the  vertical 
O  A.  If  the  line  B  g"  represents 
the  intensity  of  the  force  of  grav- 
ity, then  B  b  represents  the  in- 
tensity of  the  second  component.  FIR.  28. 
Hence,  if  we  suppose  the  amount 

of  matter  concentrated  at  B  to  be  equal  to  the  unit  of  mass,  and 
represent  the  angle  BOA  by  a,  we  shall  have,  for  the  value  of 
the  second  component,  g-  sin  a.  This  component  will  evidently 
diminish  in  intensity  as  the  pendulum  approaches  the  vertical, 
and  at  the  vertical  will  become  nothing.  It  appears,  therefore, 
that  this  force  will  be  continuous,  but  not  constant ;  and  hence, 
that  the  pendulum  will  move  with  an  accelerated,  but  not  with 
a  uniformly  accelerated  motion  (20) ,  in  the  arc  of  a  circle  whose 
radius  is  equal  to  O  B. 

Having  reached  the  vertical  O  A,  the  pendulum,  in  virtue  of  its 
momentum,  will  rise  with  a  retarded  motion  toward  O  B' ;  and 
since  the  action  of  gravitation  in  retarding  the  motion  must  be 
exactly  equal  to  its  previous  action  in  accelerating  it,  it  follows 
from  (27)  that  the  momentum  will  not  be  destroyed  until  the 
pendulum  has  moved  over  an  arc,  A  B1,  equal  to  A  B.  At  B1  it 
will  be  for  an  instant  at  rest,  and  then  fall  back  again  to  A,  re- 
mount to  By  and  thus  continue  indefinitely,  supposing  there  were 
no  resistance.  In  actual  practice,  however,  with  a  compound 
pendulum,  the  resistance  of  the  air,  the  rigidity  of  the  thread, 


68  CHEMICAL   PHYSICS. 

and  the  friction  at  the  point  of  support,  rapidly  diminish  the 
arc  through  which  it  moves,  and  finally  arrest  the  motion  al- 
together. By  diminishing  these  resistances,  the  motion  may  be 
made  to  continue  for  a  proportionally  longer  time  ;  and  a  pendu- 
lum has  been  known  to  continue  oscillating  in  a  vacuum  for 
several  hours. 

Each  motion  of  the  pendulum  from  B  to  B',  or  from  B'  to  B, 
is  called  one  oscillation,  and  the  angle  B  O  B'  is  called  the  ampli- 
tude of  the  oscillation. 

(52.)  Isochronism  of  the  Pendulum.  — :  It  is  evident  that  the 
length  of  time  required  for  a  single  oscillation  of  the  pendulum 
O  A,  Fig.  28,  must  be  absolutely  the  same,  so  long  as  the  ampli- 
tude of  the  oscillation  remains  constant ;  but  also,  what  is  more 
remarkable,  it  is  true  that  the  time  required  for  each  oscillation 
of  the  pendulum  is  but  little  influenced  by  the  amplitude  of  the 
oscillation ;  and,  for  all  practical  purposes,  the  time  of  oscilla- 
tion may  be  regarded  as  equal  for  all  amplitudes  not  exceeding 
three  or  four  degrees.  This  singular  property  of  the  pendulum 
is  termed  isochronism,  from  two  Greek  words  signifying  equal 
time,  and  the  oscillations  of  the  pendulum  are  said  to  be  iso- 
chronous. Two  oscillations  of  the  pendulum  are  not,  however, 
absolutely  isochronous,  unless  the  difference  between  their  am- 
plitudes is  infinitely  small. 

(53.)  Formula  of  the  Pendulum.  —  If  we  represent  by  T  the 
time  of  oscillation  of  a  pendulum  in  seconds,  by  /  its  length  in 
fractions  of  a  metre,  by  g-  the  acceleration  produced  by  gravity 
each  second,  and  by  it  the  ratio  of  the  circumference  of  a  circle 
to  its  diameter,  the  value  of  T  may  be  found  to  be 


21=^N)p 

when  the  amplitude  of  the  oscillation  is  infinitely  small.  If  the 
amplitude  is  not  infinitely  small,  but  only  very  small,  then  we 
have 

T=; 

when  a  is  the  ratio  of  the  length  of  the  arc  A  B,  Fig.  28,  to  the 
length  of  the  pendulum.  The  truth  of  these  formulae  cannot 
readily  be  demonstrated  without  the  aid  of  the  higher  mathe- 
matics, and  we  must  therefore  refer  the  student  to  works  on 
Analytical  Mechanics  for  the  demonstration. 


GENERAL  PROPERTIES  OF  MATTER.  69 

Several  important  truths  are  expressed  in  these  formulae  :  — 

1.  The  duration  of  an  oscillation  does  not  depend  on  its  ampli- 
tude when  this  is  infinitely  small,  and  is  but  slightly  influenced 
by  the  amplitude  even  ivhen  it  is  as  large  as  three  or  four  de- 
grees.    By   substituting,   in  [CO],  /=!,   and  g-  =  9.809,  we 
should  obtain,  for   the  time   of  vibration   of  a   pendulum  one 
metre  long,  at  the  latitude  of  Paris,   T=  1.003085.     By  sub- 
stituting in  [31]  the  same  values,  and  also  a  =  3.1416  -r-  90  = 
0.0349,  we  should  obtain,  for  the  time  of  vibration  when  the  am- 
plitude was  four  degrees,  T=  1.003161,  which  differs  from  the 
first  value  by  only  the  0.000076  of  a  second. 

2.  The  duration  of  the  oscillation  is  proportional  to  the  square 
root  of  the  length  of  the  pendulum.     Substituting,  in  equation 

[30]  ,    C  =       -  ,  which   is   a   constant  quantity  at  any  given 

place,  the  equation  becomes  T  =  C  */T.  For  a  pendulum  of 
another  length,  as  /',  we  have  T'  =  C  A/I7,  and,  comparing 
the  two, 

T  :  T1  =  VT  :  VI7  J  [32.] 

and  also 

/  :  /'  =  T2  :  T1*.  [33.] 

3.  The  duration  of  the  oscillation  of  a  pendulum  of  an  inva- 
riable length  is  inversely  proportional  to  the  square  root  of  the 
intensity  of  gravity.    Substituting,  in  equation  [30],  0  =  ^/^1, 
which  is  a  constant  quantity  when  /  is  supposed  invariable,  we 

obtain  T==  C'      _.     For  another  place,  where  the  intensity  of 

\£ 

gravity  is  g/,  we  have  T  =  C    IJL  ;  hence, 

N*3 


(54.)  Compound  Pendulum.  —  We  have  hitherto  supposed 
that  the  pendulum  is  a  heavy  mass,  of  indefinitely  small  magni- 
tude, suspended  by  a  string  or  a  rod,  having  no  weight.  Such 
a  pendulum  is,  as  has  been  stated,  a  pure  abstraction,  and  can 
never  be  realized  in  practice.  The  pendulum  which  must  be 
used  in  all  our  experiments  is  a  compound  pendulum,  consisting 
of  a  heavy  weight,  suspended  to  a  fixed  point  or  axis,  by  means 
of  a  rigid  rod  of  wood  or  metal.  The  particles  of  such  a  pendu- 


70  CHEMICAL   PHYSICS. 

lum  must  necessarily  be  at  different  distances  from  the  point  of 
suspension,  and  must  therefore  tend  to  oscillate  in  different  times. 
Hence,  the  time  of  oscillation  of  the  whole  pendulum  will  not  be 
the  same  as  that  of  a  simple  pendulum  of  the  same  length,  and 
the  difference  becomes  of  much  importance. 

The  theory  of  the  simple  pendulum  may  be  extended  to  the 
compound  pendulum,  by  regarding  the  last  as  consisting  of  as 
many  simple -pendulums  as  it  contains  material  particles.  Were 
these  free  to  move,  they  would  oscillate  in  different  times,  deter- 
mined by  their  distances  from  the  point  of  suspension  ;  but  they 
form  parts  of  a  rigid  system,  and  they  are  therefore  all  compelled 
to  oscillate  in  the  same  time.  Consequently,  the  oscillations  of 
the  particles  near  the  point  of  suspension  are  retarded  by  the 
slower  oscillations  of  those  below  them  ;  and,  011  the  other  hand, 
the  oscillations  of  the  particles  near  the  lower  end  of  the  pendu- 
lum are  accelerated  by  the  more  rapid  oscillations  of  those  above 
them.  At  some  point  on  the  axis  of  the  pendulum,  intermediate 
between  these,  there  must  be  a  particle  whose  natural  oscillation 
is  neither  accelerated  nor  retarded,  and  where  the  several  effects 
will  be  all  balanced,  all  the  particles  above  it  having  exactly  the 
same  tendency  to  oscillate  faster  that  the  particles  below  it  have 
to  oscillate  slower.  This  point  is  called  the  centre  of  oscillation, 
and  it  is  obvious  that  the  time  of  oscillation  of  a  compound  pen- 
dulum is  exactly  the  same  as  that  of  a  simple  pendulum  whose 
length  is  equal  to  the  distance  of  the  centre  of  oscillation  from 
the  point  of  suspension.  This  distance  is  the  virtual  or  acting1 
length  of  the  pendulum,  and  equations  [30]  and  [31]  will  apply 
to  compound  pendulums,  by  substituting  for  /  their  virtual 
length.  By  the  length  of  a  pendulum,  no  matter  what  may  be 
its  form,  is  always  to  be  understood  the  virtual  length,  unless 
the  reverse  is  expressly  stated. 

(55.)  Position  of  the  Centre  of  Oscillation.  —  When  the  form 
of  the  pendulum  is  given,  the  position  of  the  centre  of  oscillation 
can  be  calculated  ;  but  as  the  methods  of  calculation  involve  the 
principles  of  the  higher  mathematics,  they  cannot  readily  be  ex- 
plained in  this  connection.  The  centre  of  oscillation  can  also  be 
found  experimentally,  by  making  use  of  the  following  remarka- 
ble property  of  the  compound  pendulum,  first  demonstrated  by 
Huyghens. 

If  a  pendulum  be  inverted  and  suspended  by  its  centre  of  os- 


GENERAL  PROPERTIES  OF  MATTER.  71 

dilation,  its  former  point  of  suspension  will  become  its  new  centre 
of  oscillation,  and  the  time  of  vibration  will  remain  the  same  as 
before.  This  property  is  usually  expressed  by  saying,  that  the 
centres  of  oscillation  and  suspension  are  interchangeable. 

This  property  of  the  pendulum  may  be  verified  by 
means  of  a  reversible  pendulum,  Fig.  29.  This  pendu- 
lum is  furnished  with  two  knife-edges,  a  and  b,  which, 
when  the  pendulum  is  in  use,  rest  on  plates  of  steel  or 
agate.  If  a  is  the  axis  of  suspension,  and  b  the  axis  of 
oscillation,  determined  by  calculation,  the  pendulum  will 
be  found  to  oscillate  in  the  same  time  on  either  knife- 
edge.  If  the  position  of  the  axis  of  oscillation  is  not 
known,  it  can  easily  be  found  by  shifting  the  position  of 
the  lower  knife-edge,  until,  on  trial,  the  pendulum  is 
found  to  oscillate  in  equal  times  on  both.  The  lower 
knife-edge  is  then  in  the  axis  of  oscillation.  A  pen- 
dulum of  this  kind  was  used  by  Captain  Kater,  in  his 
determination  of  the  length  of  the  seconds  pendulum, 
mentioned  on  page  12. 

When  the  pendulum  consists  of  a  fine  thread  and  a 
heavy  ball,  the  centre  of  oscillation  very  nearly  coin- 
cides with  the  centre  of  gravity,  and  such  a  pendulum 
can  be  used  for  ascertaining  approximatively  the  virtual 
length  of  a  compound  pendulum.  By  shortening  or 
lengthening  the  thread,  a  length  can  easily  be  found 
with  which  the  pendulum  will  oscillate  in  the  same 
time  with  the  compound  pendulum.  This  length  will 
then  be  approximatively  the  virtual  length  sought. 

(56.)    Use  of  the  Pendulum  for  Measuring-  Time.  — 

If  in  the  equation  T=  it     — ,  we    substitute    for  T 

unity,  and  for  n  and  g*  the  values  already  given,  we  shall       I  1 
find,  for  the  length  of  a  pendulum  vibrating  seconds  at      ||T3" 
Paris,  the  value  /  =  0.993839  m.     The  lengths  of  pen- 
dulums vibrating  in  2,  3,  and  4  seconds  would  be  by  (33) 
4,  9,  and  16  times  this  length.     In  order  to  use  the 
seconds  pendulum  for  measuring  time,  it  is  only  necessary  to  con- 
nect with  it  a  mechanism  by  which  its  beats  may  be  recorded  and 
its  motion  maintained.    Such  a  mechanism  constitutes  a  common 
clock,  the  essential  parts  of  which  are  represented  in  Fig.  30. 


CHEMICAL  PHYSICS. 


The  toothed  wheel  R,  called  the  scape-wheel,  is  turned  by  a 
weight  or  spring,  either  directly,  as  in  the  figure,  or  through  the 
intervention  of  other  wheels.  The  revolution  of  the  scape-wheel 
is  regulated  by  means  of  a  peculiar  contrivance,  a  b,  called  the 

escapement,  which  oscillates  on  an  axis 
o  o'.  The  oscillations  are  communi- 
cated to  the  escapement  by  the  pen- 
dulum P,  through  the  forked  arm  of. 
When  the  pendulum  hangs  vertically, 
one  of  the  teeth  of  the  scape-wheel, 
cut  obliquely  for  the  purpose,  rests  on 
the  upper  side  of  the  hook  6,  and  the 
clock  remains  at  rest.  If  now  the 
pendulum  is  set  in  motion,  so  that 
the  hook  b  is  moved  from  the  wheel, 
the  tooth  which  rested  upon  it  is  set 
free,  and  the  wheel  begins  to  revolve  ; 
but  it  is  soon  arrested  by  the  hook  a, 
which  has  moved  up  to  the  wheel  as 
b  moved  from  it,  and  catches  on  its 
under  surface  the  tooth  immediately 
below.  As  the  pendulum  oscillates 
back  the  hook  a  moves  away,  the 
wheel  again  commences  to  revolve, 
but  is  arrested  a  moment  after  on  the 
opposite  side  by  the  hook  b,  which 
catches  the  tooth  next  to  the  one  it  held  before  ;  and  thus  contin- 
uously, so  that  each  oscillation  of  the  pendulum  allows  the  scape- 
wheel  to  move  forward  through  a  space  equal  to  one  half  of  one 
of  its  teeth.  If,  then,  the  wheel  has  thirty  teeth,  it  will  com- 
plete one  revolution  in  sixty  beats  of  the  pendulum,  moving  for- 
ward one  sixtieth  of  a  revolution  at  each  beat.  This  wheel  is 
the  one  on  whose  axis  the  second-hand  is  placed.  It  is  connected 
by  cogs  with  another  wheel,  which  is  made  to  occupy  sixty  times 
as  long  in  revolving,  and  this  carries  the  minute-hand ;  and  this  is 
connected  with  another  wheel,  which  revolves  in  twelve  times  the 
period,  and  carries  the  hour-hand.  Thus  the  second-hand  regis- 
ters the  beats  of  the  pendulum  up  to  sixty,  or  one  minute  ;  the 
minute-hand  registers  the  number  of  revolutions  of  the  second- 
hand up  to  sixty,  or  one  hour ;  and  the  hour-hand  registers  the 


Fig.  30. 


GENERAL  PROPERTIES  OF  MATTER.  73 

number  of  revolutions  of  the  minute-hand  up  to  twelve,  or  half 
a  day. 

If  the  pendulum  and  escapement  were  removed  from  a  clock, 
there  would  be  nothing  to  prevent  the  train  of  wheels  from  being 
turned  round  with  great  rapidity  by  the  weight  or  spring  acting 
on  it,  and  the  clock  would  speedily  run  down.  On  the  other 
hand,  were  there  not  some  means  of  communicating  to  the  pen- 
dulum occasional  impulses,  it  would  soon  be  brought  to  rest  by 
the  resistance  of  the  air  and  the  resistance  due  to  the  mode  of 
suspension.  To  prevent  this,  the  escapement  is  so  constructed  as 
to  give  a  very  slight  additional  impulse  to  the  pendulum  at  each 
oscillation.  The  ends  of  the  two  hooks,  a,  6,  are  cut  so  as  to  pre- 
sent to  the  teeth  of  the  scape-wheel  inclined  surfaces.  As  the 
tooth  of  the  wheel  leaves  one  of  these  hooks,  its  extremity 
slides  over  this  inclined  plane  with  a  considerable  force,  commu- 
nicated by  the  weight,  so  as  to  throw  the  escapement  forward 
with  a  slight  impulse  the  moment  the  tooth  is  set  free.  This  im- 
pulse is  communicated,  through  the  axis  o  o1  and  the  arm  o/,  to 
the  pendulum.  If  the  weight  is  increased,  the  force  with  which 
the  impulse  is  given  will  be  greater  ;  and  the  pendulum,  receiv- 
ing a  greater  impulse  at  each  oscillation,  will  swing  through  a 
greater  arc.  As  this  will  slightly  increase  the  time  of  each  oscil- 
lation (53),  the  addition  of  weight  will  make  the  clock  go  slower. 
The  change  of  rate  in  a  clock  caused  by  the  expansion  and  con- 
traction of  the  pendulum,  will  be  considered  in  the  chapter  on 
Heat. 

(57.)  Use  of  Pendulum  for  Measuring"  the  Force  of  Grav- 
ity. —  By  transposing,  we  obtain  from  equation  [30]  the  value 
of  #: 

e  =  i^;  [35.] 

from  which,  when  we  know  the  length  of  a  pendulum  which  os- 
cillates in  a  given  time,  T,  we  can  easily  calculate  the  value  of  g- 
for  the  place  of  experiment.  If,  in  the  last  equation,  we  place 
T=  1,  then  /  denotes  the  length  of  the  seconds  pendulum,  and 
we  obtain  for  the  value  of  g; 

ff  =  ln2.  [36.] 

In  order,  then,  to  measure  the  intensity  of  gravity  at  any  place,  we 
have  only  to  oscillate  a  pendulum  whose  virtual  length  is  known, 
7 


74  CHEMICAL   PHYSICS. 

and  observe  the  time  of  a  single  oscillation.  This  observation 
is  readily  made  by  counting  a  large  number  of  oscillations,  and 
observing  the  time  occupied  by  the  whole  number.  This  time, 
divided  by  the  number  of  oscillations,  gives  the  duration  of  a 
single  oscillation  with  great  accuracy,  because  any  error  we  may 
have  made  in  observing  the  time  is  thus  greatly  divided. 

By  this  method  Borda  and  Cassini,  in  1790,  measured  with 
.great  accuracy  the  intensity  of  gravity  at  the  Observatory  of 
Paris.  The  pendulum  which  they  used  consisted  of  a  sphere  of 
platinum,  suspended  to  a  knife-edge  by  means  of  a  fine  platinum 
wire.  The  knife-edge  rested  on  an  agate  plate,  and  the  whole 
pendulum  was  about  four  metres  long.  Instead  of  counting  di- 
rectly the  number  of  oscillations,  Borda  compared  the  motion  of 
his  pendulum  with  that  of  a  clock  placed  behind  it.  On  the  ball 
of  the  clock's  pendulum  a  vertical  mark  indicated  the  position  of  its 
axis,  and  a  small  telescope^  placed  a  few  metres  in  front,  enabled 
him  to  observe  when  the  wire  of  his  pendulum  exactly  coincided 
with  the  vertical  mark.  Starting  from  a  moment  when  the  two 
coincided,  he  observed  the  number  of  seconds  before  such  coin- 
cidence occurred  again  ;  and  knowing  this,  he  was  able  at  once  to 
calculate  the  number  of  oscillations  of  the  pendulum  which  oc- 
curred during  an  observed  number  of  seconds  by  the  clock.  Let 
v  be  the  number  of  oscillations  of  the  seconds  pendulum  between 
the  coincidences,  then  v  ±  2  will  be  the  number  of  oscillations 
of  the  experimental  pendulum  in  the  same  interval,  that  is,  in 

v  seconds,  and   will  be  the  number  in  one  second.    Hence, 

if  p  is  the  number  of  oscillations  of  the  pendulum,  and  t  the 
number  of  seconds  observed  by  the  clock,  we  shall  have 

j,-i*4£W<fc!2i  [ST.] 

V  V  L  J 

an  equation  by  which  we  can  calculate  the  number  of  oscillations 
in  a  given  time,  without  being  obliged  to  count  them.  In  these 
experiments,  the  pendulums  were  enclosed  in  glass  cases  to  pro- 
tect them  from  currents  of  air,  and  separated  from  each  other 
by  glass,  so  that  they  should  not  react  on  each  other  through 
this  fluid. 

As  the  amplitude  of  the  oscillations  is  not  infinitely  small,  but 
only  very  small,  in  such  experiments,  it  is  important  to  correct 
the  number  of  oscillations  observed  as  above,  and  substitute  for 


GENERAL   PROPERTIES   OF    MATTER.  75 

it  in  the  calculation  the  number  which  would  have  occurred  had 
the  amplitude  been  really  infinitely  small.  If  we  call  the  duration 
of  an  oscillation  which  is  infinitely  small  T,  and  that  of  one  which  is 

only  very  small  T',  we  have  from  [80]  and  [31]  T'=T(l  +  ^\ 

\  / 

where  a  is  equal  to  one  half  the  arc  which  measures  the  am- 
plitude. Now,  as  the  number  of  oscillations  in  a  given  time  is 
inversely  as  their  duration,  we  have  T'  :  T  =  n  :  n' ;  and  hence, 

[38.] 

where  n  is  the  required  number  of  oscillations,  and  n'  the  ob- 
served number.  The  amplitude  is  measured  by  means  of  a  hori- 
zontal scale  placed  behind  the  pendulum,  and,  as  it  sensibly 
diminishes  during  the  experiment,  we  take  for  the  value  of  a 
in  [38]  the  mean  amplitude  during  the  time  of  observation. 

The  value  of  g  found  by  the  above  formulae  is  a  little  too 
small,  owing  to  the  fact  that  the  force  of  gravity  acting  on  the 
mass  of  the  pendulum  is  balanced  to  a  slight  degree  by  the  buoy- 
ancy of  the  air,  and  it  is  necessary  to  correct  the  result  jbr  this 
cause  of  error.  The  principles  from  which  this  correction  may 
be  calculated  will  be  explained  in  Chapter  III.  It  will  there  be 
shown  that  a  body  is  buoyed  up  in  a  fluid  by  a  weight  equal  to 
the  weight  of  fluid  which  it  displaces.  Hence,  if  W  represents 
the  weight  of  a  body  in  a  vacuum,  and  w  the  weight  of  air  it 
displaces  at  a  given  temperature  and  under  a  given  pressure, 
then  W —  w  is  the  weight  of  the  body  in  the  air  at  this  temper- 
ature and  pressure.  If  we  put  8  =  -^ ,  the  small  fraction 

which  represents  the  ratio  of  the  weight  of  the  air  to  the  weight 
of  the  body,  we  shall  easily  obtain 


W—  w=W—  8  W=  W(\  —  8). 

Representing  the  weight  of  the  body  in  air  ( W  —  w)  by 
W1)  we  obtain,  for  the  relation  between  the  weight  of  a  body 
in  air  and  in  a  vacuum,  the  equation  W1  =  W (1 —  8).  It 
will  be  shown,  in  one  of  the  following  sections,  that  the  weights 
of  the  same  body  under  different  circumstances  are  proportional 

W1         &' 

to  the  intensities  of  gravity,  and  hence  that  -^  =  —  ;  substi- 
tuting this,  we  have,  for  the  relation  between  the  actual  intensity 


76 


CHEMICAL   PHYSICS. 


of  gravity,  g-,  and  the  apparent  intensity  when  the  experiments 
are  inade  in  air,  g-', 

"     "'  ''"''!1  '' 


It  appears,  however,  from  the  experiments  of  Bessel,  which  were 
confirmed  by  the  calculations  of  Poisson,  that  the  loss  of  weight 
which  the  pendulum  suffers  in  air  is  much  greater  when  it  is  in 
motion  than  when  at  rest,  so  that  a  still  further  correction  must 
be  made  to  eliminate  this  source  of  error  ;  but  for  the  details  of 
this  and  of  the  other  corrections  which  are  required,  we  must 
refer  the  student  to  Bessel'  s  original  Memoirs. 

(58.)  Value  of  g-.  —  By  the  method  described  in  the  last  sec- 
tion, Borda  and  Cassini  found  for  the  intensity  of  gravity  at  the 
Observatory  of  Paris  the  number  g  —  9.8088.  This  value  has 
since  been  redetermined  by  Biot,  Arago,  Mathieu,  and  Bouvard, 
who  used  the  same  process,  except  that  they  employed  a  shorter 
pendulum,  and  obtained  almost  absolutely  the  same  results. 
Bessel,  by  correcting  for  the  loss  of  weight  in  the  air  due  to  the 
motion  of  the  pendulum,  found  for  the  value  of  the  intensity  of 
gravity  at  Paris,  ,  T' 

g  =  9.8096, 

which  is  probably  the  most  accurate. 

The  value  of  g  has  also  been  determined  at  different  points  on 
the  earth's  surface,  with  more  or  less  accuracy,  by  different  ob- 
servers. Some  of  these  results  are  collected  in  the  following 
table,  which  has  been  taken  from  Daguin's  Traite  de  Physique. 
The  length  of  the  seconds  pendulum  is  easily  calculated  from  the 
values  of  g-  by  means  of  equation  [36]  . 


Stations. 

Latitudes. 

Value  of  g. 

Seconds 
Pendulum. 

Observers. 

Spitsbergen, 

79  49  58k. 

9.83141 

o!?9613 

Sabine. 

Stockholm, 

59  20  34 

9.81946 

0.99492 

Svanberg. 

Konigsberg, 

54  42   12 

9.81443 

0.99441 

Bessel. 

Paris, 

48  50  14 

9.80979 

0  99394 

Biot,  etc. 

He  Rawak, 

0     1  34S. 

9  78206 

099113 

Freycinet. 

He  de  France, 

20     9  23 

978917 

0.99185 

Duperrey. 

Cape  of  Good  Hope, 

33  55  15 

9.79696 

0.99264 

Freycinet. 

Cape  Horn, 

55  51  20 

9.81650 

099462 

Foster. 

New  Shetland, 

62  56  11 

9.82253 

0.99523 

Foster. 

It  appears  from  this  table,  that  the  intensity  of  the  force  of 
gravity  gradually  increases  with  the  latitude  as  we  go  from  the 


GENERAL  PROPERTIES  OP  MATTER. 


77 


equator  towards  either  pole.  In  general,  the  value  of  g-  for  any 
latitude  can  be  determined  sufficiently  near  for  all  purposes  of 
Physics,  by  means  of  the  formula, 

s  =  9.80604  (1  —  0.0025935  .  cos  2  A),          [40.] 

in  which  A  is  the  latitude  of  the  place,  and  9.80604  the  value 
of  g  at  the  latitude  of  45°.  By  substituting  for  A,  0°  or  90°, 
we  obtain  at  the  equator  g  =  9.780642,  and  at  the  poles  g  = 
9.83146.  It  does  not  appear,  however,  that  the  intensity  of 
gravity  is  rigorously  the  same  at  all  points  on  the  same  parallel  of 
latitude,  or  at  corresponding  points  in  the  northern  and  southern 
hemispheres.  Irregularities  in  this  respect  were  noticed  in  the 
measurement  of  the  arc  of  the  meridian  in  France,  and  also  by 
Lacaille  at  the  Cape  of  Good  Hope. 

These  variations  in  the  intensity  of  gravity  on  the  earth's  sur- 
face depend  mainly  on  two  causes  ;  first,  on  the  centrifugal 
force  due  to  the  earth's  revolution  on  its  axis,  which  is  at  its 
maximum  on  the  equator,  and  gradually  diminishes  towards  the 
poles,  where  it  disappears  ;  secondly,  on  the  spheroidal  character 
of  the  earth,  in  consequence  of  which  a  body  at  the  poles  is  more 
strongly  attracted  by  the  mass  of  the  earth  than  it  is  at  the 
equator.  We  will  consider  the  effect  of  each  of  these  causes 
in  turn. 

(59.)  Centrifugal  and  Centripetal  Force.  —  It  has  already 
been  stated  (25),  that  a  curvilinear  motion  is  the  resultant  of  two 
motions  which  obey  different 
laws.  Thus,  in  Fig.  31,  the 
parabolic  motion  of  a  ball  shot 
horizontally  from  a  fort  is  the 
resultant  of  a  uniform  motion 
in  the  direction  of  a  m,  and  of 
a  uniformly  accelerated  motion 
in  the  direction  of  an.  We 
also  know  that  this  motion  is 
the  result  of  two  forces,  one 
which  has  acted,  and  the  other 
which  is  still  acting,  on  the 
ball  ;  first,  the  projectile  force 
of  gunpowder,  which  has  given 
to  the  ball  a  certain  momentum,  Tlft),  in  virtue  of  which  it  will 


78  CHEMICAL  PHYSICS. 

continue  to  move  until  its  motion  is  arrested  by  an  equivalent 
force  acting  for  an  equivalent  time  in  the  opposite  direction; 
second,  the  force  of  gravity,  a  constant  force  both  in  direction 
and  intensity.  Compare  (27)  and  (29). 

Let  us  now  consider  the  conditions  of  Fig.  31  to  be  so  far 
changed,  that  the  constant  force  no  longer  acts  in  directions  par- 
allel to  itself,  but  in  directions  which  all  converge  to  one  point. 

Such  a  force  may  be  regarded  as 
an  attractive  force  emanating 
from  this  point,  and  is  there- 
fore frequently  called  a  cen- 
tral force.  Let  us  then  suppose 
that  in  Fig.  32  we  have,  as  be- 
fore, a  ball  moving  with  a  cer- 
tain momentum  in  the  direction 
a  m,  communicated  to  it  origi- 
nally by  a  force  acting  for  a 
given  time  with  a  given  intensi- 
ty, but  which  has  ceased  to  act. 
Let  us  also  suppose  that  the 

same  ball  is  attracted  towards  a  given  point,  (7,  by  a  force  con- 
stant in  intensity.  What  will  be  the  resulting  motion  of  the  ball  ? 
Let  t)  be  the  velocity  in  the  direction  a  m,  and  u  be  the  accelera- 
tion of  the  given  force.  In  a  small  fraction  of  a  second,  which 
we  may  take  as  small  as  we  please,  the  ball  will  move  in  the  di- 
rection a  m  over  a  space  a  /3,  equal  to  — ,  where  n  is  the  number 

of  intervals  into  which  the  unit  of  time  has  been  divided.  In  the 
same  time  it  will  move  in  the  direction  a  C  over  a  space  a  b,  equal 

to  J  — 2-  [5] .     The  resultant  of  these  motions,  on  the  principle 

of  (25),  will  be  a  curved  line  passing  through  the  point  P,  which 
can  be  found  by  completing  the  parallelogram  a  ft  Pb.  Arrived 
at  the  point  P,  the  direction  of  its  original  motion  has  so  far 
changed,  that,  if  the  central  attraction  ceased  to  act  at  that  mo- 
ment, the  original  momentum  would  cause  it  to  move  in  the 
direction  P  n,  tangent  to  the  curve  at  the  point  P,  which,  accord- 
ing to  the  principle  of  geometry,  may  be  regarded  as  the  contin- 
uation of  the  direction  in  which  it  was  moving  at  the  instant. 
The  central  force,  however,  does  not  cease  to  act,  and  during  the 


GENERAL   PROPERTIES   OP   MATTER.  79 

next  small  interval  of  time  the  same  thing  is  repeated.  In  virtue 
of  the  momentum,  the  ball  will  pass  over  the  distance  P^,  equal 

to  — ,  and  in  virtue  of  the  central  force  will  move   towards  the 

n  t) 

centre  by  an    amount,  PC,  equal  to  J  — ^.      The  resultant  of 

these  motions  will  be  a  second  curved  line,  similar  to  the  first, 
and  a  continuation  of  it,  passing  through  Q.  The  same  thing 
will  be  again  repeated  every  succeeding  interval  of  time,  and 
thus  the  motion  resulting  from  the  two  forces  will  be  a  curved 
line  bending  towards  the  central  point  C,  the  central  force  con- 
stantly changing  the  direction  of  the  original  momentum.  It  is 
easy  to  see,  that,  with  a  certain  relation  between  the  momentum 
and  the  intensity  of  the  central  force,  the  distance  of  the  ball 
from  the  centre  would  keep  always  the  same,  and  the  path  of  the. 
ball  would  be  a  circle.  If  the  central  force  were  greater  rela- 
tively to  the  momentum  than  this,  then  the  ball  would  be  drawn 
each  second  nearer  to  the  centre,  and  the  radius  of  the  curvilinear 
path  would  as  regularly  shorten  ;  if  the  central  force  were  relative- 
ly less,  the  ball  would  evidently  recede  from  the  centre,  and  the 
radius  of  its  path  would  lengthen.  If,  however,  we  suppose  that 
the  central  force  diminishes  as  the  body  recedes  from  the  centre, 
and  increases  as  it  approaches  it,  so  that  the  intensity  is  always 
inversely  as  the  square  of  the  distance,  then  it  can  easily  be 
proved  mathematically  that  the  path  of  the  ball  will  return  into 
itself,  and  will  be  an  ellipse.  We  shall  have  only  to  deal  with  that 
particular  case  where  the  path  is  a  circle.  In  this  case,  the 
ball  remaining  constantly  at  the  same  distance  from  the  centre, 
the  whole  central  force  is  expended  in  changing  the  direction  of 
the  original  motion,  and  is  evidently  just  balanced  every  instant 
by  the  inertia  of  the  mass  of  the  ball. 

The  force  which  arises  from  the  inertia  of  the  ball  is  called 
the  centrifugal  force,  while  the  central  force  by  which  it  is  re- 
strained and  kept  on  the  circumference  is  called  the  centripetal 
force.  The  term  centrifugal  force  is  very  liable  to  be  misunder- 
stood. It  is  frequently  supposed  to  imply  a  force  which,  acting 
alone,  would  cause  the  ball  to  fly  directly  from  the  centre  ;  but 
we  must  bear  in  mind  that  the  centrifugal  force  cannot  act  alone, 
since  it  has  no  independent  existence.  When  the  centripetal 
force  ceases  to  act,  then  the  centrifugal  force  ceases  to  exist,  and 
the  momentum  of  the  moving  body  tends  to  carry  it  forward  in 


80  CHEMICAL  PHYSICS. 

the  straight  line  tangent  to  the  circle  at  the  point  at  which 
the  centripetal  force  ceases  to  draw  it  from  the  circumference. 
The  body  will,  it  is  true,  then  recede  from  the  centre ;  but  it 
will  only  do  so  by  passing  along  the  tangent,  the  distance  of 
which  from  the  centre  is  continually  increasing,  and  not  by 
flying  in  a  direction  opposite  to  the  centre  of  attraction.  Its 
action,  however,  will  be  to  cause  the  particles  of  a  body  in  rapid 
revolution  to  take  their  places  at  the  greatest  possible  distance 
from  the  centre. 

The  measure  of  the  centrifugal  force  in  Fig.  32  is  obviously 
the  amount  of  restraint  required  to  keep  the  ball  on  the  circum- 
ference of  the  circle,  and  it  is  measured  by  the  intensity  of  the 
centripetal  force,  which,  on  our  supposition,  just  balances  it. 
Calling,  then,  the  centrifugal  force  (£,  the  acceleration  of  the  cen- 
tripetal force  t),  and  the  mass  of  the  ball  M,  we  have,  by  [14], 

C  =  ^Tt).  [41.] 

Since,  however,  we  only  know,  as  a  general  rule,  the  velocity  of 
the  motion  of  a  ball  on  the  circle  and  the  radius  of  the  circle,  it 
is  important  to  obtain,  if  possible,  an  expression  of  the  intensity 
of  the  centrifugal  force  in  terms  of  these  two  quantities.  This 
can  easily  be  obtained  by  the  principles  of  geometry. 

Let  a  P,  Fig.  32,  be  the  arc  described  by  the  ball  in  an  interval 
of  time  so  small  that  the  arc  may  be  considered  as  equal  to  the 

chord.  Call  this  interval  —  of  a  second,  where  n  may  be  as  large 
as  you  please.  Represent  by  t)  the  velocity  of  the  ball  on  the 
circumference ;  then  —  is  equal  to  the  length  of  the  arc  a  P. 

Represent  next,  by  tJ,  the  unknown  acceleration  of  the  cen- 
tripetal force  ;  then  the  distance  a  b,  through  which  the  ball 

would  move  under  the  influence  of  this  force  alone  in  —  of  a 

u  n 

second,  will  be,  by  [5],  \  —%.     We  have,  by  geometry,  a  b  :  a  P  = 

a  P :  aD\  from  this  proportion,  by  substituting  the  above  val- 
ues, we  obtain  £  -^  :  —  =  —  :2R,  or  t)==-^-;  and  substi- 
tuting this  value  oft)  in  [41],  we  obtain,  for  the  intensity  of 
the  centrifugal  force, 

OT  =  M  -.  [42.] 


GENERAL  PROPERTIES  OF  MATTER.  81 

We  can  give  this  expression  another  form,  which  is  more  con- 
venient for  use.  The  expression  t),  which  represents  the  velocity 
of  the  ball,  denotes  the  number  of  metres  which  it  passes  over  in 
one  second.  If,  then,  we  represent  by  T  the  number  of  seconds 
occupied  by  the  ball  in  going  once  round  the  circle  (its  period  of 
revolution),  and  by  2  R  yr,  as  usual,  the  circumference  of  the 

circle,  we  shall  have  t)  =  —  ^-^.      Substituting   this   value    in 
[42],  we  obtain 


which  is  an  expression  for  the  intensity  of  the  centrifugal  force 
in  terms  of  the  time  of  revolution,  the  radius  of  the  circle  de- 
scribed, and  the  mass  of  the  body. 

If  a  weight  is  whirled  round  at  the  end  of  a  string,  the  action 
of  the  centrifugal  force  is  shown  in  the  tension  of  the  string,  and 
the  only  difference  between  this  and  the  previous  example  is,  that 
the  resistance  of  the  string  takes  the  place  of  the  attractive  force. 
If  the  string  breaks,  the  weight  flies  off  on  a  line  which  is  a  tangent 
to  the  circle  which  the  weight  had  described.  In  like  manner, 
the  particles  of  water  on  the  rim  of  a  revolving  grindstone  tend 
to  fly  off  from  the  surface,  but  are  kept  in  place  by  the  adhesive 
attraction  of  the  stone  ;  when,  however,  the  revolution  becomes 
rapid,  the  centrifugal  force  overcomes  the  adhesion,  and  the 
water  is  thrown  off  in  lines  which  are  tangent  to  the  cylindrical 
surface.  Not  unfrequently,  when  the  revolution  is  very  rapid, 
the  centrifugal  force  overcomes  the  cohesion  between  the  parti- 
cles of  the  stone  itself,  and  serious  accidents  have  resulted  from 
this  cause. 

Since  the  earth  is  revolving  rapidly  on  its  axis,  we  should  ex- 
pect to  find,  especially  at  the  equator,  a  manifestation  of  this 
same  force  ;  and  in  fact  we  do.  All  bodies  on  the  globe  not  sit- 
uated exactly  at  the  poles  tend  to  fly  off  from  its  surface  on  lines 
tangent  to  the  parallels  of  latitude  on  which  they  revolve,  and 
are  only  prevented  by  the  force  of  gravity.  Were  the  rapidity  of 
the  earth's  revolution  more  than  seventeen  times  increased,  the 
force  of  gravity  would  not  be  sufficient  to  restrain  bodies  on 
the  equator  from  obeying  this  tendency.  As  it  is,  however,  the 
centrifugal  force  only  acts  to  diminish  the  intensity  of  the  force 
of  gravity  ;  and  this  action,  which  is  greatest  at  the  equator, 


82  CHEMICAL  PHYSICS. 

gradually  diminishes  as  we  go  towards  the  poles,  where  it  is 
nothing. 

We  can  easily  find  the  intensity  of  the  centrifugal  force  at  the 
equator,  by  substituting  in  [43] ,  for  J£,  the  value  of  the  equato- 
rial radius,  6,377,398  metres,  and  for  T  the  number  of  seconds 
in  a  day,  86,400.  The  value  of  the  centrifugal  force  then  be- 
comes, for  the  mass  M, 

C  =  M  x  0.03373, 

and  for  the  units  of  mass, 

C  =  0.03373  (units  of  force).  [44.] 

The  apparent  value  of  g  at  the  equator  is  less  than  its  true 
value  by  exactly  the  amount  of  this  force.  Hence  the  full  value 
of  the  earth's  attraction  at  the  equator  is 

9.78062  +  0.03373  =  9.81435. 

For  any  other  latitude,  the  value  of  the  centrifugal  force  is 
easily  found  by  assuming  that  the  earth  is  a  perfect  sphere.  In 
Fig.  33,  let  m  be  the  position  of  the  body 
on  the  globe ;  then  mOB  =  AmO  = 
amfis  the  latitude  of  the  place,  which 
we  will  indicate  by  A ;  also  A  m  =  R  cos  A 
is  the  radius  of  the  parallel  of  latitude  on 
which  the  body  m  is  revolving.  The  value 
of  the  centrifugal  force,  in  terms  of  the  lat- 
itude, will  be  found  by  substituting  this 
Fig  ^  last  value  for  R  in  [43] .  Making  this  sub- 

stitution, and  using  for  R  the  mean  radius  of  the  globe,  we  obtain, 
for  the  value  of  the  centrifugal  force,  mf  —  0.03367  cos  A.  This, 
however,  is  the  value  of  the  centrifugal  force  acting  in  the  direc- 
tion mf.  The  force  of  gravity  acts  in  the  direction  m  O,  and  in 
order  to  ascertain  to  what  extent  the  force  of  gravity  is  influenced 
by  the  centrifugal  force,  we  must  decompose  the  last  into  two  com- 
ponents. Let  mf  represent  the  intensity  of  the  centrifugal  force, 
then  m  a  and  m  b  will  represent  the  intensities  of  two  components  ; 
the  first  of  which,  being  opposite  in  direction,  will  tend  to  neutral- 
ize the  force  of  gravity,  while  the  second,  being  perpendicular  in 
direction,  will  produce  no  effect  on  it.  The  value  of  the  compo- 
nent maisma  =  mf  cos  A ;  and  substituting  for  mf  its  value 
as  above,  and  representing  always  by  c  that  component  of  the 


GENERAL  PROPERTIES  OP  MATTER.  83 

centrifugal  force  which  is  opposite  in  direction  to  gravity,  we 
have 

C  =  0.03367  cos2  A.  [45.] 

We  can  easily  find  how  rapid  the  rotation  of  the  globe  must 
be,  in  order  that  the  centrifugal  force  at  the  equator  should  just 
balance  the  attractive  force  of  gravity.  For  this  purpose  we 
have  only  to  substitute  for  <E,  in  [43],  the  value  of  the  attractive 
force  just  found,  and  calculate  the  corresponding  value  of  T,  which 
will  be  found  to  be  5,065  seconds.  Hence,  if  the  earth  revolved 
once  in  5,065  seconds,  or  in  lh-  24m-  25'-, —  that  is,  a  little  more 
than  seventeen  times  faster  than  it  does,  —  the  force  of  gravity 
at  the  equator  would  be  just  balanced  by  the  centrifugal  force. 

(60.)  The  Spheroidal  Figure  of  the  Earth.  — The  second 
cause,  mentioned  in  (58),  of  the  variation  of  gravity  with  the 
latitude,  is  the  spheroidal  figure  of  the  earth,  in  consequence 
of  which  a  body  at  the  poles  is  more  strongly  attracted  by  gravity 
than  at  the  equator.  The  form  of  the  earth,  as  has  been  before 
intimated,  is  not  a  perfect  sphere.  It  is  flattened  at  the  poles, 
and  its  figure  is  best  described  as  an  oblate  ellipsoid  or  spheroid. 
A  section  of  the  earth  through  a  meridian  circle  is  therefore  not 
a  circle,  but  an  ellipse  of  very  small  eccentricity,  and  the  figure 
of  the  earth  may  be  conceived  as  generated  by  the  revolution  of 
such  an  ellipse  round  its  shorter  diameter  as  an  axis.  The  flat- 
tening at  the  poles  amounts  in  round  numbers  to  about  7 fa  of 
the  equatorial  radius  ;  in  other  words,  the  polar  radius  is  about 
•3^  shorter  than  the  equatorial.  This  deviation  from  a  true 
sphere  is  so  small,  that  it  could  not  be  detected  by  the  eye  in 
a  common  globe,  but  in  the  earth  it  nevertheless  amounts  to 
over  thirteen  English  miles.  The  dimensions  of  the  earth  are 
accurately  as  follows :  *  — 

Volume  of  the  earth,     1,082,842,000,000.000  cubic  kilometres. 
Surface  of  the  earth,  509,961,000.000  square       " 

Length  of  a  quadrant,  10,000.857  kilometres. 

Equatorial  radius,  6,377.398         " 

Mean  radius  (lat.  45°),  6,366.738         " 

Polar  radius,  6,356.079         " 

Difference  between  the  equa- 
torial and  polar  radius,  21.319         " 

*  These  data  are  all  taken  from  the  table  of  constants  in  Kohler's  "  Logarithmisch- 
Trigonometrisches  Handbuch." 


84  CHEMICAL   PHYSICS. 

Were  the  earth  perfectly  spherical,  a  plumb-line  at  any  point 
on  its  surface  would  point  exactly  to  its  centre,  and  the  centre  of 
figure  would  then  be  also  the  centre  of  attraction.  The  earth 
being  spheroidal,  the  phenomena  of  gravity  upon  its  surface  be- 
come less  simple.  The  plumb-line  does  not  point  exactly  to  the 
centre  of  the  earth,  except  at  the  equator  or  at  the  poles,  and, 
moreover,  there  is  no  fixed  centre  of  gravity.  In  Fig.  34,  the 

line  A  P  is  supposed  to  represent 
a  quadrant  of  a  meridian,  of  which 
O  P  is  the  polar,  and  O  A  the  equa- 
torial radius.  Starting  from  the 
equator,  let  us  take  stations  only 
one  degree  distant  from  each  other 
on  this  meridian,  and  at  each  sta- 
tion continue  the  direction  of  the 
plumb-line  until  it  intersects  the 
plumb-line  similarly  produced  at 
the  previous  station.  If,  in  the  fig- 
ure By  C,  and  D  are  three  such 

points,  then  &,  6,  and  c  are  the  three  points  of  intersection,  and 
it  is  easy  to  see,  from  the  figure,  that  the  ninety  points  of  inter- 
section, which  would  be  obtained  by  producing  the  plumb-lines 
from  all  the  ninety  stations,  would  form  when  united  a  curved 
line,  a  b  c  p.  By  making  the  number  of  stations  infinite,  we 
should  of  course  have  an  infinite  number  of  points  of  intersec- 
tion ;  and  for  every  point  on  the  quadrant  A  P,  there  would  be 
a  corresponding  point  on  the  curve  a  p.  The  points  #,  6,  c,  etc. 
are  termed  in  geometry  centres  of  curvature ;  the  lines  A  a, 
B  b.>  C  c,  etc.  are  called  radii  of  curvature  ;  and  the  curve  a  p 
is  called  the  evolute  of  the  curve  A  P.  Now  it  can  be  easily  seen 
that  what  we  call  the  centre  of  attraction  of  the  earth  for  any 
point  on  the  quadrant  A  P  is  the  corresponding  centre  of  curva- 
ture on  the  evolute  a  p.  At  A,  for  example,  the  attraction  of 
the  earth  acts  as  if  it  originated  at  the  point  a  ;  at  j5,  as  if  it 
originated  at  the  point  6,  etc.  The  intensity  of  the  force  which 
resides  at  these  different  centres  is  not,  however,  the  same  ;  the 
intensity  at  a,  for  example,  is  less  than  at  5,  at  b  less  than  at  <?, 
etc.  It  gradually  increases  at  the  different  points  on  the  evolute 
from  a  to  p. 

What  is  true  of  the  quadrant  A  P  must  be  true  of  every 


GENERAL   PROPERTIES   OP   MATTER.  85 

quadrant ;  hence,  if  the  evolute  a  p  is  revolved  on  its  axis,  O  p, 
the  surface  generated  would  be  the  locus  of  all  the  centres  of 
attraction  for  points  on  the  upper  hemisphere  of  the  globe ;  and  if 
the  evolute  a  p'  is  revolved,  the  surface  generated  would  be  the 
locus  of  all  the  centres  of  attraction  for  points  on  the  lower  hemi- 
sphere of  the  globe. 

It  is  evident,  from  the  above,  that  a  body  placed  at  the  equa- 
tor, and  a  similar  one  placed  at  the  pole  of  the  globe,  stand  in 
different  relations  to  its  mass  as  a  whole,  and  we  should  natu- 
rallj  expect  that  they  would  be  attracted  with  different  degrees 
of  force.  Newton,  Maclaurin,  Clairaut,  and  many  other  eminent 
geometers,  have  calculated  how  great  the  variation  of  gravity, 
owing  to  the  elliptic  form  of  the  earth  alone,  ought  to  be,  in  going 
from  the  equator  to  the  pole,  and  the  results  of  their  calcula- 
tions coincide  almost  precisely  with  those  of  observation  given 
above. 

It  has  also  been  proved  by  the  same  mathematicians,  that  the 
actual  form  of  the  earth  is  almost  precisely  that  which  would  re- 
sult from  the  revolution  of  a  liquid  mass  of  the  same  volume  and 
density  once  in  twenty-four  hours ;  and  since  we  have  every  reason 
to  believe  that  the  globe  was  once  fluid,  and  that  it  is  even  so 
now,  with  the  exception  of  a  comparatively  thin  crust  on  its  sur- 
face, it  follows  that  the  cause  of  the  variation  of  gravity  just 
considered  is  itself  an  indirect  result  of  the  centrifugal  force. 

(61.)  Variation  of  the  Intensity  of  Gravity  as  we  rise  above 
the  Surface  of  the  Earth.  —  The  law  by  which  the  intensity  of 
gravity  varies  with  the  distance  from  the  centre  of  force,  can  be 
discovered  by  studying  the  effect  of  the  earth's  attraction  on  the 
moon,  as  compared  with  its  effect  on  bodies  near  its  surface.  The 
mean  distance  of  the  moon  from  the  centre  of  the  earth,  is  about 
sixty  times  the  earth's  equatorial  radius,  and  it  revolves  round  the 
earth,  in  an  orbit  which  is  very  nearly  circular,  in  27.322  days. 
By  (59),  it  follows  that  the  intensity  of  the  earth's  attraction  at 
the  moon  is  just  equal  to  the  centrifugal  force,  and  it  can  therefore 
be  calculated  by  substituting  in  [43]  the  values  of  R  and  T  just 
given.  Making  these  substitutions,  we  obtain,  for  the  value  of  the 
earth's  attraction  on  the  moon,  where  M  equals  the  mass  of  the 
moon,  G  =  Mx  0.0027.  For  the  unit  of  mass,  then,  the  intensity 
of  the  earth's  attraction  at  the  distance  of  the  moon  is  g= 0.0027. 
The  intensity  of  the  earth's  attraction  for  bodies  on  the  equator 
8 


86  CHEMICAL   PHYSICS. 

is,  as  we  have  seen,  g-  =  9.7806,  which  is  about  3,600  times  greater 
than  0.002T.  For  bodies  as  distant  as  the  moon,  we  may  consider 
the  attraction  of  the  globe  as  concentrated  at  its  centre  of  figure, 
and  hence  we  may  regard  the  moon  as  about  sixty  times  as  distant 
from  the  centre  of  attraction  as  a  body  on  the  equator.  At  sixty 
times  the  distance,  then,  the  force  is  3600  (=  602)  times  less  ; 
that  is,  the  intensity  of  the  force  of  gravity  varies  inversely  with 
the  square  of  the  distance  from  the  centre  of  attraction.  Repre- 
senting, then,  by  g  and  g'  the  intensity  of  gravity  at  the  distances 
R  and  R',  we  have  always  the  proportion, 

g-  :  g>  =  R>*  :  R*.  [46.] 

It  follows  from  the  above  discussion,  that  the  intensity  of 
gravity  must  vary  at  different  heights  above  the  sea-level  on 
the  surface  of  the  earth.  The  amount  of  this  variation  can 
easily  be  calculated  by  means  of  the  above  proportion.  Repre- 
senting by  g-  the  intensity  of  gravity  at  the  sea-level,  by  g'  the 
intensity  at  an  elevation,  A,  and  by  R  the  radius  of  the  earth, 
we  have,  from  [46],  neglecting  the  variation  in  the  centrifugal 
force  at  the  two  heights, 


g  :  g'  =  (12  +  A)2  :  #2,     and    g  =  g>  .     [47.] 

When  h  =  1000  m.,  we  have  from  [47],  g  =  g1  1.0003.  The 
amount  of  variation  is  therefore  perceptible  at  any  considerable 
elevation  above  the  sea-level.  Hence,  in  studying  the  variation  of 
the  intensity  of  gravity  on  the  surface  of  the  earth,  it  is  impor- 
tant to  reduce  the  results  of  observations  at  different  elevations 
to  the  sea-level  before  comparing  them.  This  can  always  be  done 
by  [47]  ,  when  the  elevation  is  known. 

(62.)  Law  of  Gravitation.  —  We  proved,  in  (49),  that  the 
intensity  of  the  force  of  gravitation  is  directly  proportional  to 
the  quantity  of  matter  (the  mass)  on  which  it  acts,  and  in  the 
last  section  we  have  shown  that  the  intensity  of  the  force  of  grav- 
itation is  inversely  proportional  to  the  square  of  the  distance  of 
the  masses,  on  which  it  acts,  from  the  centre  of  attraction.  By 
combining  the  two,  we  have  the  well-known  law  of  gravitation, 
which  is  expressed  in  the  following  terms  :  —  All  masses  of  mat- 
ter attract  one  another  with  forces  directly  proportional  to  the 
quantity  of  matter  contained  in  each,  and  inversely  proportional 
to  the  squares  of  their  distances  from  each  other. 


GENERAL  PROPERTIES  OF  MATTER.  87 

This  law  was  discovered  in  1666  by  Sir  Isaac  Newton,  who, 
while  reflecting  on  the  power  which  causes  the  fall  of  bodies  to 
the  earth,  and  considering  that  this  power  is  not  sensibly  dimin- 
ished, even  at  the  top  of  the  highest  mountains,  conceived  that  it 
might  extend  far  beyond  the  limits  of  the  atmosphere,  and  even 
exert  its  influence  through  all  space.  It  may  be,  he  thought,  this 
very  force  by  which  the  moon  is  retained  in  her  orbit  round  the 
earth,  and  the  whole  planetary  system  round  the  sun.  In  order 
to  verify  his'  conjecture,  he  calculated,  on  the  same  principle  used 
in  the  last  section,  the  attraction  of  the  earth  on  the  moon,  as- 
suming that  the  force  must  diminish  in  the  inverse  ratio  of  the 
square  of  the  distance,  —  an  assumption  to  which  he  was  led  by 
the  relation,  previously  discovered  by  Kepler,  between  the  times 
of  revolution  of  the  planets  and  their  distances  from  the  sun. 
The  result,  at  first,  did  not  answer  his  expectations,  because  he 
had  used  in  the  calculation  a  value  of  the  earth's  radius,  and 
hence  also  of  the  moon's  distance,  which  was  much  too  small, 
and  he  therefore  rejected  the  hypothesis  as  not  substantiated. 
Several  years  later,  Picard  measured,  with  great  accuracy  for  the 
times,  an  arc  of  the  meridian  in  France ;  and  from  his  measure- 
ment it  appeared  that  the  radius  of  the  globe  was  nearly  one  sev- 
enth greater  than  had  previously  been  supposed.  Furnished  with 
these  new  data,  Newton  resumed  his  calculations  with  complete 
success,  and  in  1687  published  his  great  work,  the  Principia,  in 
which  the  consequences  of  this  great  law  were  developed  as  far 
as  the  astronomical  and  mathematical  knowledge  of  the  times 
would  permit. 

(63.)  Absolute  Weight.  —  When  a  body  is  not  free  to  fall,  the 
force  which  gravity  exerts  upon  it  is  expended  in  pressure  against 
its  support.  This  pressure  is  called  absolute  weight.  The  abso- 
lute weight  of  a  book,  for  example,  is  the  pressure  which  it  exerts 
against  the  table  on  which  it  rests.  It  is  evident  that  this  pressure 
is  equal  to  the  intensity  of  the  force  with  which  the  book  is  attract- 
ed by  the  earth.  The  intensity  of  the  force  which  gravity  exerts  on 
a  given  mass  of  matter  we  have  represented  by  G  (49).  If,  then, 
we  represent  the  pressure  caused  by  this  force,  or  the  absolute 
weight  of  the  same  mass  of  matter,  by  tO ,  we  have  to  =  G.  Hence, 
we  can  substitute  to  for  G  in  [26]  and  [27] ,  and  shall  then  have 

to=3f.£-,  [48.] 

and 

to  :  to7  =  31 :  M'.  [49.] 


88  CHEMICAL   PHYSICS. 

In  these  formulae,  to  represents  weight  or  pressure  ;  while  in 
[26]  and  [27]  G  represents  the  intensity  of  the  force  which  is 
the  cause  of  the  pressure.  In  this  work,  to  always  stands  for  a 
certain  number  of  grammes,  and  G  for  a  certain  number  of  units 
of  force.  For  example,  let  us  suppose  that  the  quantity  of  mat- 
ter in  the  book  just  referred  to  is  equal  to  50  units  of  mass ;  we 
should  then  know,  from  [26],  that  the  intensity  of  the  force  ex- 
erted by  gravity  upon  it  was  equal  to  490  units  of  force,  and, 
from  [48],  that  its  weight  was  equal  to  490  grammes.  In  the 
first  case,  G  =  50  X  9.8  =  490  units  of  force.  In  the  second 
case,  to  =  50  X  9.8  =  490  grammes.  The  numbers  in  the  two 
cases  are  precisely  the  same,  but  they  signify  different  kinds  of 
units.  The  identity  of  the  numbers  arises  from  the  fact  that  the 
unit  of  force  is  equivalent  to  a  pressure  of  one  gramme,  so  that 
the  difference  between  G  and  to  is  rather  nominal  than  real. 

It  follows  from  [49],  that  the  weights  of  bodies  are  propor- 
tional to  the  quantities  of  matter  which  they  contain ;  in  other 
words,  that  a  body  which  contains  two,  three,  or  four  times  as 
much  matter  as  a  given  body,  will  also  weigh  two,  three,  or  four 
times  as  much.  This  fact  has  a  most  important  bearing  on 
chemistry,  since  the  chemist  is  enabled,  in  consequence  of  it, 
to  compare  the  various  quantities  of  matter  on  which  he  experi- 
ments, by  comparing  their  weights.  So  close  is  this  relation, 
that  in  common  language  we  confound  the  weight  of  a  substance 
with  its  mass ;  thus,  we  speak  of  ten  grammes  of  iron,  mean- 
ing thereby  a  quantity  of  iron  which  exerts  a  pressure  of  ten 
grammes.  It  must  be  remembered  that,  in  scientific  language, 
weight  always  means  pressure,  and  not  quantity  of  matter.  The 
word  is  most  commonly  used,  however,  to  denote  the  quantity 
of  matter  which  exerts  the  pressure. 

So  long  as  matter  is  neither  taken  from  nor  added  to  a  body, 
its  mass,  from  the  very  definition  of  the  term,  remains  constant. 
It  is  not  so,  however,  with  the  absolute  weight.  This  varies  with 
the  force  of  gravity,  and,  as  follows  from  [48],  it  is  directly  pro- 
portional to  the  intensity  of  this  force.  Hence,  the  absolute 
weight  of  a  body  increases  as  we  go  from  the  equator  to  the 
poles,  and  diminishes  as  we  rise  above  the  surface  of  the  earth, 
ft  is  very  different  on  the  different  planets  and  on  the  sun.  A 
body  weighing  a  kilogramme  on  the  earth  would  weigh  about  28 
kilogrammes  on  the  sun,  about  2.6  kilogrammes  on  Jupiter,  and 


GENERAL  PROPERTIES  OP  MATTER.  89 

only  about  160  grammes  on  the  moon.  On  the  surface  of  the 
globe,  however,  the  possible  variation  of  weight  is  but  small, 
amounting  at  most  to  T£y  of  the  whole.  Calling  this  in  round 
numbers  3-^,  it  will  be  found  that  a  body  weighing  one  kilo- 
gramme at  the  equator  would  weigh  1  kilog.  5  gram,  at  the  poles. 
(64.)  French  System  of  Weights. — Weight  is  estimated  by 
arbitrarily  assuming  a  unit  of  weight,  and  then  comparing  the 
pressure  exerted  by  other  bodies  with  that  exerted  by  the  unit. 
If,  for  example,  this  pressure  in  a  given  case  is  found  to  be  ten 
times  as  great  as  that  of  the  unit,  the  body  is  said  to  weigh  ten 
grammes,  or  ten  pounds,  as  the  unit  may  be  denominated.  The 
French  have  assumed,  as  their  unit  of  weight,  the  pressure  ex- 
erted by  one  cubic  centimetre  of  pure  water  at  4°  C.  (its  point  of 
maximum  density)  in  a  vacuum,  and  at  the  latitude  of  Paris. 
This  unit  they  call  a  gramme.  The  gramme  is  multiplied  and 
subdivided  decimally,  and  the  names  given  to  these  multiples  and 
subdivisions  are  analogous  to  those  used  in  the  case  of  the  metre. 
Thus  we  have  the 

French  System  of  Weights. 

Kilogramme,     1000  gram.  Gramme,  1.000  gram. 

Hectogramme,    100      "  Decigramme,    0.100      " 

Decagramme,       10     u  Centigramme,  0.010      " 

Gramme,  1     "  Millegramme,  0.001      « 

It  follows  from  the  last  section,  that  a  mass  of  brass  whose 
weight  is  one  gramme  at  Paris  would  weigh  less  than  a  gramme 
at  a  lower  latitude,  and  more  than  one  gramme  at  a  latitude 
higher  than  that  of  Paris.  Hence,  the  weight  of  one  cubic 
centimetre  of  water  at  4°  C.,  and  in,  a  vacuum,  is  the  standard 
gramme  only  at  the  latitude  of  Paris. 

The  great  advantage  of  this  system  of  weights  in  all  scientific 
investigations  arises  from  the  very  simple  relation  which  exists 
between  it  and  the  system  of  measures  already  described.  This 
is  so  simple,  that  it  is  almost  always  possible  to  calculate  the 
weight  of  a  substance  from  its  volume,  and  the  reverse,  mentally, 
when  the  specific  gravity  of  the  substance  is  known.  The  French 
system,  both  of  weights  and  measures,  is  exclusively  used  in  this 
volume. 

(65.)  System  of  Weights  of  the  United  States  and  of  Eng- 
land. —  In  this  country  and  in  England  two  entirely  distinct 
8* 


90  CHEMICAL   PHYSICS. 

units  of  weight  are  in  use,  called  the  Troy  Pound  and  the 
Avoirdupois  Pound.  These  units  are  entirely  arbitrary,  and 
are  represented  by  certain  masses  of  metal,  which  have  been 
declared  by  law  to  be  the  legal  standard  of  weight.  These  units 
bear  to  each  other  the  relation  of  144  to  175,  and  do  not  agree 
in  any  of  their  subdivisions  except  the  grain.  The  Troy  pound 
contains  5,760,  and  the  avoirdupois  pound  7,000  grains,  all  of  the 
same  value.  The  actual  legal  standard  of  weight  in  the  United 
States  is  the  Troy  pound,  copied  by  Captain  Kater,  in  1827,  from 
the  imperial  Troy  pound,  for  the  United  States  Mint,  and  pre- 
served in  that  establishment.  This  pound  is  a  standard  at  30 
inches  of  the  barometer  and  62°  of  the  Fahrenheit  thermometer.* 
The  English  standard  of  weight  is  connected  with  that  of  meas- 
ure, by  the  enactments  that  277.274  cubic  inches  shall  constitute 
the  Imperial  Gallon,  and  that  the  weight  of  this  volume  of  pure 
water,  weighed  in  air  of  30  inches'  pressure  at  62°  F.,  shall  be 
taken  as  10  avoirdupois  pounds,  or  70,000  grains.  Tables  of  the 
subdivisions  of  the  two  units,  showing  their  relations  to  the 
French  system,  will  be  found  at  the  end  of  this  Part,  in  connec- 
tion with  the  other  tables  of  weights  and  measures. 

(66.)  Specific  Weight.  —  The  specific  weight  of  a  substance 
is  the  weight  of  one  cubic  centimetre  of  the  substance,  and  there- 
fore bears  the  same  relation  to  the  weight  that  the  density  does 
to  the  mass  (15).  If,  then,  we  represent  specific  weight  by 
Sp.  tD,  we  have 

Sp.to  =  Q.  [50.] 

The  specific  weight  of  copper,  for  example,  at  Paris,  is  equal  to 
8.921  grammes.  The  term  specific  weight  must  not  be  con- 
founded with  specific  gravity,  which  will  be  explained  in  (69). 

The  specific  weight  of  a  substance  is  evidently  variable,  and, 
like  the  absolute  weight,  depends  on  the  intensity  of  the  force  of 
gravity. 

(67.)  Unit  of  Mass.  —  In  assuming  a  unit  of  weight,  we  have 
also  established  a  unit  of  mass.  If,  in  [48],  we  substitute  for  M 
unity,  and  for  g  the  intensity  of  gravity  at  Paris,  the  value  of 
to  becomes 


*  Report  on  Weights  and  Measures,  by  Professor  A.D.  Bache.    Thirty-fourth  Con- 
gress, Third  Session.    Ex.  Doc.  No.  27. 


GENERAL   PROPERTIES   OF   MATTER.  91 

tn  =  9.8096  grammes  ;  [51.] 

that  is,  the  unit  of  mass  weighs  at  Paris  9.8096  gram.  Any 
quantity  of  matter,  then,  which  weighs  at  Paris  9.8096  gram., 
is  the  unit  of  mass.  The  weight  of  the  unit  of  mass  evidently 
varies  with  the  intensity  of  gravity ;  thus,  at  the  poles  the  unit 
of  mass  weighs  9.8315  gram.,  at  the  equator  it  weighs  9.7806 
gram.  The  differences  are  very  much  greater  on  the  surfaces 
of  the  sun,  moon,  and  planets  ;  thus,  on  the  sun  the  unit  of 
mass  weighs  about  277.5  gram.,  on  the  moon  about  1.654  gram., 
and  on  the  planet  Jupiter  about  26.243  gram.  In  general,  a 
quantity  of  matter  which  weighs  as  many  grammes  as  the  number 
which  expresses  the  intensity  of  gravity  at  the  place  of  observa- 
tion, is  equal  to  the  unit  of  mass. 

From  equation  [48]  we  have,  by  transposition,  M  =  — .  Hence, 

in  order  to  find  the  number  of  units  of  mass  of  which  a  body 
consists,  we  have  only  to  divide  its  weight  in  grammes  by  the  in- 
tensity of  gravity  at  the  place  of  observation.  For  example,  500 
grammes  of  iron  at  Paris  contain  s5£fty  =  50.98  units  of  mass. 

(68.)  Density.  —  The  density  of  a  substance  has  been  defined 
as  the  mass  of  one  cubic  centimetre  of  the  substance  (15),  and 

n/r  IYI 

from  [1]  we  have  D  =  -p.,  or,  substituting  for  M  its  value,  — , 

M\~\  £ 

and  then  for  -^  the  symbol  Sp.  fcp,  we  obtain 

D  =  -— -r  =  ^?  (units  of  mass).          [52.] 

D   *  6 

8  921 
The  density  of  copper,  for  example,  is  equal  to  ^-^  =  0.909 

unit  of  mass.  Density  has,  therefore,  the  same  relation  to  spe- 
cific weight  that  mass  has  to  weight.  It  is  always  equal  to  the 
weight  of  one  cubic  centimetre  of  the  substance  divided  by  the 
intensity  of  gravity.  It  is  evidently  a  constant  quantity,  and 
does  not  vary  with  the  intensity  of  gravity. 

(69.)  Specific  Gravity.  —  The  specific  gravity  of  a  substance 
is  the  ratio  of  its  absolute  weight  to  that  of  an  equal  volume  of 
pure  water  at  4°  C.  and  at  the  same  locality.  If  to  represents 
the  absolute  weight  of  the  substance  at  any  place,  and  to'  the 
weight  of  an  equal  volume  of  water  at  the  same  place,  then 

^.GV.=       .  [53.] 


92  CHEMICAL   PHYSICS. 

Moreover,  since  tD  =  M.  g-,  and  ID'  =  M' .  g,  we  have,  also, 

0     ~          M .  g         M  rr  A  ., 

^•Gr-  =  M'-g=M'-  t54'] 

Hence  the  specific  gravity  of  a  substance  is  likewise  the  ratio  of 
its  mass  to  the  mass  of  an  equal  volume  of  water.  It  is,  there- 
fore, like  the  density,  a  constant  quantity,  and  does  not  vary  with 
the  intensity  of  gravity. 

In  the  French  system,  one  cuhic  centimetre  of  water  at  4°  C. 
weighs  at  Paris  one  gramme,  and  hence  at  Paris  the  weight  in 
grammes  of  a  given  volume  of  water  at  4°  C.  is  always  equal  to 
the  number  of  cubic  centimetres.  We  may  therefore  substitute 
in  [53],  for  ill',  the  volume  in  cubic  centimetres.  If  we  also 
designate  by  W  the  absolute  weight  of  a  body  at  Paris,  and  by 
Sp.  W.  the  specific  weight  at  Paris,  we  can  obtain  from  [53] 
and  [50], 

Sp.Gr.=  ~=  Sp.W.  [55.] 

From  this  equation,  it  appears  that  the  numbers  expressing 
the  specific  gravity  of  a  substance  and  its  specific  weight  at 
Paris  are  always  the  same  in  the  French  system.  The  difference, 
however,  between  the  two  is  an  essential  one.  Sp.  W.  always 
stands  for  a  certain  number  of  grammes,  but  Sp.  Gr.  is  a  ratio. 
When  we  say  that  the  specific  weight  of  copper  is  8.921  grammes, 
we  mean  that  one  cubic  centimetre  of  copper  weighs  at  Paris 
this  number  of  grammes  ;  but  when  we  say  that  the  specific 
gravity  of  copper  is  8.921,  we  merely  mean  that  a  volume  of 
copper  weighs  8.921  as  much  as  the  same  volume  of  water.  The 
first  number  is  variable,  depending  on  the  unit  of  weight  used  ; 
the  last  is  invariable,  and  hence  the  same  with  all  systems  of 
weights.  It  is  only  in  the  French  system  of  weights  that  the  two 
numbers  are  the  same. 

We  can  easily  obtain  from  [55], 

Y=-S^G-r.'    and     W~r.Sp.Gr.         [56.] 

These  simple  formulae  should  be  remembered,  as  they  will  be 
constantly  used  in  the  course  of  this  work. 

It  is  more  usual  to  refer  the  specific  gravity  of  gases  to  air, 
as  a  standard  of  comparison,  than  to  water.  It  will  be  shown 
hereafter  that  the  weight  of  a  given  volume  of  air  varies  very 


GENERAL   PROPERTIES   OF   MATTER.  93 

greatly,  both  with  the  temperature  and  the  atmospheric  pressure 
to  which  it  is  exposed  ;  and  it  is  therefore  essential,  in  using  air 
as  a  standard  of  comparison,  to  adopt  arbitrarily  a  certain  tem- 
perature and  pressure,  at  which  it  shall  be  considered  as  the  stand- 
ard. The  temperature  which  has  been  generally  agreed  upon 
is  0°  C.,  and  the  pressure  which  has  been  adopted  is  that  cor- 
responding to  a  height  of  76  c.  m.  of  the  barometer. 

We  may  then  define  the  specific  gravity  of  a  gas  as  the  ratio  of 
its  weight  to  that  of  an  equal  volume  of  air  at  0°  C.  and  under  a 
pressure  of  76  c.  m.  Representing  by  W  the  weight  of  a  given 
volume  of  gas  at  Paris,  and  by  W  and  W"  the  weights  respec- 
tively of  the  same  volumes  of  water  and  air  at  the  standard  tem- 
peratures and  pressure,  —  also  representing  by  Sp.  Gr.  the  spe- 
cific gravity  of  the  gas  referred  to  water,  and  by  Sp.  Gr.  the 
specific  gravity  referred  to  air,  —  we  have 

Sp.Gr.  =  ^,    and    Sp.  Gr.  =-^.          [57.] 

"When  the  specific  gravity  of  a  given  substance  is  referred  to 
one  standard,  it  is  frequently  required  to  calculate  its  specific 
gravity  with  reference  to  the  other,  or,  in  technical  language,  to 
reduce  the  specific  gravity  to  the  other  standard.  For  this  pur- 
pose, we  know  that  the  specific  gravity  of  air  with  reference  to 

water  is  equal  to  0.00129363.     Hence,  -^  =  0.00129363,  and 

by  substituting  the  value  of  W,  obtained  from  this  in  [57] ,  we 
can  easily  obtain 

Sp.  Gr.  =  Sp.  Gr.  0.00129363,  [58.] 

a  formula  by  means  of  which  the  reduction  can  easily  be  made. 

A  table  giving  the  specific  gravities  of  some  common  substances 
will  be  found  at  the  end  of  this  Part. 

(70.)  Unit  of  Force.  —  The  unit  of  force  has  been  defined  as 
that  force  which,  acting  on  the  unit  of  mass  during  one  second, 
will  impress  upon  it  a  velocity  of  one  metre  (29).  Since  the 
unit  of  mass  weighs  at  Paris  9.810  grammes,  we  can  also  define 
the  unit  of  force  as  that  force  which,  acting  during  one  second, 
will  impress  on  9.810  grammes  of  matter  a  velocity  of  one  metre. 
Moreover,  it  follows  from  [14]  that  a  force  which  will  impress 
during  one  second  a  velocity  of  one  metre  on  9.810  grammes  of 
matter,  is  equal  to  the  force  which  will  impress  a  velocity  of  9.810 


94  CHEMICAL   PHYSICS. 

metres  on  one  gramme  of  matter.  But  this  force  is  the  same  as 
the  force  exerted  by  gravity  on  one  gramme  of  matter.  In  other 
words,  it  is  equal  to  the  weight  of  one  gramme.  We  have,  then, 
a  new  measure  for  our  unit  of  force.  The  unit  of  force  is  the 
force  exerted  in  pressure  by  the  unit  of  weight.  When  a  weight 
of  ten  grammes,  for  example,  is  suspended  to  a  fixed  point, 
the  pressure  exerted  by  that  weight  is  equivalent  to  ten  units  of 
force. 

(71.)  Relative  Weight.  — There  are,  in  general,  two  methods 
by  which  the  weight  of  a  body  (that  is,  the  pressure  which  it  ex- 
erts) may  be  determined. 

The  first  method  consists  in  balancing  the  pressure  against  a 
spring,  and  determining  the  weight  from  the  amount  by  which  the 
spring  is  bent.  An  instrument  for  this  purpose  is  represented  in 
Fig.  35.  It  consists  of  a  steel  spring,  bent  in  the  form  of  a  V. 
To  the  end  of  the  lower  arm  is  fastened  an  iron  arc,  which  passes 
freely  through  an  opening  in  the  upper  arm,  and  ends  in  a  ring. 
To  the  end  of  the  upper  arm  a  similar  iron  arc  is  fastened,  which 
passes  through  an  opening  in  the  lower  arm,  and  terminates 
in  a  hook.  In  using  the  instrument,  the  body  to  be  weighed 
is  suspended  by  the  hook,  as  in  Fig.  35,  and 
the  number  of  grammes  by  which  the  spring 
is  bent  is  then  read  off  on  the  graduated 
arc.  Such  an  instrument  is  called  a  spring  bal- 
ance, and  indicates  at  once  the  absolute  weight 
of  a  body.  Could  it  be  made  sufficiently  deli- 
cate, it  would  show  that  the  absolute  weight  of 
a  body  varied  on  the  earth's  surface,  gradually 
increasing  from  the  equator  towards  the  poles. 
Such  an  instrument  would  give  the  absolute 
weight  of  a  body. 
Fig.  35.  The  second  method  consists  in  preparing  a  set 

of  so-called  weights,  which  are  masses  of  brass  or  platinum  weigh- 
ing exactly  one  gramme,  or  some  multiple  or  fraction  of  a  gramme, 
at  Paris.  The  weight  of  a  body  is  then  estimated  by  balancing  it 
against  these  weights  in  a  well-known  instrument  called  the  bal- 
ance. The  balance  is  merely  a  form  of  the  lever,  so  constructed 
that,  when  equal  pressures  are  exerted  on  its  two  pans,  the  beam 
stands  in  a  horizontal  position.  The  body  to  be  weighed  is 
placed  in  one  pan,  and  then  weights  are  added  to  the  other  until 


GENERAL  PROPERTIES  OF  MATTER.  95 

the  beam  of  the  balance  rests  in  a  horizontal  position.  The  sum 
of  these  weights  then  indicates  the  weight  of  the  body.  At  Paris 
the  balance  indicates  at  once  the  absolute  weight  of  a  body,  but 
not  necessarily  so  at  other  places  on  the  earth's  surface.  To  il- 
lustrate this  point,  let  us  suppose  that,  in  weighing  at  Paris,  it 
required  ten  grammes'  weight  in  one  pan  of  the  balance  to  equi- 
poise the  body  in  the  other  pan.  Suppose,  now,  that  we  trans- 
port the  whole  apparatus  to  some  point  on  the  equator.  It  is 
evident  that  our  gramme  weights  no  longer  weigh  one  gramme 
each,  but  something  less,  by  an  amount  easily  calculated  from 
the  diminution  in  the  intensity  of  gravity.  Nevertheless,  since 
the  body  has  lost  weight  in  the  same  proportion,  it  will  still 
be  balanced  by  the  ten  gramme  weights,  and  so  it  would  be  all 
over  the  globe.  This  weight,  which  is  frequently  called  relative 
weight,  will  always  be  designated  in  this  work  by  TF,  in  order  to 
distinguish  it  from  the  absolute  weight  at  other  localities,  which 
we  have  already  designated  by  to.  Hence  we  have,  from  [48], 

W=M.  9.8096,     and     to  =  M  .  g,          [59.] 

Since  the  force  of  gravity  at  any  given  locality,  and  hence  at 
Paris,  does  not  vary,  it  follows  that  the  relative  weight  of  a  body, 
or  TF",  is  a  constant  quantity  ;  the  same  at  any  point  on  the  sur- 
face of  our  globe,  and  the  same  on  the  sun,  moon,  and  planets 
as  it  is  on  the  earth. 

"We  can  easily  find  the  absolute  weight  of  a  body  at  any  local- 
ity, when  its  relative  weight  is  known.  Representing,  as  above, 
by  W  the  relative  weight  of  the  body,  and  by  to  the  absolute 
weight  required  at  the  place  in  question,  we  have,  from  [59], 

t)  :   TF=  M  .g  :  M  .  9.8096,  [60.] 

and 


that  is,  the  absolute  weight  of  a  body  at  any  place  is  equal  to  the 
absolute  weight  at  Paris  (or  the  relative  weight  of  the  body  at  the 
place)  multiplied  by  the  ratio  between  the  intensity  of  gravity  at 
the  place  and  that  at  Paris. 

Relative  weight  is  the  direct  measure  of  the  mass  of  a  body. 
Representing  by  m  the  mass  of  the  unit  of  weight,  we  have 
1  yr.  =  m.  9.8096.  By  comparing  this  equation  with  JF= 

m  .  9.8096  we  obtain  W=  —  ;  that  is,  the  relative  weight  of  a 


93  CHEMICAL  PHYSICS. 

body  indicates  the  quantity  of  matter  which  it  contains,  compared 
with  that  contained  in  one  cubic  centimetre  of  water  at  4°  C.  It 
is  therefore  a  legitimate  measure  of  the  quantity  of  matter  con- 
tained in  a  body,  and  the  word  weight  is  almost  exclusively  used 
in  this  sense  in  chemistry,  as  it  is  in  common  life. 

MECHANICAL   POWERS. 

(71  bis.)  Machines. —  By  the  aid  of  wheels,  rods,  bands  or 
cords,  and  inclined  surfaces,  power  may  be  readily  transmitted 
from  one  point  to  another,  and  the  intensity,  direction,  point, 
and  mode  of  application  of  the  acting  force  varied  in  a  multi- 
plicity of  ways.  The  numerous  contrivances  by  which  such 
changes  are  effected  are  termed,  in  general,  machines.  All  ma- 
chines, however  complicated  their  structure,  will  be  found  on 
examination  to  consist  of  a  limited  number  of  simple  parts,  gen- 
erally called  mechanical  powers,  or  simple  machines.  Among 
these  we  usually  distinguish  six ;  viz.  the  lever,  the  wheel  and 
axle,  the  pulley,  the  inclined  plane,  the  wedge,  and  the  screw. 
Of  each  of  these,  however,  there  are  many  varieties ;  and  the 
skill  of  the  inventor  is  shown  no  less  in  adapting  these  parts  of 
his  machine  to  their  special  purpose,  than  in  combining  the  parts 
so  that  they  shall  act  harmoniously  together  to  produce  the  de- 
sired result.  A  description  of  the  various  mechanical  powers, 
or  of  their  important  applications,  is  entirely  beyond  the  scope 
of  this  work.  There  is,  however,  one  important  general  princi- 
ple connected  with  the  subject  which  may  be  noticed  in  passing. 
A  machine  transmits  power  without  increasing  it  in  the  slightest 
degree.  Indeed,  more  or  less  power  is  always  lost  during  the 
transmission,  in  overcoming  friction  and  other  causes  of  resist- 
ance. The  use  of  a  machine  is  to  adapt  power  to  the  work  to 
be  done.  It  may  change  the  direction  or  the  velocity  of  the 
motion  caused  by  the  power  ;  it  may  change  the  mode  of  action 
of  the  power ;  it  may  change  the  intensity  of  the  power,  and 
enable  a  feeble  force,  by  acting  through  a  great  distance,  or 
during  a  long  time,  to  overcome  a  great  resistance.  It  may 
modify  the  action  of  the  power  in  an  infinite  variety  of  ways,  so 
as  to  produce  the  useful  effects  of  which  machinery  is  capable, 
but  it  will  be  found  in  every  case  that  the  work  done  by  the  ma- 
chine is  the  exact  equivalent  of  the  power  it  receives.  One  only 
of  the  mechanical  powers  requires  further  notice  in  this  work. 


GENERAL   PROPERTIES   OF   MATTER. 


9T 


THE   BALANCE. 

(72.)  Lever.  —  Before  studying  the  theory  of  the  balance,  it 
is  important  to  consider  the  general  theory  of  the  lever,  of  which 
the  balance  is  only  a  single  example. 

A  lever  is  any  rigid  bar,  A  B  (Fig.  36),  resting  on  a  point,  c, 
round  which  two  forces  tend  to  turn  it  in  opposite  directions. 


Fig.  36. 


Fig.  37. 


The  point  c  is  called  the  fulcrum.  The  force  applied  at  A  is  called 
the  power,  and  the  force  applied  at  B  is  called  the  resistance,  or 
the  weight.  Levers  are  commonly  divided  into  three  kinds,  ac- 
cording to  the  position  which  the  fulcrum  has  in  relation  to  the 
power  and  the  weight.  If  the  fulcrum  is  between  the  power  and 
the  weight,  as  in  Figs.  36,  3T,  the  lever  is  of  the  first  kind.  If 


1 

BI 


Fig.  38. 

the  weight  is  between  the  fulcrum  and  the  power,  as  in  Fig.  38, 
the  lever  is  of  the  second  kind.     If  the  power  is  between  the 
9 


98 


CHEMICAL  PHYSICS. 


fulcrum  and  the  weight,  as  in  Fig.  39,  the  lever  is  of  the  third 
kind. 

In  the  three  kinds  of  lever,  the  perpendicular  distances  from 
the  fulcrum  to  the  lines  of  direction  of  the  two  forces  are  called 
the  arms  of  the  lever.  If  the  lever  is  straight,  and  perpendicular 
to  the  directions  of  both  of  the  two  forces,  the  two  portions  of 
the  lever,  A  c  and  B  c,  Fig.  36,  are  themselves  the  arms  of  the 
lever.  If,  however,  the  lever  is  not  straight,  or  is  inclined  to 
the  direction  of  one  or  both  of  the  forces,  the  arms  of  the  lever 
are  the  perpendiculars,  a  c  and  b  c,  Fig.  37,  a  O  and  b  O,  Fig.  40, 
let  fall  from  the  fulcrum  on  these  directions. 

In  order  that  the  two  forces  applied  to  the  lever  should  be  in 
equilibrium,  three  conditions  are  essential :  — 

1st.  The  lines  of  direction  of  the  two  forces  must  be  in  the 
same  plane  with  the  fulcrum. 

2d.  The  two  forces  must  tend  to  turn  the  lever  in  opposite  di- 
rections. 

3d.  The  intensity  of  the  two  forces  must  be  to  each  other  in- 
versely as  the  lengths  of  the  arms  of  the  lever  to  which  they  may 
be  regarded  as  applied. 

That  these  three  conditions  are  essential  to  equilibrium  can 
easily  be  proved.  In  the  first  place,  it  is  evident  that  the  two 
forces  cannot  be  in  equilibrium,  unless  the  direction  of  their 
resultant  passes  through  the  fulcrum.  Now  it  can  easily  be 

proved,  that,  unless  the 
two  forces  are  in  the 
same  plane,  they  can 
have  no  single  result- 
ant; and  hence  follows 
the  necessity  of  the  first 
condition.  In  the  second 
place,  let  us  suppose,  Fig. 
40,  that  A  Q  and  B  P 
are  the  lines  of  direction 
of  two  forces  in  the  same 
plane  with  the  fulcrum 
O,  and  that  C  is  the  point 
where  these  directions  in- 
tersect ;  then,  in  order  that  the  direction  of  the  resultant  O  R 
should  pass  through  O,  it  is  evident  that  the  directions  of  the 


Fig.  40. 


GENERAL   PROPERTIES   OF   MATTER.  99 

components  should  be  such  that  they  would  tend  to  turn  the 
lever  in  opposite  directions. 

The  necessity  of  the  third  condition  will  be  most  readily  seen 
if  studied  under  two  cases.  In  the  first  place,  let  us  take  the 
case  where  the  two  forces  are  parallel,  as  in  Fig.  37.  It  has  been 
proved  (37)  that  the  point  of  application  of  the  resultant  of  two 
parallel  forces  divides  the  line  joining  the  points  of  application 
of  the  components  into  two  parts,  which  are  inversely  propor- 
tional to  the  intensities  of  the  forces.  Hence  it  follows,  that, 
in  order  that  the  direction  of  the  resultant  in  Fig.  37  should  pass 
through  the  fulcrum,  the  two  forces  applied  at  A  and  B  must  be 
inversely  proportional  to  A  c 
and  Be,  and  hence  also  to 
a  c  and  b  c,  which  are  the 
arms  of  the  lever.  In  the 
second  place,  let  us  suppose 
that  the  directions  of  the 
forces  are  not  parallel,  as 
in  Fig.  41.  In  this  figure, 
A  Q  and  B  P  represent  Fi 

the  directions  of  the  forces, 

which  we  will  represent  by  F  and  F1,  and  a  O  and  b  O  the  arms 
of  the  lever.  By  the  principle  of  (32),  the  effect  of  these  forces  is 
the  same  as  if  they  were  applied  respectively  at  a  and  b,  points 
which  we  may  consider  as  immovably  united  to  the  lever.  From 
0  extend  the  line  b  0  until  it  intersects  the  direction  A  Q  at  a 
point  c.  By  the  same  principle  as  above,  the  effect  of  the  force 
F  is  the  same  as  if  it  were  applied  at  c.  We  can  now  evidently 
consider  this  force  as  made  up  of  two  others  perpendicular  to 
each  other,  one  acting  in  the  direction  0  c,  which  will  be  neu- 
tralized by  the  resistance  of  the  fixed  point  0,  and  the  other  in 
the  direction  c  q  parallel  to  B  P.  Complete  the  parallelogram, 
and  let  us  suppose  that  F=  c  (?,  and  hence  that  the  component 
parallel  to  B  P  is  equal  to  c  q.  It  follows  now,  from  the  proof 
given  above,  that  there  can  only  be  equilibrium  when 


or     c= 


But  from  the  similarity  of  the  triangles  c  q  Q  and  c  0  a,  we  have 
cq  :  Oa  =  c  Q  :  0  c,  and  by  substituting  for  c  Q  and  c  q  their 
values  just  given 


100  CHEMICAL  PHYSICS. 

F'  :  Oa  =  F  :  Ob.  [65.] 

It  is,  then,  also  a  condition  of  equilibrium,  that  the  two  forces 
should  be  to  each  other  inversely  as  the  lengths  of  the  arms  of 
the  lever,  the  point  which  was  to  be  proved.  We  have  proved 
the  validity  of  the  three  conditions  of  equilibrium  for  the  first 
kind  of  lever  only ;  but  this  proof  can  easily  be  extended  to  the 
second  and  third  kinds  of  lever. 

It  follows  from  what  has  been  said,  that  the  tendency  of  the 
power  to  turn  the  lever  may  be  augmented  either  by  increasing 
the  amount  of  the  power,  or  by  increasing  the  length  of  the  arm 
of  the  lever  on  which  it  acts  ;  that  is,  by  increasing  the  perpen- 
dicular distance  of  the  direction  of  the  force  from  the  fulcrum. 
In  either  case,  the  effect  will  be  increased  in  a  corresponding 
proportion.  Thus,  if  we  remove  the  power  to  double  its  distance 
from  the  fulcrum,  we  shall  double  its  effect ;  and  if  we  remove  it 
to  half  the  distance,  we  shall  diminish  its  effect  by  one  half.  The 
perpendicular  distance  of  the  direction  of  a  force  from  the  ful- 
crum is  called  its  leverage ;  and  it  is  evident  that  the  effect  of 
any  force  applied  to  a  lever  will  be  proportional  to  its  leverage. 

From  proportion  [65]  we  obtain,  by  multiplying  together  the 
extremes  and  the  means,  F  X  O  a  =  F'  X  Ob.  The  product 
of  the  intensity  of  a  force  by  the  length  of  the  perpendicular  let 
fall  from  a  fixed  point  to  the  line  of  direction  of  the  force,  is 
called  the  moment  of  the  force  with  respect  to  the  point.  Since 
O  a  and  O  b  are  such  perpendiculars,  it  follows  that,  when  a  lever 
is  in  equilibrium,  the  moments  of  the  power  and  resistance  are 
equal. 

(73.)  The  Balance.  — The  instrument  by  means  of  which  the 
weight  of  a  substance  is  compared  with  the  unit  of  weight,  is 
called  a  Balance.  It  is  generally  made  of  brass,  and  consists 
essentially  of  an  upright  pillar  supporting  a  beam,  B  B,  Fig. 
42,  which  turns  upon  a  knife-edge,  placed  exactly  at  the  mid- 
dle of  its  length.  From  the  two  ends  of  the  beam  are  sus- 
pended the  pans,  in  which  the  weights  to  be  compared  are 
placed.  The  knife-edge  is  formed  by  a  triangular  steel  prism 
passing  through  the  beam,  whose  axis  is  exactly  at  right  angles 
with  the  plane  of  the  beam.  The  lower  edge  of  the  prism  is 
sharp,  and  rests  upon  an  agate  plane,  so  as  to  make  the  friction  as 
small  as  possible.  For  the  same  reason,  the  hooks  by  which  the 
pans  are  suspended  rest  also  on  knife-edges.  These  knife-edges 


GENERAL   PROPERTIES   OF   MATTER. 


101 


are  adjusted  perpendicularly  to  the  plane  of  the  beam,  and  on  the 
same  level  as  the  fulcrum.  The  fulcrum  is  so  placed  that  the 
centre  of  gravity  of  the  beam  shall  be  slightly  below  it,  so  that 


Fig.  42. 

when  in  equilibrium  the  beam  will  tend  to  come  to  rest  in  a 
horizontal  position.  The  centre  of  gravity  can  be  adjusted  by 
means  of  the  button  (7,  Fig.  42,  which  can  be  moved  up  or  down 
on  the  screw  to  which  it  is  fastened.  The  long  index-rod  attached 
to  the  beam  below  the  knife-edge  indicates,  by  the  graduated  arc, 
when  the  beam  is  horizontal.  When  the  balance  is  not  in  use, 
the  beam  can  be  lifted  off  from  its  bearing,  and  supported  upon 
the  brass  arms  E,  E.  These  are  attached  to  the  cross-piece  a  a, 
which  can  be  raised  or  lowered  by  turning  the  thumb-screw  O. 
The  motion  of  the  cross-piece  is  directed  by  the  two  pins  A,  A, 
which  play  loosely  through  holes  at  its  twq  ends. 

A  balance  is  evidently  a  lever  with  equal  arms,  and,  according 
to  the  principle  of  the  lever,  if  equal  weights  are  placed  in  the  two 
pans,  they  will  exactly  balance  each  other.  The  balance,  there- 
fore, enables  us  to  compare  the  weight  of  a  substance  with  the 
unit  of  weight.  We  have  simply  to  place  the  substancQ  in  one 
pan  of  the  balance,  and  then  add  weights,  which  have  been  ad- 
justed by  the  standard  unit,  to  the  other,  until  the  beam  assumes 
a  horizontal  position,  or  until  it  vibrates  to  an  equal  distance  on 
9* 


102  CHEMICAL   PHYSICS. 

both  sides  of  this  position,  —  as  can  be  observed  by  the  motion  of 
the  index  over  the  graduated  arc.  The  sum  of  the  weights  re- 
quired to  balance  the  substance  is,  then,  its  relative  weight  in 
terms  of  the  unit  of  weight  employed. 

The  usefulness  of  a  balance  depends  upon  two  points,  —  1st,  its 
accuracy,  and,  2dly,  its  sensibility  to  slight  differences  of  weight. 
An  examination  of  the  conditions  on  which  these  depend,  will 
lead  us  to  understand  better  the  principle  of  this  very  important 
instrument.  From  the  mode  in  which  the  pans  of  a  balance  are 
suspended,  it  is  obvious  that  we  may  regard  their  whole  weight 
as  concentrated  on  the  knife-edges  at  the  ends  of  the  beam.  In 
a  theoretical  consideration  of  the  subject,  we  may  therefore  leave 
the  pans  entirely  out  of  view,  and  consider  any  weight  placed  in 
them  as  directly  applied  to  the  knife-edges,  thus  reducing  the 
balance  to  a  straight  lever.  From  another  point  of  view,  the 
whole  weight  of  the  beam  and  pans  may  be  considered  as  con- 
centrated at  the  centre  of  gravity,  when  the  balance  becomes  a 
pendulum,  whose  point  of  suspension  is  the  fulcrum  of  the  beam. 
These  two  mechanical  principles,  combined  in  the  balance,  have 
constantly  to  be  kept  in  view  in  studying  its  theory.  It  will  then 
be  easy  to  understand  the  following  circumstances,  on  which  the 
accuracy  and  sensibility  of  the  instrument  depend. 

1.  It  is  necessary  that  the  distances  of  the  two  knife-edges 
from  the  fulcrum  should  be  exactly  equal;  for  if  the  distance  from 
the  fulcrum  of  the  point  of  suspension  of  one  pan  were  greater 
than  that  of  the  other,  then  a  weight  placed  in  the  first,  acting 
under  a  greater  leverage,  would  balance  a  larger  weight  in  the 
last,  and  the  larger  in  proportion  to  the  inequality  of  the  two 
arms  of  the  beam. 

2.  It  is  necessary  that  the  centre  of  gravity  of  the  beam  and 
pans  should  be  below  the  fulcrum,  and  as  near  to  it  as  possible. 
Were  the  centre  of  gravity  at  the  fulcrum,  the  beam  would  not 
oscillate,  but   remain   in   whatsoever   position   it   were   placed. 
Were  it  above  the  fulcrum,  the  beam  would  be  overset  by  the 
slightest  impulse.     When  it  is  below  the  fulcrum,  the  beam,  as 
already  stated,  may  be  regarded  as  a  pendulum,  whose  axis  co- 
incides with  the  line  joining  the  fulcrum  and  centre  of  gravity. 
As  this  line  forms  right  angles  with  the  axis  of  the  beam  in  what- 
ever position  the  latter  may  be  placed,  and  as  the  pendulum 
tends  always  to  fall  back  to  the  perpendicular  position  whenever 


GENERAL   PROPERTIES   OP   MATTER.  103 

removed  from  it,  it  follows  that,  if  we  impart  an  impulse  to  the 
beam  of  a  properly  adjusted  balance,  it  will,  after  vibrating  for 
some  time,  invariably  return  to  a  horizontal  position.  The  centre 
of  gravity  of  the  beam  is  exactly  under  the  fulcrum,  and  in  a  line 
at  right  angles  to  the  axis  only  when  the  two  pans  are  equally 
loaded.  If  unequally  loaded,  the  centre  of  gravity  is  to  the  right 
or  to  the  left  of  this  line  ;  and  in  that  case  the  beam  tends  to 
come  to  rest  at  an  angle  to  the  horizontal  position,  rapidly  in- 
creasing with  the  inequality  of  the  weight  until  the  beam  is  entirely 
overset.  In  weighing  with  a  delicate  balance,  it  is  not  necessary 
to  wait  until  the  beam  comes  to  rest,  in  order  to  ascertain  whether 
the  pans  have  been  equally  loaded.  This  can  be  ascertained  more 
promptly  by  noticing  the  amplitude  of  the  vibrations  of  the  index 
on  either  side  of  the  perpendicular,  by  means  of  the  graduated 
arc.  They  will  be  equal  only  when  the  weights  in  the  two  pans 
are  equal. 

The  sensibility  of  a  balance  depends  in  great  measure  on  the 
nearness  of  the  centre  of  gravity  to  the  fulcrum.  In  order  that 
a  small  weight,  placed  in  one  pan  of  a  balance,  should  turn  the 
beam,  it  must  evidently  overcome  two  forces  ;  first,  the  friction 
of  the  knife-edges  on  their  bearings,  and,  secondly,  the  tendency 
of  the  beam  to  remain  in  a  horizontal  position.  This  tendency 
depends,  as  has  already  been  shown,  upon  the  position  of  the 
centre  of  gravity  below  the  point  of  support.  Let  us  now  com- 
pare two  cases  in  which  the  centres  of  gravity  are  at  different 
distances  from  the  fulcrum, 
and  ascertain  in  which  case 
the  force  required  to  turn 
the  beam  will  be  the  least. 
In  Fig.  43,  suppose  the  line 
a  b  to  be  the  axis  of  the 
beam,  O  the  fulcrum,  and 
£•  or  G  the  centre  of  grav- 
ity. AVe  have  now  to  in- 
quire in  what  position  of 
the  centre  of  gravity  it  will 

require  the  least  force  to  bring  the  beam  to  a  new  position,  a'  b1. 
In  order  to  bring  the  axis  of  the  beam  to  this  position,  it  will  be 
necessary  to  bring  the  centre  of  gravity  from  g*  to  g-',  or  from  G 
to  G'.  In  the  first  case,  it  will  be  necessary  to  raise  the  whole 


104 


CHEMICAL   PHYSICS. 


Fig.  44. 


weight  of  the  beam  and  pans,  which  we  suppose  concentrated  at 
g,  through  the  perpendicular  distance  g  e ;  and  in  the  second 
case,  to  raise  the  same  weight  through  the  distance  G  E.  Since 
the  distance  g-  e  is  much  less  than  the  distance  G  E,  it  is  evi- 
dent that  it  will  require  a  less  force  in  the  first  case  than  in 
the  second.  Hence,  the  sensibility  of  the  balance  is  the  greater, 
the  nearer  the  centre  of  gravity  is  to  the  fulcrum. 

3.  It  is  important  that  the  points  of  suspension  of  the  pans 
should  be  on  an  exact  level  with  the  fulcrum.     The  importance 

of  this  condition  may  be  seen, 
by  remembering  that  an  in- 
crease of  weight  in  the  pans 
is  equivalent  to  adding  just 
so  much  weight  upon  the 
points  of  suspension,  and 
therefore  tends  to  draw. the 
centre  of  gravity  towards 
the  line  (Fig.  44)  connect- 
ing the  two.  If  this  line 
passed  above  the  fulcrum,  as 
in  Fig.  45,  then,  by  increas- 
ing the  weight  in  the  pans, 
the  centre  of  gravity  might 
be  brought  to  coincide  with, 
or  even  be  carried  above,  the 
fulcrum,  when  the  balance 
would  become  useless.  If 
this  line,  as  in  Fig.  45,  passed 
below  the  fulcrum,  an  increase  of  weight  in  the  pans  would  tend 
to  draw  down  the  centre  of  gravity  ;  and  thus,  by  increasing  its 
distance  from  the  fulcrum,  would  diminish  the  sensibility  of  the 
balance.  When,  however,  the  line  passes  through  the  fulcrum, 
as  in  Fig.  46,  the  points  of  suspension  of  the  pans  are  on  an  ex- 
act level  with  the  fulcrum,  and  an  increase  of  load  always  tends 
to  raise  the  centre  of  gravity  towards  the  fulcrum  in  proportion  to 
its  amount ;  so  that  a  well-adjusted  balance  theoretically  should 
turn  with  the  same  weight,  whatever  may  be  the  load  placed  upon 
it,  from  the  smallest  to  the  largest  of  which  its  construction  admits. 
This  last  point  can  be  still  further  illustrated  in  the  following 
manner.  It  has  already  been  shown,  that  the  weight  required  to 


Tig.  45. 


Fig.  46. 


GENERAL   PROPERTIES   OF   MATTER.  105 

turn  the  balance,  when  unloaded,  may  be  measured  by  the  force 
required  to  raise  the  centre  of  gravity  of  the  beam  and  pans 
through  a  small  arc,  G  G1  (Fig.  43),  when  applied  at  b'.  Let  us 
suppose  that  the  pans  are  loaded  with  a  weight  of  one  kilogramme 
each.  It  is  evident,  from  what  has  been  said,  that  this  is  equiv- 
alent to  condensing  a  mass  of  matter  equal  to  one  kilogramme 
at  each  of  the  points  a  and  b.  The  centre  of  gravity  of  these 
masses  must  evidently  be  at  the  middle  of  the  line  a  6,  that  is, 
at  the  fulcrum  of  the  balance.  Since,  then,  this  additional  weight 
is  supported  in  any  position  of  the  beam,  it  follows  that  the  weight 
required  to  turn  the  balance  is  still  measured  only  by  the  force 
required  to  raise  the  centre  of  gravity  of  the  beam  and  pans 
through  the  arc  (7,  G',  or,  to  generalize,  the  absolute  weight  re- 
quired to  turn  the  balance  is  the  same,  whatever  may  be  the  load. 
This,  however,  is  only  theoretically  true,  for  in  practice  the 
weight  required  increases  with  the  load,  in  consequence  of  the 
increased  friction  and  the  slight  bending  of  the  beam  which  it 
causes.  While,  however,  the  absolute  weight  required  to  turn  the 
balance  increases  from  these  causes  with  the  load,  the  proportion 
of  this  weight  to  the  whole  load  diminishes.  This  is  what  is 
usually  meant  by  the  sensibility  of  the  balance,  and  in  this  sense, 
evidently,  the  sensibility  increases  with  the  load. 

4.  It  is  important  that  the  friction  of  the  knife-edges  on  their 
bearings  should  be  as  slight  as  possible.  The  importance  of  this 
circumstance  is  so  evident,  that  it  does  not  require  illustration. 
It  is  secured  by  a  careful  construction  of  the  knife-edges,  and  by 
making  the  beam  as  light  as  is  consistent  with  rigidity. 

In  endeavoring  to  combine  these  conditions,  the  balance-maker 
meets  with  many  practical  obstacles.  If  he  endeavors  to  increase 
the  sensibility  of  his  balance  by  diminishing  the  weight  of  the 
beam,  he  soon  finds  that  he  loses  as  much  as  he  gains,  by  the  in- 
creased flexure.  If,  again,  he  attempts  to  increase  the  sensibility 
by  lengthening  the  beam,  he  soon  comes  to  a  limit,  beyond  which 
the  increased  leverage  is  more  than  compensated  by  the  increased 
friction  due  to  the  necessarily  increased  weight  of  the  beam. 
Nevertheless,  by  carefully  attending  to  the  necessary  conditions, 
balances  may  be  constructed  with  a  remarkable  degree  of  sensi- 
bility. They  have  been  made  so  delicate,  that,  when  loaded  with 
ten  kilogrammes,  they  will  turn  with  one  milligramme,  that  is, 
with  one  ten-millionth  of  the  load. 


106  CHEMICAL   PHYSICS. 

PROBLEMS. 

Centre  of  Gravity. 

51.  Two  masses  of  matter  are  immovably  united,  A  =  14  units  of 
mass,  and  B  =  10  units  of  mass.     What  is  the  position  of  their  common 
centre  of  gravity  ? 

52.  A  mass  of  matter,  A,  =  15  units  of  mass,  is  immovably  united  to 
a  second  mass,  B.     It  is  found  by  experiment  that  the  common  centre  of 
gravity  of  the  two  masses  is  nearest  to  A,  and  divides  the  line  connecting 
the  masses  into  two  parts,  which  are  to  each  other  as  2  is  to  3.     What 
is  the  mass  of  B  ? 

Intensity  of  the  Earth's  Attraction. 

In  these  problems,  the  student  is  expected  to  use  the  values  of  g  given  in  the  table 
on  page  76. 

53.  What  is  the  intensity  of  the  earth's  attraction,  at  Paris,  on  a  body 
whose  mass  is  equal  to  25  units  of  mass  ?     What  is  the  intensity  of  the 
force  of  gravity,  at  Paris,  on  bodies  whose  masses  are  respectively  20,  60, 
720,  430,  and  510  units  of  mass? 

54.  What  is  the  intensity  of  the  earth's  attraction,  at  Paris,  on  a  body 
whose  mass  is  equal  to  0.1019  unit? 

Pendulum. 

55.  What  is  the  time  of  vibration,  at  Paris,  of  a  pendulum  which  is 
0.99394  metre  long?     What  are  the  times  of  vibration  of  pendulums 
which  are  respectively  twice,  three  times,  four  times,  five  times,  and  nine 
times  this  length  ?     The  amplitude  in  each  case  is  supposed  to  be  infi- 
nitely small,  and  the  pendulum  to  oscillate  in  a  vacuum. 

56.  If  the  amplitude  of  the  oscillation  of  the  pendulum  of  the  last  ex- 
ample is  9°,  how  much  would  the  duration  of  an  oscillation  be  increased  ? 
Solve  the  same  problem  for  amplitudes  of  1°,  2°,  4°,  and  5°. 

57.  If  the  pendulum  of  a  clock,  beating  seconds  at  Paris,  were  length- 
ened by  expansion  one  ten-thousandth  of  its  length,  how  many  seconds 
would  it  lose  each  day  ? 

58.  If  a  clock,  keeping  perfect  time  at  Paris,  were  carried  to  Spitzber- 
gen,  how  much  would  it  gain  each  day,  on  the  supposition  that  all  the 
conditions,  with  the  exception  of  the  intensity  of  gravity,  remained  the 
same  ?     How  much  would  it  lose  if  carried  to  the  equator  ? 

59.  A  pendulum  on  the  equator,  0.990934  metre  long,  was  found  to 
oscillate  in  one  second.     What  is  the  intensity  of  gravity  ? 

60.  A  pendulum  at  Paris  one  metre  long  was  found  to  oscillate  in 
1.00304  seconds.     What  was  the  intensity  of  gravity  ? 

61.  A  pendulum  at  Paris  four  metres  long  was  found  to  oscillate  in 
2.00608  seconds.     What  was  the  intensity  of  gravity  ? 


GENERAL   PROPERTIES   OP   MATTER.  107 

62.  What  is  the  intensity  of  gravity  at  the  latitude  of  42°  21'  ?     What 
is  the  length  of  the  seconds  pendulum  at  this  latitude  ? 

63.  What  is  the  intensity  of  gravity,  and  what  the  length  of  the  sec- 
onds pendulum,  on  the  following  parallels  of  latitude,  viz.   15°,  22°,  56°, 
and  74°  ? 

64.  What  is  the  intensity  of  the  centrifugal  force  on  the  parallels  of 
latitude  of  5°,  20°,  30°,  50°,  and  70°  ?     What  is  the  absolute  intensity  of 
gravity  on  these  parallels  ? 

65.  What  is  the  intensity  of  gravity  at  the  summit  of  Mt.  Washington, 
New    Hampshire?     Latitude  of  Mt.  Washington,  44°  15'.     Height  of 
summit  above  the  sea-level,  2,027  metres. 

66.  What  is  the  intensity  of  gravity  at  the  summit  of  Mt.  Blanc  ?     Lat- 
itude of  Mt.  Blanc,  45°  50'.     Height  of  summit  above  the   sea-level, 
4,814  metres. 

Weight. 

67.  What  is  the  weight  of  a  body  containing  10  units  of  mass  at  Paris  ? 
What  is  the  weight  of  the  same  body  at  Boston  ?     The  latitude  of  Boston 
is  42°  21'. 

68.  What  is  the  weight  of  a  body  containing  500  units  of  mass,  at  the 
equator  and  at  the  poles  ? 

69.  What  is  the  specific  weight  of  iron  at  Paris  ?     What  are  the  spe- 
cific weights  of  lead,  tin,  mercury,  sulphur,  sodium,  and  lithium,  at  Paris  ? 
and  also  at  Boston  ? 

Mtiss. 

70.  What  is  the  mass  of  100   kilogrammes  of  iron  ?     What  are  the 
masses  of  50  grammes  of  sulphur,  of  40  grammes  of  mercury,  of  90  kilo- 
grammes of  granite,  when  the  value  of  g  is  9.810  ? 

71.  What  is  the  mass  of  75  kilogrammes  of  ice,  of  20  kilogrammes  of 
common  salt,  of  50  grammes  of  air,  when  g  =  9.810  ? 

72.  What  is  the  mass  of  a  cubic  decimetre  of  lead  ?     What  is  the  mass 
of  a  cubic  decimetre  of  ice  ?     Sp.  Gr.  of  Ice  =  0.930. 

73.  What  is  the  mass  of  1,000  cubic  metres  of  atmospheric  air  ?    What 
that  of  the  same  volume  of  hydrogen  gas  ? 

Density. 

74.  What  is  the  density  of  hammered  copper  ?     What  is  the  density 
of  the   following  substances,  —  lead,  tin,  mercury,  sulphur,   sodium,  and 
lithium  ?     Calculate  the  density  from  the  Sp.  W.  as  obtained  by  solving 
the  69th  example,  or  else  from  the  Sp.  Gr.  given  in  the  Table  at  the  end 
of  this    volume. 

75.  What  is  the  density  of  air,  of  oxygen,  of  hydrogen,  and  of  nitrogen, 


108  CHEMICAL   PHYSICS. 

at  the  temperature  of  0°  C.  and  under  a  pressure  of  76  c.  m.  ?  The 
relative  weight  of  one  cubic  decimetre  of  these  gases  will  be  found  in 
Table  II.  at  the  end  of  this  volume. 

Relative  Weight. 

76.  The  absolute  weight  of  a  body  at  Paris  is  500  gram.     What  is  its 
relative  weight  ? 

77.  The  relative  weight  of  a  body  at  New  Orleans  is  450  gram.     What 
is  its  absolute  weight  at  the  same  place  ?     The  latitude  of  New  Orleans 
is  29°  57'. 

78.  The  relative  weight  of  a  body  at  Paris  is  1,250  gram.     What  is  its 
absolute  weight  at  Boston  ? 

79.  The  relative  weight  of  a  body  is  12,300  gram.    What  is  its  absolute 
weight  at  Quito?     The  latitude  of  Quito  is  0°  13'.5,  and  its  elevation 
above  the  sea-level  is  2,908  metres. 

80.  The  relative  weight  of  a  body  is  5,450  gram.     What  is  its  mass  ? 
Find  also  the  masses  of  the  bodies  whose  weights  are  respectively  560 
gram.,  4,945  gram.,  and  500  gram. 

81.  The  relative  weight  of  a  body  is  5,255  gram.,  its  volume  is  500  cTniu3 
What  is  its  mass  ?  what  is  its  density  ?  and  what  is  its  specific  gravity  ? 

82.  The  specific  gravity  of  a  body  is  7.248,  and  its  volume  500  c7m~.3 
What  is  its  density,  mass,  and  weight  ? 

83.  The  mass  of  an  iron  cannon  is  5,000  units,  and  its  specific  gravity 
7.248.     What  is  its  volume  and  density  ? 

84.  The  specific  gravity  of  a  gas  referred  to  water  is  0.00143028,  and 
its  volume  500  nT3     What  is  its  density,  mass,  and  weight  ? 

85.  What  is  the  specific  weight,  the  mass,  and  the  density  of  500  c.  m.s 
of  mercury? 

Unit  of  Force. 

86.  A  body  having  a  density  of  2  units  and  a  volume  of  1,000  cTnf.3 
acquires,  under  the  influence  of  a  given  force,  an  acceleration  of  8  c.  m. 
each  second.     What  is  the  intensity  of  the  force  ? 

87.  A  body  whose  weight  is  100  kilogrammes  acquires  an  acceleration 
of  8  m.  each  second.     What  is  the  intensity  of  the  force  ? 

88.  A  body  whose  specific  gravity  is  2  and  whose  volume  is  50  nT.3  ac- 
quires an  acceleration  of  10  m.  each  second.     What  is  the  intensity  of 
the  force  ? 

89.  On  a  body  weighing  100  kilogrammes  a  force  of  15  kilogrammes 
is  constantly  acting.     What  acceleration  does  it  impart  to  the  body  ? 

90.  To  a  body  whose  volume  equals  10  m.3  a  force  of  300  kilogrammes 
imparts  a  constant  acceleration  of  10  m.     What  is  the  density  of  the 
body? 


GENERAL  PROPERTIES  OF  MATTER.  109 


ACCIDENTAL  PROPERTIES  OF  MATTER. 

(74.)  Divisibility.  —  We  have  now  considered  the  first  four 
of  the  general  properties  of  matter  enumerated  in  (7).  All 
of  these,  with  the  exception  of  weight,  are  essential  properties, 
and  are  necessarily  associated  with  the  very  idea  of  matter. 
The  four  general  properties  which  remain  to  be  studied  do  not 
seem  to  be  so  essential,  for  we  can  conceive  of  a  kind  of  matter 
which  should  not  possess  them.  This  is  true,  for  example,  of 
divisibility.  We  can  easily  conceive  of  a  kind  of  matter  so  hard 
as  to  be  physically  indivisible,  although  no  such  matter  is  known 
to  exist.  In  fact,  all  kinds  of  matter,  even  the  hardest,  can  be 
subdivided,  and,  so  far  as  we  know,  indefinitely  ;  the  only  limit 
to  our  power  of  subdivision  being  that  fixed  by  the  imperfection 
of  our  senses. 

The  extent  to  which,  in  some  cases,  the  subdivision  may  be 
carried  is  almost  incredible.  The  goldbeater  can  hammer  out  a 
single  gramme  of  gold  until  it  covers  a  surface  of  4,364  cTml2,  when 
the  gold-leaf  is  so  thin,  that  fifteen  hundred  such  leaves  placed 
upon  one  another  would  not  equal  in  thickness  a  single  leaf  of  ordi- 
nary writing-paper.  The  surface  of  gold  on  the  gilt  wire  used  in 
embroidery  is  much  thinner  even  than  this.  It  has  been  calcu- 
lated that  its  thickness  does  not  exceed  one  ten-millionth  of  a 
centimetre  ;  and  if  so,  with  the  aid  of  the  microscope  magnifying 
five  hundred  diameters,  a  particle  of  gold  can  be  distinguished 
upon  it  not  weighing  more  than  one  forty-two-million-millionth 
of  a  gramme. 

The  organic  kingdom  presents  us  with  examples  of  the  subdi- 
vision of  matter  which  are  still  more  remarkable.  The  micro- 
scope has  proved  the  existence  of  animals  which  are  as  minute  as 
the  particle  of  gold  mentioned  above,  and  yet  each  of  these  crea- 
tures is  composed  of  organs  of  locomotion  and  nutrition,  like 
the  larger  animals.  The  finest  human  hair  is  about  one  two- 
hundred-and-fortieth  of  a  centimetre  in  diameter.  This  is  gen- 
erally considered  very  fine ;  but  the  hair  is  a  massive  cable  in 
comparison  with  many  animal  fibres.  The  spider's  thread  is  in 
some  instances  not  more  than  one  twelve-thousandth  of  a  cen- 
timetre in  diameter,  and  yet  each  of  these  threads  is  formed 
by  the  union  of  from  four  to  six  thousand  fibrils.  It  has  been 
calculated  that  one  gramme  of  this  thread  would  reach  about 
fifty  miles. 

10 


110  CHEMICAL  PHYSICS. 

Science  has  not  succeeded  in  discovering  a  limit  to  the  divisi- 
bility of  any  one  kind  of  matter.  Nevertheless,  the  opinion  has 
been  maintained,  and  is  still  held  by  many  scientific  men,  that 
matter  is  not  indefinitely  divisible,  and  that  all  bodies  are  made 
tip  of  an  exceedingly  large  number  of  absolutely  hard,  and  hence 
indivisible  particles,  called  atoms.  According  to  the  atomic  the- 
ory, as  this  hypothesis  is  called,  the  ultimate  particles  of  matter 
are  indestructible  and  unchangeable,  and  hence  all  physical  and 
chemical  phenomena  are  caused  by  changes  in  their  relative  posi- 
tion or  grouping. 

As  these  atoms  are  supposed  to  be  far  smaller  than  the  minut- 
est portions  of  matter  which  we  can  distinguish  with  the  micro- 
scope, they  are  beyond  the  limits  of  direct  observation,  and  their 
existence  is  therefore  a  matter  of  inference  from  physical  and 
chemical  phenomena.  It  is  not  necessary,  however,  in  order  to 
explain  these  phenomena,  to  suppose  that  these  atoms  have  any 
absolute  size.  We  may,  with  Newton,  regard  them  as  infinitely 
small,  that  is,  as  mere  points,  or,  as  Boscovisch  called  them,  va- 
riable centres  of  attractive  and  repulsive  forces  ;  and  all  the  phe- 
nomena can  be  as  fully  explained  on  this  supposition  as  on  the 
other.  According  to  this  view,  matter  is  purely  a  manifestation 
of  force,  and  only  continues  to  exist  through  the  constant  action 
of  that  Infinite  Will  with  whom  all  force  originates.  As  it  will 
be  constantly  necessary  to  refer  to  these  centres  of  attractive 
and  repulsive  forces  in  matter,  we  will,  for  convenience,  term  the 
minute  portions  of  matter  in  which  they  may  be  supposed  to  re- 
side molecules,  and  the  forces  themselves  molecular  forces. 

(75.)  Porosity.  —  The  interstices  between  the  different  parts 
of  bodies  are  called  pores.  The  visible  cavities  of  the  sponge, 
for  example,  are  pores  of  a  large  size  ;  the  meshes,  of  which  its 
tissues  consist,  are  pores  of  a  smaller  size  ;  but  in  addition  to 
these,  there  are  pores  between  the  fibres  of  the  sponge  themselves, 
although  they  are  so  minute  that  they  cannot  be  seen.  In  like 
manner,  a  thin  slice  of  the  hardest  wood,  examined  under  the 
microscope,  is  found  to  be  full  of  pores  (see  Figs.  47,  48)  ;  and 
the  same  is  true,  to  a  greater  or  less  degree,  of  all  organic  struc- 
tures, as  well  as  of  the  tissues  which  are  manufactured  with 
animal  or  vegetable  fibres.  The  porosity  of  such  substances  is 
well  illustrated  by  the  process  of  filtering.  The  filters  which  are 
used  in  the  arts  and  in  chemical  experiments  are  simply  porous 


GENERAL  PROPERTIES  OF  MATTER. 


Ill 


Fig.  47. 


Fig.  48. 


bodies,  whose  pores  are  large   enough  to  allow  fluids  to  pass 

through  them,  but,  on  the  other  hand,  small  enough  to  arrest 

the  solid  particles,  which  they  hold  in 

suspension.     The   simplest   and    most 

useful  form  of  a  filter  is  a  cone   of 

porous    paper    supported   in   a    glass 

funnel. 

The  porosity  of  organic  substances 
may  also  be  illustrated  by  the  appa- 
ratus represented  in  Fig.  49.  It  con- 
sists of  a  glass  tube,  A,  closed  from 
above  by  a  plug  of  hard  wood  cut 
transversely  to  its  fibres,  or  by  a  piece 
of  chamois  skin,  as  is  represented  at  o. 
The  whole  is  surmounted  by  a  tunnel- 
shaped  cup,  which  may  be  filled  with 
mercury.  On  exhausting  the  tube  by 
means  of  an  air-pump,  the  pressure  of 
air  on  the  surface  of  the  mercury 
forces  it  through  the  pores  of  the  dia- 
phragm >  so  that  it  falls  in  showers 
through  the  tube. 

A  lump  of  chalk  plunged  under 
water,  and  placed  under  the  receiver 
of  an  air-pump,  will,  on  withdrawing 
the  air,  expel  a  torrent  of  air-bubbles,  which  had  been  concealed 


Fig.  49. 


112  CHEMICAL  PHYSICS. 

in  the  internal  pores  of  the  stone.  The  same  is  true  of  many 
other  varieties  of  stone.  There  is  a  kind  of  agate,  called  hydro- 
phane,  which  in  its  ordinary  state  is  only  semi-transparent,  but 
after  being  plunged  in  water  takes  up  about  one  sixth  of  its  bulk 
of  that  fluid,  and  becomes  nearly  as  transparent  as  glass.  The 
porosity  of  metals  was  proved  by  the  Academicians  of  Florence 
in  the  year  1661.  They  filled  a  hollow  ball  of  gold  with  water, 
and  submitted  it  to  great  pressure,  by  which  the  liquid  was 
made  to  ooze  through  the  pores  of  the  metal.  The  same  exper- 
iment has  since  been  repeated  on  different  metals,  and  with  like 
success. 

The  porosity  of  gases  and  liquids  is  proved  by  their  power  of 
penetrating  each  other  without  a  corresponding  change  of  vol- 
ume. This  is  illustrated  by  an  experiment  devised  by  Reau- 
mur. He  filled  a  long  tube  closed  at  one  end,  half  with  water 
and  the  remainder  with  alcohol.  Having  carefully  closed  the 
mouth  of  the  tube,  he  inverted  it  in  order  to  mix  the  two 
liquids,  when  he  found  that  a  contraction  of  the  liquids  took 
place. 

Another  experiment,  illustrating  the  same  property  in  regard 
to  gases,  is  the  following.  A  globe  containing  air  is  so  arranged 
that  small  quantities  of  liquids  can  be  introduced  into  it  without 
allowing  the  air  to  escape.  If,  now,  a  few  drops  of  alcohol  are 
made  to  enter  the  globe,  this  alcohol  will  evaporate  to  as  great  an 
extent  as  if  the  globe  were  empty,  and  the  space,  which  before 
contained  only  air,  will  now  contain  both  air  and  alcohol  vapor. 
If,  next,  some  ether  is  forced  into  the  globe,  this  liquid  will  also 
evaporate,  and  exactly  as  much  ether  vapor  will  be  formed  as  if 
the  globe  had  contained  previously  neither  air  nor  alcohol  vapor, 
and  we  shall  then  have  the  space  occupied  simultaneously  by 
air,  alcohol  vapor,  and  ether  vapor.  In  like  manner,  we  may  in- 
troduce any 'number  of  volatile  liquids  into  the  globe,  and  yet,  so 
far  as  we  know,  each  of  these  will  evaporate  to  the  same  extent 
as  if  the  globe  were  entirely  empty,  provided  only  that  these  sub- 
stances do  not  act  chemically  on  each  other.  We  may  thus  have, 
as  the  result  of  spontaneous  evaporation,  twenty  or  thirty  differ- 
ent vapors,  all  existing  simultaneously  in  the  same  space. 

By  the  experiments  which  have  been  cited,  the  porosity  of  most 
substances  can  be  abundantly  proved.  The  porosity  of  glass, 
however,  and  of  many  other  substances,  does  not  admit  of  such 


GENERAL  PROPERTIES  OF  MATTER.  113 

proof;  yet  in  these  substances  the  porosity  is  rendered  quite  evi- 
dent by  the  changes  of  bulk  which  they  undergo  under  the  in- 
fluence of  heat  and  cold. 

We  make  an  obvious  distinction  between  the  large  pores,  which 
exist  especially  in  organized  bodies,  and  the  intermolecular  spa- 
ces. The  first  arise  from  the  want  of  continuity  of  the  matter, 
and  may  be  regarded  in  a  measure  as  accidental,  varying  with 
the  structure  and  organization  of  the  body.  They  are  frequently 
visible  to  the  naked  eye,  or  at  least  become  evident  with  the  aid 
of  the  microscope.  The  last  arc  the  exceedingly  minute  and  in- 
visible spaces  which  exist  between  the  molecules  of  matter.  Those 
philosophers  who  have  admitted  the  existence  of  atoms,  have  gen- 
erally concurred  in  the  belief  that  the  atoms  even  of  the  densest 
solids  are  very  much  smaller  than  the  spaces  which  separate 
them.  Sir  John  Herschel  asks  why  the  atoms  of  a  solid  may  not 
be  imagined  to  be  as  thinly  distributed  through  the  space  it  oc- 
cupies, as  the  stars  that  compose  a  nebula  ;  and  compares  a  ray 
of  light  penetrating  glass  to  a  bird  threading  the  mazes  of  a 
forest. 

(76.)  Compressibility  and  Expansibility.  —  The  property  of 
porosity  necessarily  implies  that  of  compressibility  and  expansi- 
bility. According  to  the  atomic  theory,  any  body  is  capable  of 
an  indefinite  expansion,  because  we  may  conceive  of  the  dis- 
tance between  the  atoms  as  being  indefinitely  increased.  It 
could  only,  however,  be  compressed  till  the  atoms  come  in  con- 
tact. According  to  the  other  theory  of  the  constitution  of  mat- 
ter, advanced  in  (74),  a  body  is  capable  of  being  both  con- 
tracted and  expanded  indefinitely.  These  changes  of  volume 
are  most  readily  effected  by  the  action  of  heat,  and,  so  far  as  we 
know,  all  bodies  may  be  indefinitely  expanded  by  heat  and  con- 
tracted by  cold.  These  effects  of  heat  will  be  considered  at 
length  in  Chapter  IV.,  and  we  shall  therefore  only  allude  in  this 
place  to  a  few  examples  of  compression  produced  by  mechanical 
means. 

Pieces  of  oak,  ash,  or  elm,  plunged  into  the  sea  to  the  depth 
of  2,000  metres,  and  drawn  up  after  two  or  three  hours,  have 
been  found  to  contain  four  fifths  of  their  weight  of  water,  and  to 
acquire  such  an  increase  of  density  as  to  indicate  the  contraction 
of  the  wood  into  about  half  its  previous  volume.  Some  of  the 
metals  have  their  bulk  permanently  diminished  by  hammering ; 
10* 


114 


CHEMICAL   PHYSICS. 


and  so  also  in  the  process  of  coining,  the  volume  of  the  metal  is 
sensibly  diminished  by  the  pressure  to  which  it  is  submitted  under 
the  die.  The  stone  columns  of  buildings,  also,  when  they  sus- 
tain great  weights,  are  frequently  very  sensibly  shortened.  This 
was  the  case  with  the  columns  which  support  the  dome  of  the 
Pantheon  at  Paris. 

It  was  long  supposed  that  liquids  were  incompressible  ;  but 
they  are  now  known  to  be  compressible,  although  only  to  a  slight 

degree.  The  compressibility  of  liquids 
may  be  illustrated  by  the  apparatus  rep- 
resented in  Fig.  50.  It  consists  of  a 
very  thick  cylindrical  vessel  of  glass, 
eight  or  nine  centimetres  in  diameter, 
which  is  closed  at  the  bottom  and  sup- 
ported on  a  basement  of  wood.  To  the 
top  is  cemented  a  brass  cap,  into  which 
screws  a  copper  plate,  which,  when  in  its 
place,  completely  closes  the  cylinder ; 
but  which  can  be  unscrewed  at  pleas- 
ure, in  order  to  remove  and  replace  the 
tubes  A  and  B  within  the  cylinder.  To 
this  plate  are  adapted  the  tunnel  R,  for 
introducing  water  into  the  cylinder,  and 
a  cylinder  with  a  piston  for  exerting 
pressure,  which  can  be  moved  by  the 
screw  P.  Within  the  apparatus  is  the 
elongated  glass  bulb  A,  which  is  filled 
with  the  liquid  on  which  the  experiment 
is  to  be  made.  This  bulb  opens  into  a 
bent  capillary  glass  tube,  whose  open 
end  is  plunged  in  the  mercury  which  covers  the  bottom  of  the 
vessel.  At  the  side  of  this  apparatus  is  a  manometer  tube,  B, 
which  indicates,  in  a  way  which  will  be  hereafter  described,  the 
amount  of  pressure. 

In  using  the  apparatus,  the  bulb  A  is  first  filled  with  the  liquid 
to  be  compressed.  This  is  then  supported,  as  represented  in  the 
figure,  in  the  interior  of  the  cylinder,  with  the  open  end  of  the 
tube  dipping  under  the  mercury.  The  cylinder  is  now  filled 
with  water,  and  the  pressure  applied  by  turning  the  screw  P. 
The  mercury  will  then  be  seen  to  rise  in  the  capillary  tube,  indi- 


Fig.  50. 


GENERAL  PROPERTIES  OF  MATTER. 


115 


eating  a  compression  of  the  fluid  contained  in  the  bulb.  In 
order  to  measure  the  amount  of  compression,  the  capillary  tube 
is  graduated  into  parts  of  equal  capacity,  each  of  which  bears  a 
known  relation  to  the  capacity  of  the  bulb.  The  total  amount 
of  compression,  however,  which  we  can  thus  produce,  amounts 
only  to  a  few  millionths  of  the  original  volume. 

The  compressibility  of  gases  is  far  greater  than  that  of  either 
of  the  other  conditions  of  matter.  If  we  take  a  glass  cylinder 
closed  at  one  end,  Fig.  51,  and  insert  into 
it  an  accurately-fitting  piston,  it  will  be 
found  impossible  to  force  the  piston  into 
the  tube,  if  it  be  full  of  water ;  but  if  full 
of  air,  the  force  of  the  arm  is  sufficient  to 
drive  the  piston  down  so  as  to  reduce  the 
volume  of  air  ten  or  twenty  times,  if  the 
piston  is  small.  We  feel  the  resistance 
increase  in  proportion  to  the  compression  ; 
but,  whatever  may  be  the  force  exerted, 
we  cannot  make  the  piston  touch  the  bot- 
tom of  the  tube.  The  compressibility  of 
many  gases  is  also  limited  by  the  fact  that 
they  are  reduced  by  great  pressure  to  a 
liquid  state. 

(77.)  Elasticity.  —  The  property  which 
all  bodies  possess  to  a  certain  extent,  of 
resuming  their  original  form  or  volume 
when  the  force  which  altered  this  form  or 
volume  ceases  to  act,  is  called  elasticity. 
This  property  is  the  manifestation  of  a  ten- 
dency which  the  particles  of  bodies  possess,  to  maintain  a  certain 
distance  or  position  with  regard  to  each  other,  and  to  resume  that 
distance  or  position  when  they  have  been  disturbed.  The  phe- 
nomena of  elasticity  may  be  developed  in  solids  by  compression, 
by  tension,  by  flexure,  or  by  torsion.  In  fluids,  however,  elasticity 
can  be  developed  only  by  compression,  and  it  is  only  this  form 
of  elasticity,  therefore,  which  can  be  regarded  as  a  general  prop- 
erty of  matter. 

All  fluids,  both  liquid  and  gaseous,  are  perfectly  elastic  ;  and 
this  elasticity  is  unlimited  in  extent,  since  they  resume  exactly 
their  original  volume  as  soon  as  the  pressure  by  which  this  was 


Fig.  61. 


116  CHEMICAL   PHYSICS. 

diminished  is  removed,  however  long  it  may  have  been  ap- 
plied. 

Gases  tend  to  expand  indefinitely,  and,  other  circumstances 
being  equal,  a  definite  volume  always  corresponds  to  a  given 
pressure.  If  the  pressure  is  increased,  the  volume  diminishes, 
and  if  the  pressure  is  diminished,  the  volume  increases.  Hence, 
gases  are  frequently  called  permanently  elastic  fluids. 

The  elasticity  of  solids  is  not  perfect  and  unlimited,  like  that 
of  fluids.  In  some  solids,  such  as  glass,  it  appears  to  be  perfect ; 
for  no  force,  however  great  or  long  continued,  will  cause  glass  to 
take  a  set,  as  it  is  called,  that  is,  will  cause  a  permanent  change 
either  in  form  or  bulk.  But  then  this  elasticity  is  confined  within 
very  narrow  limits  ;  for  if  the  displacement  of  the  particles  ex- 
ceeds a  very  small  amount,  the  body  is  crushed.  In  other  solids, 
as  in  India-rubber  or  the  metals,  the  elasticity  is  less  limited  ; 
but  in  these,  if  the  compressing  force  exceeds  a  certain  amount, 
or  is  continued  beyond  a  limited  time,  there  remains  a  permanent 
change  of  form  or  bulk.  Within  these  limits,  however,  which 
differ  very  greatly  in  different  substances,  all  solids  appear  to 
be  perfectly  elastic.  It  is  in  the  limit  of  elasticity  that  we  find 
the  great  differences  between  bodies.  Thus,  a  ball  of  steel  or  of 
ivory  will  be  as  elastic  up  to  a  certain  point  as  a  ball  of  India- 
rubber,  as  may  be  proved  by  dropping  the  three  balls  upon  a 
hard  surface  from  the  same  height,  and  then  marking  the  heights 
to  which  they  rebound ;  but  while  the  elasticity  of  the  India-rubber 
extends  to  almost  any  degree,  that  of  the  others  is  very  limited. 
Even  lead  and  pipe-clay,  which  are  generally  considered  as  en- 
tirely devoid  of  elasticity,  show  an  elasticity  as  perfect  as  that  of 
the  best-tempered  steel,  but  within  very  narrow  limits. 


CHAPTER    III. 

THE  THREE   STATES   OF  MATTER. 

(78.)  Molecular  Forces.  —  The  forces  which  are  supposed  to 
emanate  from  the  molecules  of  matter,  and  which  we  have  termed 
molecular  forces,  are  either  attractive,  tending  to  draw  together 
the  molecules  of  a  body,  or  repulsive,  tending  to  drive  them  apart. 
The  three  states  of  matter  seem  to  depend  on  the  relative  inten- 
sity of  these  forces.  When  the  attractive  forces  are  in  excess,  tho 
molecules  of  a  body  are  held  together  more  or  less  firmly,  and  we 
have  the  solid  state.  When  the  attractive  forces  are  nearly  bal- 
anced by  the  repulsive  forces,  the  molecules  are  in  equilibrium 
and  endued  with  freedom  of  motion  among  themselves,  and  we 
have  the  liquid  state.  Finally,  when  the  repulsive  forces  are  in 
excess,  the  molecules  tend  to  recede  from  each  other,  and  we 
have  a  state  of  permanent  tension,  which  we  call  a  gas. 

In  regard  to  the  mode  of  action  of  these  molecular  forces,  we 
have  little  or  no  accurate  knowledge,  and  all  our  theories  in  re- 
gard to  them  are  inferences  from  the  phenomena  which  the 
aggregations  of  these  molecules,  the  masses  of  matter,  exhibit. 

The  attractive  forces  act  only  through  extremely  small  distances. 
Several  facts  may  be  cited  in  illustration  of  this.  If,  when  the 
flat  surfaces  of  two  hemispheres  of  lead  are  tarnished,  they  are 
pressed  together,  they  will  not  adhere.  If,  however,  the  super- 
ficial coating  of  oxide  is  removed  with  a  sharp  knife,  and  the 
two  clean  surfaces  are  then  pressed  together,  they  adhere  with 
great  force.  The  process  of  welding  iron  affords  an  illustration 
of  the  same  fact.  In  order  to  unite  two  bars  of  iron,  the  ends 
to  be  joined  are  first  softened,  by  heating  them  to  a  white  heat  in 
a  forge,  and  then  hammered  together  on  an  anvil.  The  com- 
plete union  of  the  bars  cannot  be  attained  in  this  process  unless 
the  coating  of  oxide,  which  forms  in  the  forge  on  the  heated 
surfaces,  is  dissolved  by  sprinkling  on  the  ends  of  the  bars  pow- 
dered borax,  or  some  similar  substance.  So  also  pieces  of  wax, 
dough,  India-rubber,  and  other  soft  substances,  cannot  be  made 


118  CHEMICAL   PHYSICS. 

to  adhere  when  their  surfaces  are  covered  with  dust,  but  can  be 
united  firmly  together  when  the  surfaces  are  clean.  Finally, 
plates  of  polished  glass  have  been  known,  simply  from  resting  on 
each  other  in  the  warehouse,  to  adhere  so  firmly  as  to  resist  all 
efforts  to  separate  them,  breaking  as  readily  in  any  other  direc- 
tion as  at  the  plane  of  junction.  The  thinnest  film  of  tissue- 
paper  interposed  between  them  is  sufficient  to  prevent  any  such 
adhesion. 

The  repulsive  forces  do  not  appear  to  be  so  inherent  in  the  par- 
ticles of  matter  as  the  attractive  force.  They  seem  to  be  due  to 
the  action  of  an  external  agent,  called  heat.  This  opinion  is  sup- 
ported by  many  facts^  The  first  effect  of  heat  on  a  solid  is  to 
expand  it,  that  is,  to  separate  the  molecules  from  each  other ;  but 
as  it  accumulates  in  the  body,  it  changes  its  condition,  first  into  the 
liquid,  and  subsequently  into  the  gaseous  state.  So  also,  when 
two  plates  of  glass  are  pressed  firmly  together,  the  minute  interval 
which  still  separates  them  is  increased  by  heating.  The  particles 
of  finely  divided  and  infusible  powders  repel  each  other  when 
intensely  heated,  and  the  powders  roll  round  in  the  crucible  as  if 
they  were  liquid  ;  and  lastly,  when  water  is  dropped  into  a  heated 
metallic  dish,  it  does  not  moisten  the  sides  of  the  dish,  but  is 
repelled  by  it  and  assumes  a  globular  form.  The  repulsion  is 
so  great,  that,  if  the  dish  is  pierced  with  holes,  like  a  sieve,  the 
water  will  not  run  out.  Since,  then,  heat  evidently  increases  the 
repulsive  forces  between  the  molecules  of  matter,  it  is  natural  to 
conclude  that  it  is  the  cause  of  these  forces,  and  this  hypothesis 
is  generally  admitted. 

In  studying  the  phenomena  of  matter  due  to  these  molecular 
forces,  it  will  be  convenient  to  class  them  under  two  heads : 
first,  those  phenomena  caused  by  the  action  of  these  forces  be- 
tween homogeneous  molecules,  such  as  the  molecules  of  the  same 
substance  ;  secondly,  those  phenomena  caused  by  the  action  of 
the  forces  between  heterogeneous  molecules,  such  as  those  of  dif- 
ferent substances.  To  the  first  class  belong  those  phenomena 
which  characterize  the  solid,  liquid,  and  gaseous  conditions  of 
matter ;  to  the  second,  the  phenomena  of  capillarity  (or  adhe- 
sion) and  diffusion. 


THE   THREE   STATES   OP   MATTER.  119 

MOLECULAR  FORCES  BETWEEN  HOMOGENEOUS   MOLECULES. 

I.  CHARACTERISTIC  PROPERTIES  OF  SOLIDS. 

Among  the  characteristic  properties  of  solids,  we  shall  consider 
the.  following:  —  Crystalline  Form,  Elasticity,  Resistance  to  Rup- 
ture, and  Hardness. 

Crystallography. 

(79.)  Crystalline  Form.  —  The  force  which  holds  together 
the  molecules  of  solids  is  called  cohesion;  and  the  most  ob- 
vious effect  of  this  force  is  to  retain  the  molecules  in  a  fixed 
position  with  reference  to  each  other,  and  hence  to  give  to  the 
solid  a  more  or  less  permanent  form.  Almost  all  solids,  when 
they  are  formed  slowly,  under  circumstances  such  that  the 
molecules  are  free  to  arrange  themselves  in  accordance  with 
the  tendencies  of  the  molecular  forces,  assume  definite  external 
forms.  These  forms,  with  certain  limitations,  are  always  the 
same  for  the  same  substance,  but  may  differ  in  different  sub- 
stances. They  are,  therefore,  essential  forms,  depending  upon 
the  nature  of  the  substance.  Such  forms  are  called  crystals,  and 
the  processes  by  which  they  are  obtained  are  called  processes  of 
crystallization. 

The  larger  number  of  inorganic  solids  which  we  meet  with  in 
every-day  life,  do  not  appear  to  have  any  regularity  of  outward 
form.  Their  form  is  generally  accidental,  one  which  has  been 
given  by  art,  or  which  is  due  to  the  accidental  circumstances 
under  which  the  solid  has  been  placed.  In  some  cases,  how- 
ever, if  we  break  the  solid  and  examine  the  fracture,  it  will  be 
seen  that  the  solid  is  an  aggregation  of  minute  crystals  closely 
packed  together.  This  is  the  case  with  granite  and  many  other 
rocks.  Other  solids  split  readily  along  certain  planes,  called 
planes  of  cleavage.  Both  these  classes  of  bodies  are  said  to 
have  a  crystalline  structure.  In  many  cases,  however,  no  indi- 
cations of  a  crystalline  structure  can  be  seen ;  but  in  almost  all, 
the  solid  can  be  made  to  assume  a  regular  crystalline  form  by 
one  of  the  processes  described  in  the  next  section. 

(80.)  Processes  of  Crystallization.  —  The  conditions  of  crys- 
tallization are  freedom  of  motion  in  the  molecules  from  which 
the  solid  is  forming,  and  sufficient  time  for  the  molecules  to  ar- 


120  CHEMICAL   PHYSICS. 

range  themselves  in  obedience  to  the  molecular  forces.  These 
conditions  are*  generally  obtained  in  one  of  four  ways. 

T^liQ  first  consists  in  dissolving  the  solid  in  water  or  some  other 
solvent,  and  allowing  the  liquid  to  evaporate  slowly.  As  the  solid 
is  slowly  deposited,  it  assumes  the  crystalline  form.  This  method 
is  the  most  universally  applicable,  and  the  one  by  which  crystals 
are  usually  formed  in  nature.  The  best  method  of  applying  it 
consists  in  making  a  concentrated  solution  of  the  substance  in 
water,  placing  the  solution  in  a  shallow  dish,  covering  the  dish 
with  porous  paper  fastened  tightly  round  the  edges  to  prevent 
dust  from  settling  upon  the  liquid,  and  leaving  it  in  a  moderately 
warm  place  until  the  crystallization  is  completed.  When  the 
substance  is  not  soluble  in  water,  it  can  generally  be  dissolved  in 
alcohol,  ether,  sulphide  of  carbon,  or  melted  boracic  acid,  instead 
of  water.  Sulphur,  for  example,  may  be  crystallized  from  a  so- 
lution in  sulphide  of  carbon ;  and  alumina  may  be  crystallized 
by  dissolving  it  in  melted  boracic  acid,  and  exposing  the  solution 
to  the  intense  heat  of  a  porcelain  furnace.  At  this  very  high 
temperature  the  boracic  acid  slowly  evaporates.  Most  substances 
are  more  soluble  in  hot  water  than  in  cold,  and  these  can  also  be 
crystallized  by  making  a  concentrated  hot  solution,  and  allowing 
it  to  cool ;  the  excess  of  the  solid  in  solution  over  that  which  cold 
water  will  dissolve,  is  deposited  in  crystals.  Unless,  however, 
the  quantity  of  the  solution  is  very  considerable,  large  and  per- 
fect crystals  are  not  so  frequently  formed  in  this  way  as  by  slow 
evaporation.  A  small  quantity  of  solution  cools  so  rapidly,  that 
sufficient  time  is  not  afforded  for  perfect  crystallization. 

The  second  method  consists  in  melting  the  solid  in  a  crucible, 
and  allowing  the  liquid  to  cool  very  slowly.  When  a  solid  crust 
forms  on  the  surface,  this  is  broken,  and  the  remaining  liquid 
turned  out,  when  the  inside  of  the  crucible  is  found  lined  with 
crystals.  Sulphur  and  many  of  the  metals  may  be  crystallized 
in  this  way. 

The  third  method  consists  in  converting  the  solid  into  vapor, 
and  subsequently  condensing  the  vapor  in  a  cool  receiver,  —  a 
process  which  is  called  sublimation.  Iodine,  arsenic,  arsenious 
acid,  and  many  other  substances,  can  be  crystallized  by  this 
method. 

The  fourth  method  consists  in  very  slowly  decomposing  some 
chemical  compound  containing  the  substance,  either  by  electricity 


THE   THREE   STATES    OP   MATTER.  121 

or  by  the  action  of  some  chemical  agent.  The  crystals  of  metals 
formed  in  the  processes  of  electro-metallurgy  are  the  best  exam- 
ples of  this  method. 

(81.)  Definitions.  —  A  crystal  is  always  bounded  by  plane 
faces,  and  is  therefore  a  polyhedron.  The  faces  of  the  diamond 
and  of  some  other  crystals  are  at  times  curved  ;  but  in  such 
cases  the  apparently  curved  surface  can  generally  be  seen  to  be 
made  up  of  a  large  number  of  very  small  planes.  The  terms 
of  solid  geometry  are  used,  without  change  of  meaning,  in  crys- 
tallography. Thus  we  speak  of  faces,  edges,  plane  angles,  intor- 
facial  angles,  and  solid  angles.  The  axis  of  a  crystal  is  a  line 
passing  through  its  centre,  round  which  two  or  more  faces  arc 
symmetrically  arranged.  In  every  crystal,  at  least  three  such 
lines  can  be  distinguished.  In  Figs.  52,  53,  and  54,  the  axes  are 
indicated  by  dotted  lines. 


Fig.  52.  Fig.  53.  Fig.  54. 

(82.)  Systems  of  Crystals.  —  A  crystal  is  a  solid  bounded  by 
planes  arranged  symmetrically  round  one  or  another  of  six  sys- 
tems of  axes. 

1.  The  first  system  (Fig.  55)  is 
called  the  Monometric  System,  and 
consists  of  three  axes,  of  equal 
length  and  at  right  angles  to  each 
other.  The  length  of  each  semi- 
axis  we  shall  represent  in  this  work 
by  «,  and  the  system  of  axes  by  the 
symbol  a  :  a  :  a.  It  is  hardly  ne- 
cessary to  observe,  that,  as  crystals 
may  vary  very  greatly  in  size,  the 
absolute  lengths  of  the  axes  must  rig.  55. 

vary  to  the  same  extent,  and  that  it  is  the  relative  lengths  only 
which  are  constant. 

11 


122  CHEMICAL  PHYSICS. 

2.  The  second  system  (Fig.  56)  is  called  the  Dimetric  System, 
and  consists,  like  the  last,  of  three  axes  at  right  angles  to  each 
other.  The  two  axes  in  the  horizontal 
plane  of  the  figure  are  called  the  lateral 
axes,  and  are  equal  to  each  other.  We 
shall  represent  the  length  of  each  half  of 
these  axes  by  a.  The  third  is  called  the 
vertical  axis,  and  is  either  longer  or  short- 
er than  the  other  two.  We  shall  represent 
the  length  of  each  half  of  this  axis  by  b. 
The  symbol  representing  this  system  of 
axes  is  a  :  a  :  b.  The  ratio  between  a 
and  b  is  irrational.  Thus,  in  crystals  of 
tin,  the  ratio  between  the  axes  is  a  :  b  = 

1 :  0.3857.    In  the  monometric  system  there  can  be  but  one  set  of 
axes  ;  but  in  this  system  there  can  be  as  many  sets  of  axes  as 
the  number  of  possible  irrational  ratios  between  a  and  b,  which 
is  of  course  infinite.     The  ratio  for  crys- 
tals of  the  same  substance  is  always  the 
same ;  but  it  differs  for  crystals  of  different 
substances,  no  two  substances  having  the 
same  ratio. 

3.  The  third,  system  (Fig  57)  is  called 
the  Hexagonal   System,  and  consists  of 
four  axes.     Three  of  these  are   in    the 
same  plane,  the  horizontal  plane  of  the 
figure,  and  are  called  lateral  axes.    They 
are  equal  in  length,  and  have  the  same 
relative  position  as  the  diagonals  of  a  reg- 
ular hexagon  (Fig.  58).     The  common  length  of  the  six  halves 
of  these  lateral  axes  we  shall  represent  by  a.     The  fourth  axis, 
called  the  vertical  axis,  is  at  right  angles  to  the  other  three,  and 
is  either  shorter  or  longer  than  their  common 
length.     The  length  of  one  half  of  this  axis  we 
shall  represent  by  b,  and  the  symbol  of  the  sys- 
tem of  axes   is  a  :  a  :  a  :  b.     The   relation  be- 
tween a  and  b  is,  as  in  the  last  system,  irrational. 
Fi   5g  Thus,  in  crystals  of  antimony,  a  :  b  =  1 :  1.3068, 

and  in  crystals  of  carbonate  of  lime  (calcite), 
a  :  b  =  1  :  0.8543.     Here,  as  in  the  last  system,  the  ratio  is  con- 


THE   THREE   STATES    OF   MATTER.  123 

stant  in  crystals  of  the  same  substance,  but  differs  in  crystals  of 
different  substances. 

4.  The  fourth  system  (Fig.  59)  is  called  the  Trimetric  System, 
and  consists  of  three  axes,  all  at  right  angles  to  each  other,  but 
all  of  unequal   length.      One   of  these 

axes  is  selected  as  the  vertical  axis,  and 
the  length  of  one  half  of  this  axis  will 
be  represented  in  this  work  by  b.  The 
shorter  of  the  two  lateral  axes  is 
called  the  br  achy  diagonal,  and  its  half- 
length  will  be  represented  by  a.  The 
longer  is  called  the  makrodiagonal,  and 
its  half-length  will  be  represented  by  c. 
The  symbol  of  this  system  of  axes  is  Fi  59 

a  :  b  :  c.     The    relation    between    a,  b, 

and  c  is  irrational.  In  crystals  of  sulphur,  a  :  b  :  c  =  1  : 
2.340  :  1.233. 

5.  The  fifth  system  (Fig.  60)  is  called  the  Monoclinic  System, 
and  consists  of  three  unequal  axes.     The  two  lateral  axes  are  at 
right  angles  to  each  other.     The  third 

axis,  called  the  vertical  axis,  is  at  right 
angles  to  one  of  the  lateral  axes,  but  is 
inclined  to  the  other.  The  length  of  one 
half  of  the  vertical  axis  we  shall  repre- 
sent by  b.  The  one  of  the  lateral  axes 
which  is  at  right  angles  to  the  vertical 
axis  is  called  the  orthodiagonal,  and  its 
half-length  will  be  represented  by  a. 
The  lateral  axis  which  is  inclined  to  the 
vertical  axis  is  called  the  klinodiagonal, 

and  its  half-length  will  be  represented  by  c.  The  value  of  the 
acute  angle  which  the  vertical  axis  b  makes  with  the  klinodiago- 
nal  c  will  be  represented  by  a.  The  symbol  of  this  system  is  the 
ratio  a  :  b  :  c,  with  the  angle  a.  For  the  crystals  of  the  same 
substance,  the  ratio  between  a,  b,  and  c,  and  the  value  of  a,  are 
constant ;  but  they  differ  in  crystals  of  different  substances.  In 
crystals  of  sulphate  of  iron,  for  example,  a :  b  :  c  =1 : 1.495  : 1.179, 
and  a  =  75°  40',  while  in  crystals  of  gypsum  a :  b  :  c  =  1 :  0.413  : 
0.691,  and  a  =  81°  26'. 

6.  The  sixth  system  (Fig.  61)  is  called  the  Triclinic  System, 


124 


CHEMICAL   PHYSICS. 


Fig.  61. 


and  consists  of  three  unequal  axes,  which  are  all  inclined  to  each 
other.  One  of  these  axes  is  selected  as  the  vertical  axis,  and  the 
half-length  of  this  axis  will  be  represent- 
ed by  b.  The  half-lengths  of  the  two 
lateral  axes  will  be  represented  by  a  and 
c.  The  angles  of  inclination  between  the 
axes  will  be  represented  as  follows :  — 

a  on  b  by  ^/, 
a  on  c  by  ft, 
b  on  c  by  a. 

The  symbol  of  this  system  is  the  ratio 
a  :  b  :  c,  with  the  angles  a,  ft,  y.  In 
crystals  of  sulphate  of  copper,  a  :  b  :  c  = 
1  :  0.9738  :  1.7683,  and  a  =  82°  21'.5,  ft  =  77°  37'.5,  -y  = 
73°  10'.5.  In  crystals  of  bichromate  of  potash,  a  :  b  :  c  = 
1  :  0.9886  :  1.794,  and  a  =  82°,  ft  =83°  47',  ;/=  89°  8'.5. 

All  crystals  which  have  the  same  system  of  axes  are  said  to 
belong  to  the  same  crystalline  system;  and  hence  all  crystals 
may  be  classified  under  six  crystalline  systems,  corresponding  to 
the  systems  of  axes  just  described.  The  systems  of  crystals  have 
the  same  names  as  the  systems  of  axes. 

(83.)  Centre  of  Crystal,  and  Parameters.  —  The  point  at 
which  the  axes  of  a  crystal  intersect  is  called  the  centre  of  the 
crystal. 

If  we  suppose  the  axes  of  a  crystal  indefinitely  produced,  it  is 
evident  that  each  of  its  planes,  if  also  produced,  must  intersect 
each  of  the  axes,  either  at  a  finite  or  at  an  infinite  distance  from 
its  centre.  The  distances  of  the  points  of  intersection  from  the 
centre  are  called  the  parameters  of  the 
planes.  Each  of  the  planes  of  the  crystal 
represented  in  Fig.  62,  for  example,  would, 
if  produced,  intersect  the  three  axes  of  the 
monometric  system  at  distances  from  the 
centre  equal  to  a  :  3  a  :  3  a  respectively, 
a  representing,  as  stated  above,  the  length 
of  any  semi-axis.  These  lengths  are  the 
parameters  of  each  plane  of  the  crystal. 
When  a  plane  is  parallel  to  a  given  axis,  it  may  be  regarded  as 
intersecting  it  at  an  infinite  distance  from  the  centre,  and  hence 


Fig.  62. 


THE   THREE   STATES   OF   MATTER. 


125 


Fig.  C3. 


Fig  64. 


its  parameter  measured  on  this  axis  is  infinity.  The  faces  of  a 
cube,  for  example,  intersect  one  axis  of  the  monometric  sys- 
tem at  the  distance  a  from  the  centre  (Fig. 
63),  and  are  parallel  to  the  other  two. 
The  parameters  of  each  face  are  therefore 
a  :  oo  a  :  cca.  So,  also,  each  of  the  faces 
of  the  dodecahedron  (Fig.  64)  intersects 
two  of  the  axes  of  the  monometric  system 
at  the  distance  a  from  the  centre,  and  is 
parallel  to  the  third  axis.  Hence  the  pa- 
rameters of  each  face  are  a  :  a  :  oo  a. 

It  has  already  been  stated  that  the  crys- 
tals of  a  given  substance  have  always  axes 
of  the  same  relative  lengths,  and  with  the 
same  relative  inclination.  It  is  also  true 
that  the  parameters  of  the  planes  of  any 
crystal  of  a  given  substance  are  always 
equal,  either  to  the  lengths  of  the  semi- 
axes  on  which  they  are  measured,  or  else  to  some  simple  multi- 
ples or  submultiples  of  these  lengths.  Hence  it  follows,  that  the 
parameters  of  any  plane  of  a  crystal  may  always  be  expressed 
very  simply  in  terms  of  its  axes,  as  above.  , 

(84.)  Similar  Axes.  —  In  any  system  of  axes,  one  axis  or  one 
semi-axis  is  said  to  be  similar  to  another  axis  or  to  another  semi- 
axis^  when  the  two  have  the  same  length  and  the  same  inclina- 
tions to  the  other  axes  or  semi-axes.  It  is  important  to  apply  this 
definition  to  the  different  systems,  and  distinguish  the  similar 
axes  in  each. 

1.  In  the  monometric  system,  all  the  axes  and  all  the  semi-axes 
are  similar. 

2.  In  the  dimetric  system,  the  two  lateral  axes  are  similar,  and 
also  the  four  halves  of  these  axes  are  similar.     The  two  halves  of 
the  vertical  axis  are  also  similar  to  each  other,  but  they  are  not 
similar  to  the  halves  of  the  lateral  axes. 

3.  In  the  hexagonal  system,  the  three  lateral  axes  are  similar, 
and  their  six  halves  are  also  similar.     The  two  halves  of  the  ver- 
tical axis  are  also  similar  to  each  other,  but  not  similar  to  the 
halves  of  the  lateral  axes. 

4.  In  the  trimetric  system,  all  three  axes  are  dissimilar,  but  the 
two  halves  of  each  axis  are  similar  to  each  other.     By  referring 

11* 


126  CHEMICAL   PHYSICS. 

to  the  notation  given  in  the  previous  sections,  it  will  be  seen  that 
in  the  first  four  systems  similar  semi-axes  have  in  every  case  been 
designated  by  the  same  letter,  and  that  the  dissimilar  semi-axes 
have  been  distinguished  by  different  letters. 

5.  In  the  monoclinic  system,  not  only  the  three  axes  are  all 
dissimilar,  but  moreover  the  two  halves  of  the  same  axis  are  not 
in  all  cases  similar  to  each  other.     The  two  halves  of  the  ortho- 
diagonal  are  similar,  but  the  two  halves  of  the  klinodiagonal,  al- 
though they  have  the  same  length,  have  not  the  same  inclination 
to  any  one  half,  say  the  upper  half,  of  the  vertical  axis,  and  are 
therefore  dissimilar.     The  same  is  true  reciprocally  of  the  two 
halves  of  the  vertical  axis.     In  order  to  distinguish  the  dissimilar 
halves  of  these  axes,  we  will  accent  the  b  when  it  refers  to  the 
lower  half  of  the  vertical  axis,  and  also  accent  the  c  when  it 
refers  to  the  half  of  the  klinodiagonal,  which  is  inclined  to  b  at 
an  obtuse  angle.     The  notation  of  the  monoclinic  system  of  axes 
is,  then,  as  follows  :  — 

a  =  either  half  of  the  orthodiagonal. 
b  =  the  upper  half  of  the  vertical  axis. 
b'  =  the  lower  half  of  the  vertical  axis. 
c  =  the  half  of  the  klinodiagonal  which 
is  inclined  to  b  at  an  acute  angle. 
c'  =  the  half  of  the  klinodiagonal  which 
is  inclined   to  b  at   an   obtuse 
angle. 
a  =  angle  of  b  on  c. 

It  is  evident  that  the  angle  of  b  on  c 
is  equal  to  the  angle  of  b'  on  c',  being 

vertical  angles ;  and  hence,  that  b  and  c  together  are  similar  in 
position  to  b'  and  c'  together. 

6.  In  the  triclinic  system,  all  the  semi-axes  are  dissimilar,  and 
the  two  halves  of  each  axis  may  be  distinguished  by  accentuation, 
as  in  the  monoclinic  system. 

(85.)  Similar  Planes.  —  Similar  planes  are  those  whose  param- 
eters, measured  on  similar  semi-axes,  are  equal.  There  is  no  diffi- 
culty in  distinguishing  similar  planes,  by  means  of  this  definition, 
in  any  except  the  last  two  systems  of  axes,  since  in  all  the  other 
systems  those  planes  are  similar  which  in  the  notation  here 
adopted  have  equal  parameters,  and  none  others. 

In  the  monoclinic  and  triclinic  systems,  however,  two  planes 


THE   THREE    STATES    OF   MATTER. 


127 


Fig.  66. 


are  similar,  not  only  when  they  have  equal  parameters,  but 
also  when  the  parameters,  measured  on  the  dissimilar  halves  of 
the  same  axes,  are  in  both  cases  oppositely  accented.  For  ex- 
ample, in  the  monoclinic  system,  two  planes  are  similar  whose 
parameters  are  a  :  2  b  :  c,  and  a  :  2  b1 :  c'.  In  the  two  symbols, 
the  two  halves  of  the  dissimilar  axes  are  oppositely  accented. 
On  the  other  hand,  two  planes  whose  parameters  are  a  :  2  b  :  c, 
and  a  :  2  b  :  c',  are  not  similar. 

In  the  triclinic  system,  since  the  six  semi-axes  are  all  dissimi- 
lar, no  two  planes  are  similar,  unless  the  three  parameters  of  the 
one  are  all  accented  oppositely  to  the  three  parameters  of  the 
other.  Thus,  two  planes  are  similar  whose  parameters  are 
a  :  b  :  2  c,  and  a'  :  b'  :  2  c',  respectively. 

(86.)  Holohedral  Crystalline  Form.  — 
A  holohedral  crystalline  form  is  the  union 
of  all  the  possible  similar  planes  which  can 
be  arranged  around  a  given  system  of  axes. 
Thus,  the  form  of  Fig.  66  is  the  union  of  all 
the  possible  planes  having  the  parameters 
a  :  a  :  2  a,  which  can  be  arranged  round 
the  monometric  system  of  axes.  So  also 
the  form  of  Fig.  67  is  the  union  of  all 
the  possible  planes  having  the  parameters 
a  :  a  :  oo  a  :  b,  which  can  be  arranged  round 
the  hexagonal  system  of  axes.  Both  of 
these  are  therefore  holohedral  forms. 

It  must  not,  however,  be  inferred  from 
these  examples  that  a  crystalline  form  is  al- 
ways a  crystal,  and  that  it  always  encloses 
space.     The  word  form  is  used  in  crystal- 
lography in  the  technical  sense,  as  defined 
above.     A  form  may  consist  of  only  two  planes, 
basal  planes  of  the  hexagonal  prism  (Fig.  68) 
are  a  crystalline  form,  because  they  are  all  the 
possible    planes,   having  the   parameters    oo  a  : 
oo  a  :  GO  a  :  £,  which  can  be  arranged  round  the 
hexagonal  system  of  axes.     In  like  manner,  the 
six  planes  on  the  convex  surface  of  the  prism, 
being    all    the    planes    having    the   parameters 
a:  a:  oo  a  :  oo  6,  which  can  be  arranged  round 


FL'.  67. 


Thus,  the  two 


Fig.  68. 


128  „,.  CHEMICAL  PHYSICS. 

the  same  system  of  axes,  form  another  holohedral  crystalline 
form.  In  neither  case  does  the  form  enclose  space.  It  requires 
the  combination  of  the  two  forms  to  complete  the  crystal.  In  the 
triclinic  system  no  crystalline  form  can  consist  of  more  than  two 
planes ;  and  hence  the  combination  of  at  least  three  crystalline 
forms  is  required  in  this  system  to  complete  a  crystal. 

The  parameters  of  one  of  the  planes  are  used  as  the  symbol  of 
the  holohedral  crystalline  form.  Thus,  the  parameters  printed 
below  the  Figs.  66  and  67  not  only  denote  the  position  of  each 
plane  of  the  form  with  reference  to  the  axes,  but  they  are  also 
used  as  the  symbol  of  the  form  itself.  "When  a  crystal  consists 
of  two  or  more  crystalline  forms,  like  the  one  represented  in 
Fig.  68,  we  use  as  the  symbol  of  the  crystal  the  several  symbols 
of  the  crystalline  forms  of  which  it  consists,  written  one  after 
the  other,  or  one  beneath  the  other,  as  convenience  may  dictate. 
Examples  of  these  symbols  may  be  seen  beneath  the  figures  of 
crystals  on  this  and  the  few  following  pages. 

(87.)  Hemihedral  Crystalline  Form.  —  A  hemihedral  crystal- 
line form  is  the  union  of  one  half  of  the  possible  similar  plane s, 
which  can  be  arranged  round  a  given  system  of  axes.  The  form 
represented  in  Fig.  69  is  the  union  of  all  the  possible  planes  hav- 
ing the  parameters  a  :  a  :  a,  which  can  be  arranged  round  the 

Fig.  69. 

Kg.  70.  Fig.  71. 


(a  :  a  :  a).  —  %  (a  :  a  :  a). 


monometric  system  of  axes,  and  is  therefore  a  holohedral  form. 
The  form  of  Fig.  70  is  the  union  of  one  half  of  the  planes  hav- 
ing the  same  parameters,  and  arranged  round  the  same  system 
of  axes.  It  is,  therefore,  a  hemihedral  form.  This  form  is  called 
the  tetrahedron,  and  it  may  be  regarded  as  derived  from  the  oc- 
tahedron, by  suppressing  every  other  plane  of  this  form  and  pro- 
ducing the  rest.  Hence,  it  is  frequently  called  the  hemihedral 
form  of  the  octahedron.  The  form  of  Fig.  70  is  obtained  by  pro- 


THE  THREE   STATES   OF   MATTER.  129 

ducing  one  set  of  the  alternate  planes  of  the  octahedron  of  Fig.  69. 
If,  now,  we  suppress  this  set  of  planes,  and  produce  the  other  set 
of  the  alternate  planes  of  the  octahedron,  we  shall  obtain  a  second 
tetrahedron  ;  differing,  however,  from  the  first  only  in  relative 
position.  This  form  is  said  to  be  the  negative  of  the  first.  We 
use,  as  the  symbol  of  a  hemihedral  form,  the  symbol  of  the  cor- 
responding holohedral  form,  preceded  by  the  fraction  J,  and  we 
distinguish  between  the  two  hemihedral  forms  of  which  the 
holohedral  form  may  be  supposed  to  consist,  by  means  of  the 
signs  plus  and  minus,  as  shown  by  the  symbols  beneath  Figs. 
70  and  71. 

(88).  Tetartohedral  Crystalline  Forms. — A  tetartohedral  crys- 
talline form  is  the  union  of  one  quarter  of  the  possible  similar 
planes  which  can  be  arranged  round  a  given  system  of  axes. 
Such  forms  are  met  with  among  crystals,  but  they  are  of  compar- 
atively rare  occurrence.  They  are  designated  by  writing  the 
fraction  J  before  the  symbol  of  the  corresponding  holohedral 
form. 

(89.)  Simple  and  Compound  Crystals.  —  A  crystal  is  said  to 
be  simple,  when  it  is  bounded  by  the  planes  of  one  crystalline 
form  only  ;  and  to  be  compound,  when  it  is  bounded  by  the  planes 
of  several  crystalline  forms.  Thus,  the  crystals  represented  by 

Fig.  74 

Fig.  72. 


:  oo  a  :  oo  a.  a  :  a  :  6.  a  :  a  :  ao  a  : 


Figs.  72,  73,  and  74  are  simple,  because  in  each  case  all  the 
planes  which  bound  the  crystal  have  the  same  parameters.  On 
the  other  hand,  the  crystals  represented  by  Figs.  75,  76,  and  77 
are  compound  crystals,  because  there  are  two  or  more  sets  of 
planes  on  each  crystal,  of  which  the  planes  have  different  param- 
eters. The  faces  of  the  crystals  are  lettered,  and  below  each 
crystal  the  parameters  of  each  set  of  planes  are  given  opposite  to 
the  corresponding  lettering. 


130 


Fig.  75. 


CHEMICAL  PHYSICS. 

Fig.  76. 


Fig.  7< 


a  =  a  :  oo  a  :  oo  6, 
o  =  a  :  a  :  b, 
3  =  a  :  a  :  3  6. 


—  4  (a  :  a  :  co  a  :  .',  &), 
2  7-*  ==  —  i  (a  :  a  :  oo  a  :  2  fc). 


Most  of  the  crystals  which  we  meet  with  are  compound  crys- 
tals. Indeed,  in  the  monoclinic  and  triclinic  systems,  we  cannot 
have  a  simple  crystal,  because  in  these  systems  no  single  crys- 
talline form  will  enclose  space,  and  simple  crystals  are  seldom 
found  in  any  of  the  systems,  with  the  exception  of  the  mono- 
metric  and  hexagonal. 

(90.)  Dominant  and  Secondary  Forms.  —  It  is  seldom  that 
the  faces  of  the  various  forms  of  which  a  compound  crystal 
consists  are  equally  developed  and  conspicuous.  As  a  general 
rule,  the  faces  of  one  form  are  more  prominent  than  those  of  the 
others,  and  give  to  the  crystal  its  general  aspect.  This  form  is 
then  called  the  dominant  form,  and  the  others  are  called  sec- 
ondary forms.  Figs.  78,  79,  and  80  represent  three  compound 
crytals,  each  of  which  consists  of  faces  of  a  cube  combined  with 


Fig  78. 


Fig.  79. 


:  oo  a  :  oo  a, 


Fig.  80. 


a  :  a  :  a, 

a  :  oo  a  :  oo  a. 


those  of  an  octahedron.  In  Fig.  78,  the  faces  of  the  cube  are  dom- 
inant, and  those  of  the  octahedron  are  secondary.  In  Fig.  79, 
the  two  sets  are  equally  developed,  and  in  Fig.  80  the  faces  of 
the  octahedron  are  dominant.  In  writing  the  symbols  of  com- 
pound crystals,  we  always  write  the  symbols  of  the  dominant 
form  first,  and  the  symbols  of  the  secondary  forms  in  the  order 
of  their  prominence. 


THE   THREE    STATES   OP   MATTER. 


131 


When  the  faces  of  the  dominant  form  are  so  much  developed 
as  to  give  their  general  aspect  to  the  crystal,  it  is  usual  to  de- 
scribe the  crystal  as  having  the  dominant  form  modified  by  the 
faces  of  the  secondary  forms.  For  example,  the  crystal  repre- 
sented in  Fig.  78  would  be  described  as  a  cube  modified  by  an 
octahedron,  and  the  crystal  of  Fig.  80  as  an  octahedron  modified 
by  a  cube.  In  Fig.  78,  the  solid  angles  of  the  cube  have  been 
replaced  by  planes  of  an  octahedron,  and  in  Fig.  80  the  solid  an- 
gles of  the  octahedron  have  been  replaced  by  planes  of  a  cube. 

(91.)  Definitions.  —  A  crystalline  form  may  modify  another 
in  different  ways,  and  several  technical  terms  are  used  in  de- 
scribing these  modifications,  which  it  is  important  to  understand. 

Truncation.  —  When  the  edge  of  a  crystal  is  replaced  by  a  plane 
equally  inclined  to  the  adjacent  faces,  and  forming  with  them 
parallel  edges,  the  edge  is  said  to  be  truncated.  In  like  manner, 
a  solid  angle  is  said  to  be  truncated  when  it  is  replaced  by  a 
plane  equally  inclined  to  the  similar  adjacent  faces.  Figs.  81, 

Fig  83. 


Fig  81. 


Fig  82. 


a  :  oo  a  :  oo  a, 
a  :  a  :  oo  a. 


Fig.  84. 


82,  83  are  examples  of  truncation  of  edges,  and  Figs.  78,  79,  80 
are  examples  of  truncation  of  solid  angles. 

Bevelling.  —  If  an  edge  is  replaced  by  two 
planes,  as  in  Fig.  84,  each  of  which  is  in- 
clined to  the  adjacent  face  at  the  same  angle, 
and  which  form  with  these  faces  parallel  in- 
tersections, the  edge  is  said  to  be  bevelled. 

Similar  edges  are  those  formed  by  the  in- 
tersection of  two  planes  which  are  similar 
each  to  each.  Similar  solid  angles  are 
those  formed  by  the  union  of  three  or  more 
planes  which  are  similar  each  to  each. 


132  CHEMICAL  PHYSICS. 

The  modifications  on  crystals  follow  one  of  two  simple  laws :  — 

1.  All  the  similar  parts  of  a  crystal  are  simultaneously  and 
similarly  modified. 

2.  Half  the  similar  parts  of  a  crystal  are  simultaneously  and 
similarly  modified  independently  of  the  other  half. 

It  sometimes,  although  more  rarely,  happens,  that  only  one 
quarter  of  the  similar  parts  of  a  crystal  are  simultaneously  and 
similarly  modified. 

The  modifying  planes  which  are  distributed  on  the  edges  and 
solid  angles  of  the  dominant  form  in  accordance  with  the  first 
law,  are  the  planes  of  holohedral  forms  ;  those  which  are  distrib- 
uted in  accordance  with  the  second  law,  are  the  planes  of  hemi- 
hedral  forms. 

(92.)  Forms  of  Crystals  belonging-  to  the  various  Systems.  — 
We  shall  only  be  able,  in  this  place,  to  give  figures  of  the  most 
important  forms  in  each  system,  and  must  refer  the  student  to 
the  special  works  upon  Mathematical  Crystallography,  for  a 
full  development  of  the  subject.  As  it  is  difficult  for  unpractised 
persons  to  obtain  a  perfect  conception  of  solids  from  projections, 
the  student  is  advised  to  prepare  models  of  the  more  important 
forms.  These  can  be  readily  made  with  the  outlines  of  crystal 
forms  which  are  given  in  several  German  works  on  Crystallogra- 
phy, and  which  have  in  several  cases  been  published  separately.* 
Crystal  models  of  wood  or  of  porcelain  can  be  obtained  from 
dealers  in  philosophical  instruments  ;  but  by  far  the  most  in- 
structive models  are  made  with  glass  faces  fastened  together  with 
strips  of  colored  paper  pasted  on  the  edges.  Each  set  of  similar 
edges  is  distinguished  by  its  special  color,  and  the  axes  are  indi- 
cated by  colored  strings  within  the  model.  The  mode  of  com- 
position of  compound  forms  may  be  beautifully  illustrated  by 
making  the  dominant  form  of  card,  and  then,  outside  of  this 
and  enclosing  it,  the  secondary  form  of  glass. 

MONO-METRIC  SYSTEM. 

The  simple  holohedral  forms  of  the  monometric  system  are 
seven  in  number,  and  are  named  as  follows,  the  numbers  above 
the  figures  corresponding  to  the  numbers  before  the  names. 

*  Krystallformennetze  zum  Anfertigen  von  Krystallmodellen,  von  Dr.  Adolf  Kenn- 
gott.  Wien,  1856.  To  be  procured  from  B.  Westermann  &  Co.  of  New  York. 


THE   THREE   STATES   OP   MATTER. 


133 


Simple  Holohedral  Forms. 
i. 


a  :  m  a  :  oo  a. 


1.  a 

2.  a 

3.  a 

4.  a 

5.  a 

6.  a 

7.  a 


Octahedron. 


a  :  a. 

a  :  m  a.      Trigonal  triakis-octahedron. 
ma  \ma.  Tetragonal  triakis-octahedron. 
m  a  :  n  a.   Hexakis-octahedron. 
a  :  oo  a.      Rhombic  dodecahedron, 
m  a  :  oo  a.  Tetrakis-hexahedron. 
oo  a  :  oo  a.  Hexahedron  (cube). 

12 


Kg.  85. 

Solid  bounded  by  8  equilateral  triangles. 

"          "  "  3  x  8  isosceles  " 

"  3X8  quadrilaterals. 

"  6x8  scalene  triangles. 

"  12  rhombs. 

"  4x6  isosceles  triangles. 

"  6  squares. 


134  CHEMICAL  PHYSICS. 

Three  of  these  forms  —  the  octahedron,  a :  a  :  a,  the  dodecahe- 
dron, a  :  a  :  GO  a,  and  the  hexahedron,  a  :  co  a  :  GO  a  —  have  inva- 
riable parameters,  and  therefore  do  not  admit  of  any  variation 
in  the  relative  position  of  their  planes.  They  are  frequently 
called  the  fundamental  forms  of  the  system.  The  parameters 
of  the  remaining  four  forms  are  variable,  and  the  exact  position 
of  their  planes  depends  on  the  values  given  to  m  and  w,  which 
are  always  very  simple  rational  numbers.  The  relation  between 
the  forms  can  easily  be  seen  from  the  disposition  of  the  crystals 
in  the  above  figures.  For  example,  in  the  trigonal  triakis-octahe- 
dron,  when  the  value  of  m  is  unity,  the  solid  angle  o  disappears, 
and  the  form  becomes  an  octahedron.  As  we  give  to  m  larger  and 
larger  values,  the  angle  o  becomes  more  and  more  prominent ; 
and,  finally,  when  m  =  oo,  the  two  planes,  meeting  at  the  edge 
d,  coincide,  and  the  form  becomes  the  dodecahedron.  There 
may,  therefore,  be  an  infinite  number  of  trigonal  triakis-octahe- 
drons,  varying  between  the  two  limits  of  the  octahedron  on  the 
one  side,  and  the  dodecahedron  on  the  other.  By  drawing  a 
series  of  these  forms  with  gradually  increasing  values  of  m,  the 
relation  can  easily  be  made  evident  to  the  eye.  In  like  manner, 
the  tetragonal  triakis-octahedron  is  an  intermediate  form  between 
the  octahedron  and  the  cube,  and  within  these  two  limits  there 
may  be  an  infinite  number  of  forms  with  different  values  of  m. 
In  fact,  however,  only  a  very  few  of  the  possible  varieties  of 
either  of  these  forms  have  been  found  in  nature,  the  most  fre- 
quent occurring  values  of  m  being  f,  2,  f,  and  3. 

Again,  the  tetrakis-hexahedron  is  a  variable  form,  intermediate 
between  the  dodecahedron  and  the  cube.  When  m  =  1,  the  pair 
of  faces  meeting  at  m  coincide,  and  we  have  the  dodecahedron. 
As  the  value  of  m  increases,  the  solid  angle  at  A  becomes  more 
and  more  obtuse,  until,  when  m  =  oo,  the  four  planes  meeting  at 
A  coincide,  and  we  have  a  cube.  Finally,  the  hexakis-octahedron 
is  the  central  form  of  the  triangular  group.  It  can  easily  be  seen 
that  it  is  intermediate  between  the  octahedron  and  the  tetrakis- 
hexahedron,  between  the  cube  and  the  trigonal  triakis-octahedron, 
and,  lastly,  between  the  dodecahedron  and  the  tetragonal  triakis- 
octahedron.  To  trace  out  these  relations,  both  in  the  symbols 
and  the  forms,  is  left  for  an  exercise  to  the  student. 


THE  THREE   STATES    OP   MATTER. 


135 


Simple  Hemihedral  Forms. 
1.  Oblique  Hemihedral  Forms. 


-j-  i  (a  :  a  :  oot/) 


-f-  j  (a  :  m  a  :  oo 

Fig.  86. 


-f  i(<: 


' "). 


There  are  two  groups  of  simple  hemihedral  forms  in  the  reg- 
ular system.  The  opposite  planes  of  the  characteristic  forms 
of  the  first  of  these  groups  are  inclined  to  each  other,  while 


136 


CHEMICAL  PHYSICS. 


those  of  the  second  are  parallel.  Hence  the  forms  of  the  first 
group  have  been  called  oblique  hemihedral  forms ;  those  of  the 
second,  parallel  hemihedral  forms.  The  symbols  of  the  oblique 
hemihedral  forms  are  formed  by  writing  J  before  the  symbol  of 
the  corresponding  holohedral  form  enclosed  in  parentheses,  thus : 
\  (a  :  m  a  :  m  a).  The  symbols  of  the  parallel  hemihedral  forms 
are  formed  by  writing  £  before  the  symbol  of  the  corresponding 
holohedral  form  enclosed  in  brackets,  thus :  J  [a  :  m  a  :  m  a~\ . 

The  oblique  hemihedral  forms  of  the  monometric  system, 
which  are  seven  in  number,  are  represented  in  Fig.  86.  Each 
of  these  forms  has  a  holohedral  form  corresponding  to  it  in  posi- 
tion in  Fig.  85.  They  are  named  as  follows  :  — 


a  :  a).  Tetrahedron. 

«  :  ma).  Tetragonal  triakis-tetrahedron. 

m  a  :  m  a).  Trigonal  triakis-tetrahedron. 

main  a).  Hexakis-tetrahedron. 

a  :  oo  a).  Dodecahedron. 

ma  :  oo  a).  Tetrakis-hexahedron. 

oo  a  :  oo  a).  Hexahedron  (cube). 


Solid  bounded  by 
4  equilateral  triangles. 
3x4  quadrilaterals. 
3X4  isosceles  triangles. 
6X4  scalene         " 
12  rhombs. 
4x6  triangles. 
6  squares. 


The  mode  by  which  the  tetrahedron  is  derived  from  the  oc- 
tahedron has  already  been  explained.  In  Fig.  87,  the  planes 
of  the  octahedron  which  are  suppressed  are 
shaded,  and  those  which  are  extended  are  left 
light.  By  comparing  this  figure  with  the  fig- 
ure  of  the  hexakis-octahedron  (Fig.  88),  in 
which  the  parts  corresponding  in  position  to  the 
shaded  parts  of  the  octahedron  have  also  been 
shaded,  and  the  reverse,  it  will  be  seen  that  a 
group  of  six  planes  corresponds  in  position, 
on  this  form,  to  a  single  plane  on  the  octahe- 
dron. If,  now,  we  extend  the  parts  on  this 
form  corresponding  to  the  parts  which  were 
extended  on  the  octahedron,  that  is,  every 
other  set  of  six  planes,  those  left  light  in  the 
figure,  we  shall  obtain  the  hexakis-tetrahedron, 
a  form  which  bears  the  same  relation  to  the 
tetrahedron  that  the  hexakis-octahedron  does 
to  the  octahedron. 
In  like  manner,  if  we  apply  the  same  principle  to  the  trigonal 
triakis-octahedron  and  to  the  tetragonal  triakis-octahedron,  extend- 


Fig.  88. 


a  :  m  a  :  n  a. 


THE   THREE   STATES   OF   MATTER. 


137 


Fig  89. 


a  :  oo  :  GO  a. 


fig.  90. 


ing  in  these  cases  every  other  set  of  three  planes,  and  suppressing 
the  alternate  sets,  we  shall  obtain  the  tetragonal  triakis-tetrahe- 
dron and  the  trigonal  triakis-tetrahedron.  It  will  be  noticed, 
however,  that  the  trigonal  triakis-octahedron  gives  the  tetragonal 
triakis-tetrahedron,  and  the  reverse. 

On  Fig.  89,  the  portions  of  the  cube  corresponding  in  position 
to  the  planes  of  the  octahedron  which  were  suppressed  are  shaded, 
and  it  can  be  easily  seen,  that,  if  those  portions 
of  the  cube  faces  which  are  not  shaded  are  ex- 
tended, they  will  form  again  a  cube.  The  same 
is  true  of  the  tetrakis-hexahedron,  as  may  be 
seen  by  Fig.  90,  and  also  of  the  dodecahedron. 
In  other  words,  the  same  process  by  which  the 
tetrahedron  is  derived  from  the  octahedron,  ap- 
plied to  these  three  forms,  reproduces  these 
forms  again.  These  forms  are  at  once  both 
holohedral  and  oblique  hemihedral  forms,  and 
have  therefore  a  place  in  both  groups. 

The  seven  oblique  hemihedral  forms  bear 
similar  relations  to  each  other  to  those  sus- 
tained by  the  holohedral  forms,  which  have 
been  already  fully  explained.  The  tetrahedron, 
the  dodecahedron,  and  the  cube  are  invariable 
forms.  The  rest  admit  of  limited  variation  in  the  position  of 
their  faces,  depending  on  the  values  of  their  parameters.  Thus, 
the  tetragonal  triakis-tetrahedron  is  an  intermediate  form  between 
the  tetrahedron  and  the  dodecahedron,  admitting  of  every  possible 
variation  between  these  two  limits.  So  also  tlie  trigonal  triakis- 
tetrahedron  is  an  intermediate  form  between  the  tetrahedron  and 
the  cube,  and  the  hexakis-tetrahedron  an  intermediate  between  all 
the  forms  of  the  groups.  These  relations  can  easily  be  studied 
out  by  the  student,  both  by  means  of  the  symbols  and  also  by 
means  of  the  figures  of  the  forms. 

Corresponding  to  each  of  the  hemihedral  forms  of  Fig.  86, 
there  is  an  inverse  form,  which  would  be  generated  by  extending 
the  alternate  planes,  or  sets  of  planes,  which  were  suppressed 
before.  The  negative  forms  differ  from  the  corresponding  posi- 
tive forms  only  in  their  position.  In  any  case,  if  the  negative 
form  is  turned  round  on  its  vertical  axis  one  quarter  of  a  revolu- 
tion, it  will  coincide  with  the  positive  form. 
12* 


138 


CHEMICAL  PHYSICS. 
2.  Parallel  Hemihedral  Forms. 


\         -{-  %  [a  :  ma:  na], 
6. 


-f  i  [a  :  a  :  oo  a]. 


-f-  i  [a  :  m  a  :  oo  a]. 
Fig.  91. 


[a  :  c»  a  :  co  a]. 


The  parallel  hemihedral  forms  of  the  monometric  system  may 
be  generated  by  extending  alternate  pairs  of  planes  of  the  hexakis- 
octahedron,  or  the  portions  of  planes  which  correspond  to  these  pairs 
on  the  other  forms.  In  Fig.  92,  the  planes  of  the  hexakis-octahe- 


THE   THREE   STATES   OF   MATTER. 


139 


dron,  which  are  suppressed  in  this  process,  are 
shaded,  and  those  to  be  extended  left  light.  The 
extension  of  the  latter  set  of  planes  leads  to  the 
central  form  of  Fig.  91,  which  is  called  the  diakis- 
dodecahedron.  If,  now,  we  extend  the  portions  of 
planes  on  the  other  forms  which  correspond  to  the 
alternate  pairs  on  the  hexakis-octahedron  in  po- 
sition, we  shall  obtain  in  the  case  of  the  tetrakis-hexahedron  the 
pentagonal  dodecahedron;  but  in  all  the  remaining  five  forms 
this  extension  will  reproduce  the  original  form.  In  Figs.  93,  94, 

Fig.  93.  Fig.  94.  Fig.  95.  Fig.  96. 


a  :ma  :  na. 


a  :  a  :  m  a. 


:  oo  a  :  oo  a. 


95,  96,  the  portions  which  correspond  in  position  to  the  alter- 
nate pairs  of  the  hexakis-octahedron,  on  the  octahedron,  the  two 
triakis-octahedrons,  the  dodecahedron,  and  the  cube,  are  left  light, 
and  it  can  easily  be  seen  that  the  extension  of  these  portions 
will  reproduce  the  original  form.  It  appears,  therefore,  that  the 
same  process  by  which  the  diakis-dodecahedron  is  derived  from  the 
hexakis-octahedron,  and  the  pentagonal  dodecahedron  from  the 
tetrakis-hexahedron,  applied  to  the  other  five  simple  holohedral 
forms,  reproduces  these  forms  again.  These  forms  are,  therefore, 
at  once  holohedral  and  parallel  hemihedral  forms,  and  have  a 
place  in  both  groups.  It  will  also  be  noticed  that  the  rhombic 
dodecahedron  and  the  cube  belong  to  all  three  groups. 

It  is  not  necessary  to  enumerate  the  names  of  the  seven 
simple  forms  of  this  group,  since  they  are  the  same  as  those 
of  the  holohedral  group,  with  the  exception  of  the  two  whose 
names  have  just  been  given.  The  symbols  of  the  parallel  hemi- 
hedrons  are  the  same  as  those  of  the  corresponding  oblique  hemi- 
hedrons,  with  the  exception  that  the  bracket  is  used  in  place  of 
the  parenthesis.  The  forms  of  Fig.  91  are  all  positive,  but  a  cor- 
responding group  of  negative  forms  can  easily  be  constructed,  by 
extending  the  alternate  planes  or  portions  of  planes  which  were 
suppressed  before,  that  is,  those  which  are  shaded  in  Figs.  92, 
93,  94,  95,  96. 


140  CHEMICAL  PHYSICS. 

The  relations  between  the  seven  parallel  hemihedral  forms  are 
similar,  in  all  respects,  to  those  which  exist  between  the  forms  in 
the  other  two  groups.  The  octahedron,  the  rhombic  dodecahe- 
dron, and  the  cube  are,  as  before,  invariable  forms.  The  remain- 
ing four  are  variable  forms,  the  exact  position  of  the  planes  de- 
pending on  the  values  of  the  parameters.  Since,  after  the  details 
already  given,  the  relations  of  these  forms  can  easily  be  traced  by 
the  student,  we  need  not  dwell  upon  the  subject. 

Compound  Forms. 

It  is  only  the  forms  of  the  same  group  which  arc  found  united 
on  the  same  crystal.  For  example,  we  find  the  cube  and  the 
rhombic  dodecahedron,  which  are  common  to  the  three  groups, 
combined  with  any  one  of  the  other  simple  forms  of  the  system,  but 
we  never  find  the  octahedron  combined  with  the  hexakis-tetrahe- 
dron,  nor  the  pentagonal  dodecahedron  combined  with  the  tetra- 
hedron. In  order  to  become  familiar  with  the  compound  forms  of 
this  system,  the  best  method  is  to  study  each  form  in  succession, 
and  consider  how  it  will  be  modified  by  each  of  the  other  forms 
of  the  system,  when  it  is  the  dominant  form  in  the  combination. 
After  the  description  which  has  been  given  of  the  simple  forms  of 
the  system,  the  student  will  be  able,  with  a  little  study,  to  dis- 
cover the  nature  of  the  modifications  in  each  case,  and  he  can 
confirm  his  results  by  referring  to  the  figures  of  the  compound 
forms  given  in  the  larger  works  on  Crystallography.*  We  will 
take  the  case  of  the  octahedron  as  an  illustration. 

The  cube  modifies  the  octahedron  by  truncating  its  solid  angles. 
The  rhombic  dodecahedron  modifies  it  by  truncating  its  edges ; 
the  tetragonal  triakis-octahedron  by  replacing  its  solid  angles 
by  four  planes,  which  are  variously  inclined  on  the  faces  of  the 
octahedron,  the  inclination  depending  on  the  value  of  m  in  the 
symbol  of  the  modifying  form,  a:  ma:  m  a.  The  trigonal  triakis- 
octahedron  bevels  the  edges  of  the  octahedron,  the  interfacial 
angle  between  the  bevelling  planes  and  the  faces  of  the  octahe- 
dron depending  on  the  value  of  m  in  the  symbol  of  the  modifying 
form,  a  :  a  :  m  a.  The  hexakis-octahedron  replaces  the  solid  an- 
gles of  the  octahedron  by  eight  planes,  whose  inclination  on  the 
faces  of  the  dominant  form  depends  on  the  values  of  m  and  n  in 

*  See  the  plates  of  Naumann's  "  Lehrbuch  dcr  Krystallographie."     Leipzig.    1 830. 


THE   THREE   STATES    OF   MATTER. 


141 


the  symbol  of  the  modifying  form,  a:  ma  in  a.  Finally,  the 
tetrakis-hexahedron  replaces  the  solid  angles  of  the  octahe- 
dron by  four  planes  inclined  on  the  edges  of  the  dominant 
form  at  angles  which  depend  on  the  value  of  m  in  the  symbol 
a  :  m  a  :  oo  a. 

We  give  below  several  figures  of  compound  crystals.  The 
symbols,  which  are  also  added,  will  furnish  a  sufficient  descrip- 
tion of  the  forms. 


a  :  oo  a  :  oo  a, 
a  :  a  :  a. 


a  :  oo  a  :  oo  a, 
a  :  a  :  oo  a. 


a  :  oo  a  :  oo  a, 
a  :  m  a  .  ao  a. 


a  :  a  :  a, 

a  :  oo  a  :  oo  a. 


a  :  oo  a  :  oo  a, 
a  :  a  :  ooa, 


+  Ha:a:a), 
—  £  (a  :  a  :  a). 


Fig.  97. 


CHEMICAL  PHYSICS. 

DIMETRIC  SYSTEM. 
Simple  Holohedral  Forms, 


The  most  important  simple  forms  of  the  dimetric  system  are 
represented  in  Fig.  98,  and  the  forms  have  been  grouped  so  that 
the  relation  between  them  can  be  easily  seen.  We  can  study  this 


THE   THREE   STATES   OF   MATTER.  143 

relation  to  the  best  advantage,  by  commencing  with  No.  2,  which 
is  called  the  square  octahedron,  and  whose  symbol  is  a  :  a  :  b. 
When  the  length  of  the  semi-axis  b  is  greater  than  that  of  o,  as 
is  the  case  in  crystals  of  sulphate  of  nickel,  where  a  :  b  = 
1  :  1.906,  then  the  octahedron  is  acute,  like  No.  3.  When, 
however,  the  length  of  the  semi-axis  b  is  less  than  that  of  a,  as 
is  the  case  in  crystals  of  acid  phosphate  of  potassa,  where 
a  :  b  =  1  :  0.664,  then  the  octahedron  is  obtuse,  like  No.  2. 

In  the  monometric  system,  we  can  have  only  one  octahedron  ; 
but  in  the  dimetric  system  the  same  substance  frequently  pre- 
sents several  octahedrons.  In  all  cases,  however,  if  we  reduce 
the  octahedrons  to  the  same  base,  the  lengths  of  their  vertical 
axes  will  bear  to  each  other  very  simple  and  rational  ratios. 
Thus,  for  example,  on  crystals  of  sulphate  of  nickel  we  find  octa- 
hedrons, where  the  ratio  of  the  two  semi-axes  is  not  only  1 : 1.906, 
but  also  1  :  0.953  and  1  :  0.635.  The  first  of  these  octahedrons 
has  been  selected  as  the  principal  form  of  this  substance,  because 
it  is  the  one  which  is  the  most  frequently  seen,  and  which,  in  com- 
pound crystals,  is  generally  the  dominant  form.  To  the  planes 
of  this  form  we  give  the  symbol  a  :  a  :  b,  and  then  the  symbols 
of  the  other  octahedrons  are  a  :  a  :  \  b,  and  a  :  a  :  £  b. 

When  a  substance  presents  several  octahedrons,  we  are  guided 
in  the  selection  of  one  of  these  for  the  principal  form  by  many 
circumstances.  Among  these  may  be  mentioned  the  frequency 
of  occurrence,  the  predominance  of  the  planes  of  the  different 
octahedrons  on  compound  crystals,  the  position  of  the  planes  of 
cleavage,  and  the  crystalline  form  of  other  substances  which  are 
analogous  in  composition  and  homceomorphous*  with  it.  The 
selection  is  in  all  cases,  however,  more  or  less  arbitrary,  and  we 
must  be  careful  in  comparing  the  crystalline  forms  of  different 
substances  to  keep  this  fact  in  view,  since  otherwise  we  might  be 
led  to  erroneous  conclusions,  f 

Having,  then,  in  the  case  of  a  given  substance  crystallizing  in 
the  dimetric  system,  selected  one  octahedron  as  the  principal 
form,  and  given  to  it  the  symbol  a  :  a  :  b,  we  may  have  on  crys- 
tals of  this  same  substance  an  infinite  number  of  other  octahe- 
drons, having  the  general  symbol  a  :  a  :  mb,  where  m  is  always 

*  Two  substances  are  said  to  be  homceomorphous,  when  they  crystallize  in  forma 
which  arc  closely  allied. 

t  See  Dana's  System  of  Mineralogy,  Vol.  I.  p.  192  and  following. 


144  CHEMICAL  PHYSICS. 

a  very  simple  rational  integer  or  fraction.  Thus  we  may  have 
octahedrons  whose  symbols  are 

a  :  a  :  2  b,  or  a  :  a  :  J  b.    , 

a  :  a  :  3  6,  «  a  :  a  :  $  b. 

a  :  a  :  4  6,  "  a  :  #  :  J  6. 

As  the  value  of  w  increases,  the  octahedrons  become  more  and 
more  acute ;  and  finally,  when  m  =  oo,  the  octahedral  planes 
become  parallel  to  the  vertical  axis,  and  we  have  the  square 
prism  whose  symbol  is  a  :  a  :  co  b  (No.  4,  Fig.  98).  This  we 
may  regard  as  one  limit  of  the  series  of  octahedrons.  On  the 
other  hand,  as  the  value  of  m  diminishes,  the  octahedrons  be- 
come more  and  more  obtuse  ;  and  finally,  when  m  =  o,  the  octa- 
hedral planes  coincide  with  the  basal  plane,  No.  1,  which  we  may 
regard  as  the  other  limit  of  the  series.  The  symbol  of  the  basal 
plane  may  be  written  either  a  :  a  :  0  &,  or,  as  is  more  usual, 
oo  a  :  oo  a  :  b,  which  is  obtained  from  the  first  by  multiplying  each 
parameter  by  oo,  remembering  that  0  X  co  =  1. 

It  will  be  noticed  that  neither  the  square  prism  nor  the  basal 
plane  encloses  space,  and  therefore  neither  can  alone  constitute 
a  crystal.  The  two  combined  form  a  square  prism  with  its  basal 
plane,  which  is  therefore  a  compound  crystal. 

In  the  monometric  system,  the  axes  of  the  octahedron  always 
unite  the  vertices  of  the  opposite  solid  angles.  In  the  dimetric 
system,  also,  the  vertical  axis  always  unites  the  vertices  of  the 
two  solid  angles  forming  the  summits  of  the  octahedron,  but  the 
lateral  axes  may  have  two  positions.  They  may  either  unite  the 
solid  angles  or  the  centres  of  opposite  basal  edges.  The  two  posi- 
tions which  these  axes  may  assume  are  represented  in  Figs.  99, 
100,  which  represent  sections  through  the  base  of  the  octahedron. 

We  may  thus  have  two  octa- 
hedrons, such  as  Nos.  3  and 
11,  of  different  dimensions, 
but  yet  having  axes  which 
are  perfectly  equal.  The  fa- 
ces of  the  octahedron  whose 
Fl*-99-  F|s-m  base  is  represented  by  Fig. 

100  have  the  same  position  as  the  edges  of  the  octahedron  whose 
base  is  represented  by  Fig.  99.  We  distinguish  the  two  octahe- 
drons by  calling  the  one  represented  in  No.  3  the  direct  octahe- 


THE  THREE   STATES   OF   MATTER.  145 

dron,  and  the  one  represented  in  No.  11  the  inverse  octahedron. 
Since  the  external  appearance  of  the  two  octahedrons  is  precisely 
the  same,  it  is  not  always  possible  to  determine  to  which  form  a 
given  crystal  belongs ;  and  this  fact  introduces  a  still  further 
difficulty  in  determining  the  principal  form  of  a  substance. 

The  general  symbol  of  the  inverse  octahedron  is  a  :  oo  a  :  m  6, 
where  m  represents  any  simple  rational  integer  or  fraction.  Thus 
we  may  have  inverse  octahedrons  on  crystals  of  the  same  sub- 
stance, whose  symbols  are 

a  :  oo  a  :  b,  or  a  :  oo  a  :  \  b. 

a  :  &  a  :  2b,  "  a  :  oo  a  :  J  b. 

a  :  GO  a  :  3  b,  "  a  :  oo  a  :  J  b. 

The  limit  of  this  series  of  octahedrons  on  one  side  is  a  square 
prism,  No.  12,  whose  symbol  is  a  :  oo  a  :  oo  b  ;  and  on  the  other 
side  the  basal  plane,  whose  symbol  is  a  :  oo  a :  o  6,  or  oo  a :  oo  a  :  b. 
Between  the  direct  octahedron,  No.  3,  and  its  corresponding 
inverse  octahedron,  No.  11,  there  is  an  intermediate  form,  No.  7, 
which  may  be  called  the  dioctahedron.  The  parameters  of  the 
faces  of  this  form  are  a  :  m  a  :  n  b.  When  m  =  1  this  form 
becomes  the  direct  octahedron,  and  when  m  =  oo  it  passes  into 
the  inverse  octahedron.  Again,  for  any  constant  value  of  m,  for 
example,  m  =  2,  as  in  the  figure,  we  may  have  an  infinite  series 
of  dioctahedrons  with  different  values  of  n.  As  the  value  of  n 
increases,  these  dioctahedrons  become  more  and  more  acute ;  and 
when  n  =  oo,  they  pass  into  the  octagonal  prism,  No.  8.  As  the 
value  of  n  diminishes,  they  become  more  and  more  obtuse  ;  and 
when  n  =  0,  they  pass  into  the  basal  plane,  No.  5.  For  any 
other  value  of  w,  for  example,  m  =  3,  we  may  have  a  similar 
series  ;  and  hence  there  may  be  an  infinite  number  of  series  of 
dioctahedrons  and  an  infinite  number  of  forms  in  each  series. 

Hemihedral  Simple  Forms. 

By  extending  the  alternate  planes  of  the  square  octahedron, 
two  tetrahedrons  may  be  obtained  similar  to  the  two  tetrahedrons 
of  the  monometric  system,  but  differing  from  them  in  the  rela- 
tive length  of  their  vertical  axis.  We  may  evidently  have  a 
series  of  either  positive  or  negative  tetrahedrons,  corresponding 
with  the  system  of  octahedrons,  and  varying  between  a  square 
prism  on  one  side  and  the  basal  plane  on  the  other.  In  like 
13 


146 


CHEMICAL   PHYSICS. 


manner,  by  extending  the  alternate  planes  or  the  alternate  sets 
of  planes  of  the  dioctahedron,  we  may  obtain  several  hemihedral 
forms.  The  hemihedral  forms  of  this  system,  however,  rarely 
occur  except  as  modifying  holohedral  forms. 


Compound  Forms. 


Fig  102. 


Fig 


Fig.  101 


a  :  co  a  :  006, 
a  :  a  :  b. 


a  :  a  :  6, 
a  :  oo  a  :  oo  6, 
co  a  :  oo  a  :  b. 


a  :  oo  a  :  oo  &, 

a  :  a  :  6, 
a  :  3  a  :  3  6. 


When  the  two  principal  octahedrons  combine,  the  inverse  octa- 
hedron truncates  the  edges  of  the  direct  octahedron,  as  in  Fig.  101, 
which  also  presents  the  two  basal  planes.  Fig.  102  represents  a 
combination  of  the  principal  octahedron,  o,  with  an  octahedron 
of  the  same  class,  §,  and  with  an  octahedron  of  the  second  class, 
2  d.  Fig.  103  represents  a  combination  of  the  square  prism  of  the 
first  class,  g*,  with  the  principal  octahedron,  o.  Fig.  104  represents 
a  combination  of  the  square  prism  of  the  second  class,  a,  with 
the  principal  octahedron,  o,  in  which  the  prism  is  the  dominant 
form.  Fig.  105  represents  the  same  combination,  in  which  the 
octahedron  is  the  dominant  form,  with  the  addition  of  the  basal 
planes.  The  composition  of  the  two  remaining  crystals  can  easily 
be  mado  out  from  tlio  symbols  below  the  figures. 


THE  THREE  STATES  OF  MATTER. 

HEXAGONAL  SYSTEM. 
Simple  Holohedral  Forms. 

2  3. 


14T 


a  :  a  :  oo  u  :  o  &.      a  :  a  :  oo  a  :  —  6.         a  :  a  :  ao  u  :  6.        a  :  a  :  oc  a  :  m  6.        a  :  a  :  oo  a  :  ao  6. 


tn  a  '.  a.  :  p  a  :  Q  b.     m  a  :  n  :  p  a  :  ~  b.         in  a  \  a  :  p  <i  :  b.     in  a  :  a  :  p  a  :  n  b      m  a  :  a  :  p  a  '.  <x,  b. 
11  12.  13.  14.  16. 


2a:a:2a:oi.      2a:a:217:—  6.        2a  :  n  :2n  :  b.      2a:a;-a:m&.       2a:a:2a:x6. 


The  simple  forms  of  the  hexagonal  system  are  closely  allied  to 
those  of  the  dimetric  system.  They  are  represented  in  Fig.  108, 
and  the  relation  between  them  is  indicated  by  the  arrangement  of 
the  forms  in  the  figure.  The  fundamental  form  of  this  system  is 
called  the  hexagonal  pyramid*  No.  3.  The  crystals  of  the  same 
substance  may  present  a  number  of  these  hexagonal  pyramids,  but 
we  always  find  that,  when  they  have  the  same  base,  the  lengths  of 
their  vertical  axes  stand  to  each  other  in  very  simple  ratios.  As 

*    The  term  pyramid  is  not  used  here  in  the  geometrical  sense. 


148  CHEMICAL  PHYSICS. 

in  the  dimetric  system,  we  select  one  of  these  for  the  principal 
form,  and  give  to  it  the  symbol  a  :  a  :  oo  a  :  b.  The  general 
symbol  of  the  other  hexagonal  pyramids  of  the  same  substance 
is  then  a :  a:  oo  a  :  m  &,  in  which  m  is  always  some  very  simple 
integer  or  fraction.  As  the  value  of  m  increases,  the  pyramid 
becomes  more  and  more  acute  ;  and  when  m  =  oo,  it  passes  into 
the  hexagonal  prism,  No.  5.  On  the  other  hand,  as  the  value  of 
m  diminishes,  the  pyramid  becomes  more  and  more  obtuse,  and 
finally  passes  into  the  basal  plane,  No.  1  This  series  of  pyramids 
are  called  hexagonal  pyramids  of  the  first  order,  to  distinguish 
them  from  the  hexagonal  pyramids  represented  in  the  lower 
row  of  forms  in  Fig.  108,  which  are  called  hexagonal  pyramids 
of  the  second  order. 

In  the  hexagonal  pyramids  of  the  second  order,  the  lateral 
axes  unite  the  centres  of  edges,  as  in  Fig.  110,  while  in  those  of 

the  first  order  they  unite 
opposite  solid  angles,  as 
in  Fig.  109.  The  lengths 
of  the  axes  in  the  two  fig- 
ures are  the  same.  The 
intersection  of  one  of  the 
faces  of  the  pyramid  of 
the  second  order  with  the 
Fig'm  Fi=-110'  basal  plane,  is  the  line 

E  E,  Fig.  110,  and  it  can  easily  be  seen  that  this  plane,  if  ex- 
tended, would  intersect  the  three  lateral  axes  at  distances  from 
the  centre  of  2  a,  #,  and  2  a  respectively.  The  symbol  of  the 
principal  pyramid  of  this  class  (No.  13  of  Fig.  108)  is  therefore 
2  a  :  a  :  2  a  :  b,  and  the  general  symbol  of  other  pyramids  of  the 
second  class  2  a  :  a  :  2  a  :  m  6,  where  m  is  always  some  simple 
rational  integer  or  fraction.  As  the  value  of  m  increases  or 
diminishes,  this  series  of  pyramids  passes  through  the  same  va- 
riations of  form  as  those  of  the  first  class.  The  two  limits  are 
the  hexagonal  prism,  where  m  =  oo,  and  the  basal  plane,  where 
w  =  o. 

It  will  be  noticed  that  the  planes  of  the  hexagonal  pyramid  and 

prism  of  the  second  order  have  the  same  position  as  the  edges  of 

the  corresponding  forms  of  the  first  order,  and  will  therefore 

truncate  these  edges  when  the  two  forms  enter  into  combination. 

Intermediate  between  the  two  classes  of  hexagonal  pyramids 


THE   THREE    STATES   OF   MATTER. 


149 


Mm 


m  a  :  a  :  p  a  :  n  b. 


are   the  dihexagonal  pyramids  (Fig.  111).  rig.  in. 

This  form  is  bounded  by  twenty-four  sca- 
lene triangles,  and  the  symbol  of  the  prin- 
cipal form  of  the  class  is  m  a  :  a  :p  a  :  b,  in 
which  m  and  p  are  so  related  that  p  =  ^-^ 
When  m  =  1  then  p  =  oo,  and  this  form 
passes  into  the  hexagonal  pyramid  of  the 
first  order,  and  when  m  —  2  then  p  =  2, 
and  it  passes  into  the  hexagonal  pyramid  of 
the  second  order.  The  general  symbol  of 
other  dihexagonal  pyramids  is  ma:  a:  pa: 
n  by  where  n  is  any  rational  fraction  or  in- 
teger. When  n  =  oo,  the  form  passes  into  the  dihexagonal  prism, 
No.  10  of  Fig.  108,  and  when  m  ==o,  it  passes  into  the  basal  plane, 
No.  6  of  Fig.  108. 

Simple  Hemihedral  Forms. 

The  hemihedral  forms  of  this  system  occur  more  frequently  in 
nature  than  the  holohedral  forms,  and  therefore  demand  special 
attention.  The  most  important  of  them  are  represented  in  Fig. 
115  (see  next  page),  in  which  the  forms  have  been  grouped 
so  as  to  show  the  relations  between  them.  In  studying  these 
forms,  we  will  commence  with  the  rhombohedron,  Nos.  2,  3,  4  of 
Fig.  115. 

Rhombohedron. — The  rhombohedron  is  bounded  by  six  equal 
and  similar  rhombs.  Its  edges  are  of  two  kinds ;  —  first,  six  sim- 


Fig.  112. 


Fig.  113. 


Fig.  114. 


+  i  (a  :  a  :  oo  a  :  b). 


a  :  a  :  ao  a  :  b. 


—  |  (a  :  a  .  oc  a  :  6). 


ilar  terminal  edges,  marked  X  in  Fig.  112  ;  secondly,  six  similar 
lateral  edges,  which  are  lettered  Z.  The  solid  angles  are  also  of 
two  kinds  ;  —  first,  two  similar  vertical  solid  angles,  lettered  C, 
consisting  of  three  equal  plane  angles ;  secondly,  six  lateral  solid 
13* 


150 


CHEMICAL  PHYSICS. 


angles,  lettered  J£,  which  are  similar  to  each  other,  but  do  not 
consist  of  equal  angles.     The  vertical  axis  of  the  rhombohedron 


connects  the  vertical  solid  angles.  The  lateral  axes  connect  the 
centres  of  opposite  edges. 

The  interfacial  angles  formed  at  the  terminal  edges  X  are  all 
equal  to  each  other.  This  angle  is  one  of  the  most  important 
characters  of  the  rhombohedron,  and  we  shall  call  it  the  rhombo- 
hedral  angle,  and  distinguish  it  by  the  same  letter  which  we  have 
used  to  denote  the  edge.  When  this  angle  is  acute,  the  rhombo- 
hedron is  said  to  be  acute,  and  when  it  is  obtuse,  the  rhombohe- 
dron is  said  to  be  obtuse. 

The  sections  of  the  rhombohedron  passing  through  two  opposite 


THE   THREE    STATES    OF   MATTER.  151 

terminal  edges  are  rhombs  which  are  perpendicular  to  two  of  the 
faces  of  the  form.  There  are  three  such  sections  in  every  rhom- 
bohedron,  and  they  are  called  principal  sections.  One  of  these, 
C  E  C'  E1,  is  represented  in  Fig.  112. 

The  crystals  of  a  given  substance  frequently  present  a  number 
of  rhombohedrons,  both  obtuse  and  acute  ;  but  when  these  rhom- 
bohedrons  have  the  same  lateral  axes,  their  vertical  axes  always 
bear  to  each  other  a  very  simple  proportion.  One  of  these  rhom- 
bohedrons, which  is  selected  on  the  same  grounds  as  those  already 
stated  in  connection  with  the  diinetric  system,  is  termed  the 
principal  rhombohcdron. 

The  principal  rhombohedron  may  be  regarded  as  formed  from 
the  principal  hexagonal  pyramid,  by  extending  the  alternate  planes 
until  they  cover  the  rest.  As  there  are  two  sets  of  alternate 
planes,  it  is  evident  that  we  can  obtain  by  this  method  two  rhom- 
bohedrons which  are  perfectly  equal,  and  which  differ  from  each 
other  only  in  position.  We  shall  call  them  the  positive  and  nega- 
tive rhombohedrons,  and  distinguish  them  by  writing  the  signs 
plus  and  minus  before  the  symbols.  These  symbols  are  given 
below  Figs.  112,  114,  and  it  will  be  seen  that  they  are  formed 
after  the  analogy  of  the  symbols  of  the  hemihedral  forms  in  the 
monometric  system. 

Since  every  hexagonal  pyramid  will  give  by  this  method  two 
rhombohedrons,  it  is  evident  that,  corresponding  to  the  series  of 
hexagonal  pyramids,  Fig.  108,  we  have  two  series  of  rhombohe- 
drons. The  general  symbols  of  these  two  classes  of  rhombohe- 
drons are 

-f-  \  (a  :  a  :  oo  a  :  m  Z>),     and     —  J  (a  :  a  :  oo  a  :  m  b). 

As  the  value  of  m  increases,  the  rhombohedrons  become  more  and 
more  acute,  and  finally,  when  m  =  oo,  they  pass  into  the  hex- 
agonal prism,  No.  5,  Fig.  115.  On  the  other  hand,  as  the  value 
of  m  diminishes,  the  rhombohedrons  become  more  and  more 
obtuse,  and  when  m  =  o  they  pass  into  the  basal  plane,  No.  1, 
Fig.  115. 

Of  the  series  of  possible  rhombohedrons  with  any  given  values 
of  the  axes,  there  are  several  which  stand  to  each  other  in  an  im- 
portant relation.  Commencing  with  the  principal  positive  rhom- 
bohedron,  -)-  J  (a  :  a  :  co  a  :  b),  No.  3,  Fig.  115,  we  find  that  the 
planes  of  the  negative  rhombohedron  —  \ ,(a :  a  :  oo  a  :  \  &),  No.  2, 


152  CHEMICAL  PHYSICS. 

have  the  same  position  as  its  terminal  edges,  and  therefore 
truncate  them  This  rhombohedron  is  called  the  first  obtuse 
rhombohedron.  Again,  the  faces  of  the  positive  rhombohedron 
+  i  (fl  :  a  '•  °°  a  :  i  &)  truncate  the  edges  of  the  first  obtuse 
rhombohedron,  and  it  is  called  the  second  obtuse  rhombohe- 
dron, and  so  on.  On  the  other  hand,  the  faces  of  the  principal 
rhombohedron  truncate  the  edges  of  the  negative  rhombohedron 
—  J  (a  :  a  :  cca  :  2  6),  No.  4,  which  is  called  the  first  acute 
rhombohedron.  The  faces  of  the  first  acute  rhombohedron  trun- 
cate the  edges  of  the  positive  rhombohedron  ~[~  \  (&  '•  a  '•  oo  a :  4  6), 
which  is  called  the  second  acute  rhombohedron,  and  so  on. 

The  rhombohedrons  which  form  this  series  are,  then,  as  fol- 
lows :  — 


Third  obtuse  rhombohedron,  —  J  (a 

Second   "                 "  +  J  (a 

First       "                 "  —  \  (a 

Principal  rhombohedron,  -J-  \  (a 

First  acute  rhombohedron,  —  \  (a 

Second  "                 «  + 1  (a 

Third     "                 «  —  \  (a 


a 


oo  a  :  |  6)  =  —  i  R. 
oo  a  :  J  b)  =  +  J  R. 


oo 


oo  a  :  b)     =  +  R. 
oo  a  :  2  b)  =  —  2  R. 
oo  a  :  4  b)  =  +  4  JS. 
oo  a  :  8  ^  =  —  8  R. 


And  in  this  series  each  rhombohedron  truncates  the  terminal 
edges  of  the  one  which  follows  it.  In  crystals  of  the  mineral 
calcite,  almost  all  the  above  rhombohedrons  have  been  observed, 
and  a  large  number  of  others,  not  belonging  to  the  series,  but  in- 
termediate between  the  members  of  it.  The  general  appearance 
of  these  crystals  varies  from  almost  flat  plates,  where  the  ter- 
minal angle  X  =  160°  42',  to  sharp  needles,  where  the  angle 
X  =  60°  20'. 

As  the  regular  symbol  of  the  rhombohedron  is  inconveniently 
long,  we  frequently  abbreviate  it  in  practice,  and  write,  as  the 
symbol  of  the  principal  rhombohedrons  of  a  given  substance, 
db  R.  For  other  rhombohedrons  we  use  the  general  symbol 
db  m  R,  in  which  m  is  the  same  quantity  as  the  m  in  the  reg- 
ular symbol.  The  abbreviated  symbols  of  the  series  of  acute  and 
obtuse  rhombohedrons  have  been  given  after  the  corresponding 
regular  symbols  in  the  above  table,  and  by  comparing  the  two  the 
use  of  the  abbreviation  can  be  easily  understood. 

Intermediate  between  the  obtuse  and  acute  rhombohedrons 
there  is  a  possible  form,  where  X  =  90°.  This  is  the  case  when 


THE   THREE   STATES   OF   MATTER. 


153 


Fig  117. 


a  :  m  b  =  1  :  A/  j  .  The  rhombohedron  then  becomes  the  cube, 
which  may  therefore  be  regarded  as  a  form  of  the  hexagonal 
system.  In  like  manner,  all  the  other  simple  forms  of  the  mono- 
metric  system  may  be  regarded  as  forms  of  the  hexagonal  system, 
but  in  this  system  they  are  compound  forms.  In  consequence  of 
this  analogy,  the  crystals  of  the  two  systems  frequently  resemble 
each  other  very  closely,  especially  when  they  have  been  irregu- 
larly formed. 

Scalenohedron. —  By  comparing  together  Figs.  116  and  117, 
on  which  the  similar  parts  have  been  similarly  lettered,  it  will  be 
seen  that  in  the  posi- 
tion occupied  by  one 
plane  on  the  hexagonal 
pyramid  there  are  two 
planes  on  the  dihex- 
agonal  pyramid  ;  and 
hence,  that  we  must 
extend  the  alternate 
pairs  of  planes  on  the 
dihexagonal  pyramid, 
in  order  to  apply  to  it 
the  same  method  by 
which  we  obtained  the 

rhombohedron  from  the  hexagonal  pyramid.  If,  then,  we  extend 
the  alternate  pairs  of  planes  on  the  dihexagonal  pyramid,  commen- 
cing with  the  two  front  upper  planes  of  Fig.  116, 
we  shall  obtain  the  form  represented  in  Fig.  118, 
and  called  a  scalenohedron;  or,  by  extending  the 
planes  suppressed  in  the  last  case,  a  second  scale- 
nohedron, differing  from  the  first  only  in  position. 
The  two  are  distinguished,  like  the  rhombohe- 
drons,  as  positive  and  negative  scalenohedrons. 
The  scalenohedron,  which  is  derived  from  the 
principal  dihexagonal  pyramid,  will  be  called 
the  principal  scalenohedron,  and  its  symbol  is 
±  £  (m  a  :  a  :  p  a  :  b).  The  general  symbol  of 
other  scalenohedrons  is  ±  |  (m  a  :  a  :pa  :  nb). 
As  the  value  of  n  diminishes,  the  scalenohedron 
becomes  more  and  more  obtuse,  and  finally,  when  n=  o,  merges 


m a : a :p  a 


Fig.  118. 


-f-  J  (m  a :  a  :  p  a  :  b). 


154  CHEMICAL  PHYSICS. 

in  the  basal  plane.  On.  the  other  hand,  with  increasing  values 
of  w,  the  scalenohedron  becomes  more  and  more  acute,  and  when 
n  =  oo  merges  into  the  hexagonal  prism. 

By  bringing  together  the  rhombohedron  and  the  scalenohedron, 
as  has  been  done  in  Fig.  119,  it  will  be  noticed  that  the  lateral 
edges  of  the  two  forms  have  a  similar  position 
towards  the  axes,  so  that  for  every  scalenohe- 
dron there  must  be  a  rhombohedron  whose  lat- 
eral edges  coincide  with  the  lateral  edges  of  the 
other  form.  This  rhombohedron  is  called  the 
inscribed  rhombohedron  of  the  scalenohedron. 
The  scalenohedron  may  evidently  be  formed 
from  the  inscribed  rhombohedron  by  prolong- 
ing the  vertical  axis,  and  then  drawing  lines 
from  the  ends  of  the  vertical  axis  thus  pro- 
duced to  the  lateral  solid  angles  of  the  rhom- 
bohedron. It  is  evident  that  we  may  thus 
make  from  every  rhombohedron  #n  infinite 
number  of  scalenohedrons,  whose  form  will 
depend  upon  the  extent  to  which  the  vertical 
axis  has  been  elongated.  We  find,  however, 
that  the  semi-vertical  axis  of  the  scalenohe- 
dron is  always  some  simple  multiple  of  that 
of  the  inscribed  rhombohedron.  Hence  we 
may  use,  as  the  abbreviated  symbol  of  the  scalenohedron,  the  ab- 
breviated symbol  of  the  corresponding  inscribed  rhombohedron, 
with  an  exponent  indicating  how  many  times  its  semi-vertical 
axis  is  greater  than  that  of  the  rhombohedron.  If,  as  in  Fig.  119, 
the  inscribed  rhombohedron  is  the  principal  rhombohedron,  -f-  -K, 
and  the  semi-vertical  axis  of  the  scalenohedron  is  three  times 
that  of  the  rhombohedron,  the  abbreviated  symbol  of  the  rhombo- 
hedron is  -f-  -R3.  The  general  symbol  for  any  scalenohedron  is 
±  m  Rn,  in  which  ±  m  R  is  the  symbol  of  the  inscribed  rhom- 
bohedron. It  has  already  been  stated,  that  the  number  of  the 
possible  rhombohedrons  on  the  crystals  of  a  given  substance  is 
infinite,  and  it  now  appears  that  for  every  rhombohedron  there 
may  be  an  infinite  number  of  scalenohedrons  ;  so  that  the  num- 
ber of  possible  scalenohedrons  on  the  crystals  of  a  given  sub- 
stance is  infinitely  greater  than  the  infinite  number  of  possible 
rhombohedrons.  The  mineral  calcite  has  a  great  tendency  to 


THE   THREE   STATES    OF   MATTER. 


155 


crystallize  in  scalenohedrons  (dog-tooth  crystals),  and  no  less 
than  thirty-eight  rhombohedrons  and  seventy-six  scalenohedrons 
have  been  observed  among  the  crystals  of  this  substance.* 

Besides  the  two  hemihedral  forms  which  have  been  described, 
there  are  two  other  hemihedral  forms  in  the  hexagonal  system, 
which  may  be  derived  from  the  dihexagonal  pyramid. 

The  first  of  these  is  obtained  by  extending  the  alternate  pairs 
of  planes,  united  at  a  lateral  edge,  A  E,  Fig.  120,  where  the  al- 
ternate planes  are  distinguished  by  the  shad- 
ing. As  we  extend  the  shaded  or  the  un- 
shaded planes  of  Fig.  120,  we  obtain  one 
or  the  other  of  two  hexagonal  pyramids, 
which  differ  from  each  other  and  from  the 
hexagonal  pyramids  already  described  only 
in  the  position  of  the  axes.  The  lateral 
axes  of  the  pyramids  thus  derived  do  not 
unite  the  opposite  solid  angles,  as  is  the  case 
with  pyramids  of  the  first  order  (Fig.  100) ; 
nor  yet  the  centres  of  opposite  edges,  as  is 
the  case  with  pyramids  of  the  second  order 
(Fig.  110)  ;  but  points  on  the  lateral  edges  intermediate  between 
the  centre  and  the  ends. 

The  second  of  these  hemihedral  forms  is  obtained  by  extend- 
ing the  alternate  pairs  of  planes  united  at  a  lateral  solid  angle, 


Fig.  120. 


Fig.  121. 


Fig.  122. 


Fig.  123. 


as  shown  by  the  shading  in  Fig.  121.  According  as  the  un- 
shaded or  the  shaded  planes  are  extended,  we  obtain  the  two 
forms  represented  in  Figs.  122,  123.  They  are  called  the  hex- 


*  See  Dana's  System  of  Mineralogy,  Vol.  II.  p.  437,  for  the  symbols  of  these  forms. 


156 


CHEMICAL   PHYSICS. 


agonal  trapezohedrons.  The  two  forms  derived  from  the  same 
dihexagonal  pyramid  differ  from  each  other,  not  only  in  the  abso- 
lute position  of  the  form,  but  also  in  the  relative  position  of  their 
planes.  They  are  distinguished  as  the  rig-lit  and  left  trapezohe- 
drons, and  their  symbols  are  respectively 

r    \  (m  a  :  a  :  p  a  :  w6),      and      /    |  (m  a  :  a  :p  a  :  nb). 

Tetartohedral  Forms. 

By  extending  the  alternate  planes  of  the  right  hexagonal  tra- 
pezohedron  (Fig.  121),  we  can  obtain  two  forms,  differing  from 
each  other  only  in  position,  whose  symbols  are 

±  r  J  (m  a  :  a  :  p  a  :  n  &)  ; 

and,  in  like  manner,  from  the  left  hexagonal  trapezohedron  two 
other  forms  may  be  obtained,  whose  symbols  are 

±  I  J  (m  a  :  a  :  p  a  :  n  &) . 

Each  of  these  four  forms  is  bounded  by  six  isosceles  trapeziums, 
and  they  are  therefore  called  trigonal  trapezohedrons.  They 
are  evidently  tetartohedral  forms  of  the  dihexagonal  pyramid. 

These  tetartohedral  forms  are  never  found  isolated  in  nature  ; 
but  they  appear  very  frequently  on  crystals  of  quartz  in  combina- 
tion with  other  forms.  The  crystals  of  this  mineral  are  usually  a 
combination  of  a  hexagonal  prism  with  a  hexagonal  pyramid  of 
the  same  order  (Fig.  125),  and  the  trigonal  trapezohedrons  ap- 
pear as  modifying  planes  on  the  solid  angles.  In  Fig.  124,  the 


Fig.  124. 


Fig.  125. 


Fig.  126. 


lateral  solid  angles  are  modified  by  the  planes  of  the  positive 
right-trigonal  trapezohedrons,  and  in  Fig.  126,  by  the  planes  of 


THE   THREE   STATES   OF   MATTER. 


157 


the  positive  left-trigonal  trapezohedron.  The  two  negative  forms 
would  modify  in  a  similar  way  the  set  of  solid  angles,  which  are 
not  modified  in  the  figures. 

The  difference  of  form  between  the  right  and  left  trapezohe- 
dron is  found  to  be  accompanied  with  remarkable  differences  of 
optical  properties,  which  will  be  explained  in  the  section  on  the 
circular  polarization  of  light. 

Compound  Forms. 

The  crystal  represented  by  Fig.  127  is  a  combination  of  the 
hexagonal  prism  with  the  basal  plane,  the  symbols  of  which  are 
given  in  this  order  below  the  figure.  On  the  crystal  represented  by 


Fig.  i2a 


Fig.  127. 


Fig.  128. 


a  :  a  :  co  a  :  oo  b, 
CD  a  :  oo  a  :  oo  a  :  b. 


—  J  (a  :  a  :oo  a  :  J  b), 
-f-  ^  ( a  :  a  :  oo  a  :  b). 


+  R    — 


-f  2  B. 


Fig  130. 


Fig  131. 


(a:a:ao  a  :  b), 

4-  j  (  ooa  :  oo  a  :  oo  a  :  b). 


Fig.  128  there  are  evident- 
ly the  faces  of  two  rhom- 
bohedrons,  the  one  positive 
and  the  other  negative.  If 
we  assume  that  the  faces  let- 
tered r  are  those  of  the  prin- 
cipal rhombohedron,  72,  then 
it  is  evident  that  the  faces 
lettered  r/2  are  those  of  the 
first  obtuse  rhombohedron, 
J  R,  because  they  truncate  the  vertical  edges  of  the  rhombohe- 
dron R.  As  the  planes  of  the  first  obtuse  rhombohedron  are 
much  larger  than  those  of  the  principal  rhombohedron,  it  is  not 
at  once  evident  from  the  figure  that  the  first  are  truncating 
planes ;  but  on  a  model  this  fact  could  easily  be  discovered,  by 
noticing  that  the  edges  formed  by  any  plane,  r/25  with  the  two 
adjacent  planes,  r,  are  in  every  case  parallel  (91).  If,  in  Fig. 
129,  we  assume  that  the  faces  r  are  those  of  the  principal  rhom- 
bohedron, then  the  faces  r/8 ,  which  truncate  the  edges  of  the  prin- 
14 


158 


CHEMICAL   PHYSICS. 


Fig.  132. 


Fig.  133. 


cipal  rhombohedron,  belong  to  the  first  obtuse  rhoinbohedron, 
—  4  R,  and  the  faces  2  r  to  the  first  acute  rhombohedron  —  2  R ; 
because  the  edges  of  this  form  are  truncated  by  the  faces  r  of  the 
principal  rhombohedron.  Fig.  130  represents  a  combination  of  the 
principal  rhombohedron  with  its  second  acute  rhombohedron,  4  R. 
Fig.  131  represents  the  combination  of  the  principal  rhombohedron 
with  the  basal  plane.  It  will  be  noticed  how  closely  this  form  re- 
sembles the  octahedron  of  the  monometric  system,  audit,  i:i  fact, 
merges  into  the  octahedron  when  the  angle  of  a  on  r  is  equal 

to  109°  28'  16",  which  is  the 
case  when  the  axes  of  the 
rhombohedron  are  to  each  oth- 
er as  1  :  2.4495.  It  will  be 
remembered  that  the  cube 
may  be  regarded  as  a  rhom- 
bohedron, in  which  a  :  b  = 
I  :>1.2247.  Hence  the  octa- 
hedron may  be  regarded  as 
+  .R3  +  R.  the  first  acute  rhombohedron 

of  the  cube  combined  with  the 
basal  plane.  The  compound  form  of  Fig.  132  consists  of  a 
hexagonal  prism  of  the  first  order  combined  with  the  rhombo- 
hedron —  |  R.  Finally,  Fig.  133  represents  a  combination  of 
a  scalenohedron,  R3,  with  the  rhombohedron  R. 

TRIMETRIC  SYSTEM. 
Simple  Forms. 

Fig.  134. 

Fig.  135.  Fig.  136. 


The  fundamental  form  of  this  system  is  the  rhombic  octahedron, 
so   called  because  the  three  principal  sections  made  by  planes 


THE   THREE   STATES   OP   MATTER.  159 

passing  through  the  axis  are  all  rhombs.*  This  fact  is  illustrated 
by  Figs.  135,  136,  137,  which  represent  these  sections,  and  which 
have  been  lettered  to  correspond  with  Fig.  134.  The  same  sub- 
stance frequently  crystallizes  in  several  octahedrons.  In  such 
cases  we  select  one  of  these  as  the  principal  octahedron,  giving  to 
it  the  symbol  a  :  b  :  c,  and  we  then  find  that  the  parameters  of 
the  planes  of  the  other  octahedrons  always  stand  in  some  simple 
relation  to  those  of  the  one  thus  selected.  Besides  the  octahe- 
drons, the  only  other  simple  forms  of  this  system  are  rhombic 
prisms  and  terminal  or  basal  planes. f  The  relation  of  these 
forms  can  be  best  understood  by  studying  their  symbols. 

Having  given  to  the  principal  form  the  notation  a  :  b  :  c,  then 
the  other  octahedrons  which  the  same  substance  can  present 
will  be  expressed  by  the  following  symbols :  — 

1.  a  :  m  b  :  c,  3.     m  a  :  b  :  c, 

2.  a  :  b  :  m  c,  4.     m  a  :  b  :  n  c, 

in  which  m  and  n  are  always  very  simple  rational  numbers.  The 
first  three  of  these  symbols  may  evidently  be  regarded  as  partic- 
ular cases  of  the  third. 

The  number  of  possible  octahedrons  in  which  a  given  sub- 
stance may  crystallize  in  the  trimetric  system  is  evidently  infinite ; 
but  the  number  which  have  in  any  case  been  observed  is  ex- 
tremely limited,  including  only  a  few  of  the  possible  values  of 
m  and  n,  together  with  the  rhombic  prisms  and  terminal  planes 
which  result  when  m  and  n  are  made  equal  either  to  infinity  or 
zero. 

If  in  No.  1  we  put  m  =  oo,  the  symbol  becomes  a  :  oo  b  :  c9 
which  represents  a  rhombic  prism  whose  axis  is  the  axis  of  b.  If 
m  =  o,  the  symbol  becomes  a  :  o  b  :  c  =  oo  a  :  b  :  oo  e,  which  is 
the  symbol  of  the  basal  planes  of  the  same  prism.  If  in  No.  2 
we  put  m  =  oo,  we  obtain  the  symbols  of  a  rhombic  prism  whose 
axis  is  the  axis  of  c ;  and  if  we  put  m  =  o,  we  obtain  the  symbol 
of  the  basal  planes  of  the  same  prism.  So  also,  if  in  No.  3  we 
put  m  equal  to  infinity  and  zero,  we  obtain  the  symbols  of  a 
rhombic  prism  parallel  to  the  axis  of  a  and  of  its  basal  planes. 

*  A  section  of  a  crystal  is  called  a  principal  section  when  it  contains  two  of  the  axes. 

t  Planes  placed  at  the  ends  of  any  axis,  and  parallel  to  the  plane  of  the  other  two, 
are  called  terminal  planes.  Such  planes,  when  they  form  the  base  of  a  crystal,  are 
called  basal  planes. 


160 


CHEMICAL   PHYSICS. 


The  general  symbol  No.  4  maybe  put  in  the  three  following  forms: 


nc. 


1.    a  :  nb  :  mcy         2.   n  a  :  m  b  :  c,         3.    m  a  :  b 

If  in  No.  1  we  put  n  =  o>,  we  obtain  a  rhombic  prism  parallel 
to  the  axis  of  ft,  whose  symbol  is  a  :  oo  b  :  m  c  ;  if  n  =  o,  we  ob- 
tain the  basal  plane  of  this  prism.  If  in  No.  2  we  put  n  =  oo, 
we  obtain  a  rhombic  prism  parallel  to  the  axis  of  a,  whose  sym- 
bol is  oo  a  :  m  b  :  c  ;  if  n  =  o,  we  obtain  the  basal  planes  of 
this  prism.  If  in  No.  3  we  put  n  =  oo,  we  obtain  a  rhombic 
prism  parallel  to  the  axis  of  c,  whose  symbol  is  m  a  :  b  :  GO  c ;  if 
n  =  o,  we  obtain  the  basal  planes  of  this  prism. 

Compound  Forms. 

We  give  below  several  figures  of  the  compound  forms  of  this 
system,  and  beneath  each  the  symbols  of  the  simple  forms  of 

Fig.  138.  Fig.  139.  Fig.  140.  Fig.  141. 


o  =  a  :  b  :  c, 


ooa  :  b  :  e, 
oo  a  :  6  :  oo  c. 

Fig  142. 


f  =  QO  a  :  b  :  c, 
2/  =  ooa  :  2  b  :  e. 

Fig.  143. 


o  =  a  :  b  :  c, 
a  =  a  :  006  :oo  c, 
b  =  oo  a  :  oo  6  :  e. 


a  :  as  b  :  c, 
a:Kb:  we, 
oo  «  :  b  :  oo  c. 
Fig.  144. 


_/"=  oo  a  :  6  .-  c. 
c  =  oo  a  :  i  :  ooe. 


Fig.  145. 


THE   THREE   STATES   OF   MATTER.  161 

which  it  consists,  opposite  to  the  letters  on  the  faces  of  the  crys- 
tal. With  the  aid  of  these  symbols,  the  student  will  easily  be 
able  to  see  the  relations  of  the  forms  without  any  further  de- 
scription. 

Hcmihedral  Forms. 

FJg.  146.  Fig.  147.  Fig  148. 


+  i  (a  :  6  :  c).  -l(a-.b:c). 

The  most  important  hemihedral  form  of  this  system  is  the 
rhombic  sphenoid,  Figs.  147,  148.  It  may  be  developed  by  ex- 
tending the  alternate  planes  of  the  rhombic  octahedron,  Fig.  146. 
If  we  extend  the  shaded  planes,  we  obtain  the  positive  sphenoid, 
Fig.  147  ;  and  if  we  extend  the  planes  which  arc  not  shaded,  the 
negative  sphenoid,  Fig.  148.  The  rhombic  sphenoid  is  a  tetra- 
hedral  form,  and  is  bounded  by  four  scalene  triangles.  It  will 
be  remembered  that  the  two  tetrahedrons,  derived  from  the  octa- 
hedron of  the  monometric  system,  differed  from  each  other  only 
in  position,  and  that,  by  turning  one  round  the  vertical  axis 
through  a  quarter  of  a  revolution,  the  two  would  coincide.  It  is 
different  with  the  two  sphenoids.  They  differ  from  each  other 
in  the  relative  position  of  their  planes,  and  by  turning  one  on  its 
axis  it  cannot  be  brought  into  a  position  in  which  it  will  coincide 
with  the  other.  The  two  forms  are  related  to  each  other  as  the 
left  hand  is  to  the  right  hand,  or  as  an  object  is  to  its  image  in  a 
mirror.  Hence,  we  call  the  positive  a  right  form,  and  the  nega- 
tive a  left  form. 

The  two  sphenoids  never  occur  in  nature  except  in  combination 
with  other  forms,  and  the  presence  of  one  or  the  other  of  these 
14* 


162  CHEMICAL  PHYSICS. 

forms  on  a  crystal  is  associated  with  certain  remarkable  optical 
properties.  By  neutralizing  a  solution  of  racemic  acid,  half  with 
soda  and  half  with  ammonia,  a  bibasic  salt  is  formed,  called  the 
racemate  of  soda  and  ammonia,  which  can  be  readily  crystallized 
by  evaporating  the  solution.  The  crystals  thus  formed  are  of  two 
kinds,  part  resembling  Fig.  149,  and  part  Fig.  150.  The  two 


Fig.  149.  Fig.  150. 

kinds  of  crystals  resemble  each  other  in  their  general  appear- 
ance. They  both  have  the  planes  of  the  vertical  rhombic  prisms 
(i  and  i  2"),  the  terminal  planes  (i  I  and  i  I),  the  basal  planes 
(o),  the  planes  of  two  prisms  parallel  to  the  brachydiagonal 
(I  and  2  z)  ;  but  in  addition  to  these,  there  appear  on  the  first 
kind  of  crystals  (Fig.  149)  the  planes  of  the  positive  sphenoid, 
-f-  J,  and  on  the  second  kind  of  crystals  (Fig.  150)  those  of  the 
negative  sphenoid,  —  J.  If,  now,  we  arrange  a  crystal  of  each 
sort,  as  in  the  figures,  with  the  terminal  planes  i  I  in  front,  it 
will  be  seen  that  the  upper  sphenoid  plane  is  in  the  first  figure  on 
the  right,  and  in  the  second  on  the  left,  of  the  observer ;  so  that, 
if  we  place  one  form  before  a  mirror,  the  image  will  have  ex- 
actly the  second  form.  In  these  two  forms  there  are  present  two 
varieties  of  tartaric  acid,  into  which  the  rac°mic  acid  di- 
vides in  the  process  of  crystallization.  In  the  crystals  of  Fig. 
149,  the  two  bases  are  united  with  a  variety  of  tartaric  acid, 
which  has  the  power  of  rotating  the  plane  of  polarization  of  a 
ray  of  light  to  the  right ;  and  in  Fig.  150,  with  a  variety  of  tar- 
taric acid  resembling  the  other  in  all  its  chemical  relations,  but 
differing  in  its  crystalline  form,  and  rotating  the  plane  of  polari- 
zation to  the  left. 

The  sphenoid  is  the  only  hemihedral  form  in  this  system  which 
encloses  space,  and  which  therefore  could  alone  form  a  crystal. 
Other  hemihedral  forms  have  been  observed,  but  they  never  ap- 


THE   THREE   STATES   OF   MATTER. 


163 


pear  except  in.  combinations  modifying  one  half  of  the  similar 
edges  or  solid  angles  of  the  dominant  form,  and  they  can  there- 
fore be  easily  recognized. 


Fig  151. 


MONOCLINIC  SYSTEM. 
Simple  Forms. 

In  the  monoclinic  system,  as  has  been  already  stated,  no  single 
crystalline  form  can  enclose  space ;  and  hence  we  have  no  simple 
crystals.     Fig.  151   represents  an  octahedron  belonging  to  this 
system ;  but  this  is  not  a  simple  crystal, 
because  it  is  bounded  by  faces  of  two  kinds. 
The     triangular     faces    B  A  C,    B  A1  C, 
B'  AC',  and  B'  A'  C'  arc   not   similar   to 
the   faces   B  A  C",   B  A1  C",   D  A  C,   and 
B1  A'  C,  and  therefore  belong  to  a  different 
form.     The  first  set  of  faces,  if  extended, 
would   evidently  form  a   rhombic   prism ; 
and  the  second  set  of  faces,  if  extended, 
would  also  form  a  rhombic  prism  differing 
from   the    first.     These    two    prisms    may 
be  appropriately  termed  hemi-octahedrons  ; 
and  in  order  to  distinguish  them,  we  shall  name  the  one  whoso 
planes  are  over  the  acute  angle  a,  Fig.  151,  the  positive  hemi- 
octahedron,  and  the  other  the  negative  hemi-octahedron.     This 
distinction  is  necessary,  because  it  frequently  happens  that  one  of 
these  hemi-octahedrons  is  present  on  a 
crystal  without  the  other,  or  at  least  that 
the  faces  of  one  are  far  more  dominant 
than  those  of  the  other. 

Adopting  the  notation  of  Fig.  152,  al- 
ready described  (85),  the  symbol  of  the 
positive  hemi-octahedron  is  a  :  b  :  c,  or 
a  :  b'  :  c'.  The  first  symbol  consists  of 
the  parameters  of  the  two  upper  right- 
hand  planes  of  the  form,  Fig.  151,  and  the 
second  of  those  of  the  two  lower  left-hand 

planes  ;  either  symbol  may  be  used  at  pleasure.  The  symbol  of  the 
negative  hemi-octahedron  is  a  :  b  :  c',  or  a  :  b'  :  c  ;  the  first  being 
the  parameters  of  the  two  upper  left-hand  planes,  and  the  second 


104  CHEMICAL   PHYSICS. 

those  of  the  two  lower  right-hand  planes.  Either  symbol,  as  be- 
fore, may  be  used  as  the  symbol  of  the  form,  but  for  the  sake  of 
uniformity  we  shall  use  in  both  cases  the  first  of  the  two  symbols. 
The  symbols  of  the  two  hemi-octahedrons,  of  which  the  octa- 
hedron of  this  system  consists,  are,  then, 

a  :  b  :  c,  and  a  :  b  :  c' ; 

but  it  must  be  remembered  that  these  symbols  include  not  only 
the  planes  whose  parameters  they  actually  express,  but  also  the 
planes  which  have  the  same  parameters  oppositely  accented. 

In  this  system,  as  has  been  already  stated  (82-85),  not  only 
the  relative  length  of  the  axes  may  vary,  but,  moreover,  the  angle 
of  inclination  of  the  vertical  axis  b  to  the  klinodiagonal  c  varies 
also.  When,  however,  the  crystals  of  the  same  substance  pre- 
sent planes  of  several  pairs  of  hemi-octahedrons,  we  always  find 
that,  although  the  relative  lengths  of  the  axes  of  these  forms 
may  differ,  yet  the  angle  of  inclination,  cc,  is  the  same  in  all. 
We  select  in  this  system,  as  in  the  last  three,  one  pair  of  these 
hemi-octahedrons  as  the  principal  form,  and  give  to  it  the  sym- 
bols a  :  b  :  c  and  a  :  b  :  c'.  The  general  symbol  of  other  hemi- 
octahedrons  of  the  same  substance  is,  then, 

m  a  :  n  b  :  p  c,         or         m  a  :  n  b  :  p  c', 

the  quantities  m,  w,  and  p  being  always  simple  rational  integers 
or  fractions,  and  one  of  them  being  always  unity. 

The  forms  which  are  most  frequently  met  with  in  this  system 
are  those  which  result  when  either  m=oo,  w  =  cc,  or  p  =  00, 
or  when  m  =  o,  n  =  o,  or  p  =  o,  in  the  general  symbols. 

In  making  n  =  co,  and  p—  i,  the  general  symbols  become 
m  a  :  co  b  :  c,  and  m  a  :  GO  b' :  c1.*  Since  the  dissimilar  semi-axes 
are  oppositely  accented  in  the  two  symbols,  they  are  both  equiva- 
lent symbols  of  the  same  oblique  rhombic  prisms  parallel  to  the 
axis  b.  When,  also,  m  =  i,  we  obtain  the  symbol  of  the  principal 
of  these  oblique  prisms,  a  :  co  b  :  c. 

In  making  m  =  co  and  p=i,  in  the  general  symbols,  we 
obtain  the  two  symbols  co  a  :  n  b  :  c,  and  co  a  :  n  b  :  c'.  These 
symbols  are  not  equivalent,  and  each  represents  two  opposite  and 
parallel  planes,  which  are  also  parallel  to  the  orthodiagonal. 
The  two  planes  represented  by  the  first  symbol  are  over  the  acute 

*  Since  6  and  b'  are  halves  of  the  same  straight  line,  the  parameters  oo  b  and  oo  b1 
are  in  all  respects  equivalent,  and  may  therefore  be  substituted  for  each  other. 


THE   THREE   STATES    OF   MATTER. 


165 


anglo  a,  and  arc  therefore  narrower  than  the  two  planes  repre- 
sented by  the  second  symbol,  which  are  over  the  obtuse  anglo 
180°  —  a.  The  two  sets  of  planes  evidently  bear  the  same  rela- 
tion to  each  other  as  the  two  hemi-octahedrons,  and  may  therefore 
be  called  the  positive  and  negative  orthodiagonal  Jicmi-prisms. 
AVhcn  n  =  i,  the  two  symbols  become  cca  :  b  :  e,  and  co  a  :  b  :  c'. 

Finally,  if  we  put  p  =  ex,  and  m  =  i,  in  the  general  symbols, 
we  obtain  a  :  n  b  :  co  c  in  both  cases,  which  is  the  symbol  of 
horizontal  rhombic  prisms  parallel  to  the  kliiiodiagonal,  called 
the  klinodiagvnal  prisms.  When  n  =  i,  the  symbol  becomes 
a  :  b  :  oc  c. 

Substituting  m  =  o,  and  multiplying  all  the  parameters  by  oo, 
the  general  symbols  become  in  both  cases  a  :  co  b  :  oo  c,  which  is 
the  symbol  of  a  form  consisting  of  two  terminal  planes  parallel 
to  the  planes  of  the  axes  b  and  c.  In  like  manner,  if  we  put 
n  =  o,  or  p  =  o,  we  obtain  the  symbols  of  terminal  planes  par- 
allel to  the  planes  of  the  axes  <z,  c  or  a,  b  respectively. 


Fig.  153. 


Compound  Forms. 
•tout 


Fig.  155. 


i  ses  a  :  oo  6  :  c, 

0  =  oo  a  :  b  :  oo  e. 


t  =  a :  oo  6  :  e, 

0  =  oo  a  :  /;  :  oo  c, 

»t'=a:  006:  oo  e. 


t  =  n  :  a>  6:  e, 
0  =  oo  a  :  6  :  oo  c, 
*  r  =  ooa:  ao  6 :  c. 


Fig.  Io3  represents  the  combination  of  the  principal  oblique 
rhombic  prism,  with  its  basal  planes.     Fig.  154  represents  tho 


Fig  156. 


Fig  157. 


Fig  Ii8. 


t  =  a :  ooft:c, 
0  =  oo  a  :  6  :  ooe, 
•  i  —  oo  a :  b  :  e1. 


i  =  <r :  oo  6 :  e, 

0  =  oo  a  :  6  :  oc  c, 

C  »'  =  a  :  oo  6  :  oo  et 

+  »  =  oo  «  :  6  :  e. 


t  =  n  :  oo  A  :  c, 
0  =  oo  a  :  ft  :  oo  c, 

+  1  =  a  :  !, :  c. 


166 


CHEMICAL  PHYSICS. 


same  combination,  with  the  addition  of  two  terminal  planes  at  the 
end  of  the  orthodiagonal.     Fig.  155  represents  the  same  combina- 


i  =  a.  :  oo  b  :  e, 

0  =  oo  a  :  b  :  oc  e, 

1  =  a  :  b  :  e*. 


Fig.  160. 


Fig.  Id. 


i  =  a  r  oo  ft  :  c, 

0  =  oo  a  :  b  :  <x>  er 

1  =  a  :  oo  b  :  oo  c, 


f  =  a  :  oo  A  :  e, 
*  ?'  =  a  :  oa  6  :  os  c, 
-f  1  =  a  :  ft  :  c, 


Fig  162 


tion,  with  the  addition  of  two  planes  at  the  end  of  the  klino- 
diagonal.     Fig.  156  represents  still  the  same  combination,  with 

the  addition  of  the  two  planes  of 
the  negative  orthodiagonal  hemi- 
prisin.  Fig.  157  represents  the 
same  combination  as  Fig.  154, 
with  the  addition  of  the  two 
planes  of  the  positive  orthodiago- 
nal hemi-prism.  Fig.  158  is  the 
same  combination  as  Fig.  153, 
with  the  addition  of  the  positive 


0=ooo:6:c»f, 
»  =  a  :  6  :  o»  c. 


principal  hemi-octahedron. 


Fig   163 


Fig.  159  is  also  the  same  combina- 


Fig.  164. 


•4-  »  =  oo  a  :     :  et 

—  i  =  QO  a  :  b  :  e', 

t'  =  a  :  6  :  oo  e. 


THE   THREE    STATES   OF   MATTER.  167 

tion,  with  the  addition  of  the  negative  hemi-octahedron.  Fig. 
160  is  the  same  combination  as  Fig.  154,  with  the  negative 
hemi-octahedron.  Fig.  161  is  the  same  with  both  hemi-octahe- 
drons.  Fig.  162  represents  the  same  combination  as  Fig.  153, 
with  the  addition  of  the  four  planes  of  the  prism  parallel  to  the 
klinodiagonal.  Fig.  163  is  the  same  combination  as  Fig.  160,  ex- 
cept that  the  planes  of  the  negative  hemi-octahedron  are  more 
dominant,  and  the  basal  planes  do  not  appear.  Lastly,  Fig.  164 
represents  a  combination  of  all  the  forms  which  have  appeared 
on  the  previous  figures  of  this  system. 

Hemihedral  Forms. 

The  hemihedral  forms  of  this  system  only  appear  as  modifying 
planes  on  the  edges  or  solid  angles  of  the  holohedral  forms,  and 


Fig.  165.  Fig.  166.  Fig.  167. 

can  easily  be  distinguished,  because  they  modify  only  one  half  of 
the  similar  edges  or  solid  angles  of  the  form.  Fig.  165  represents 
a  compound  form,  in  which  ordinary  tartaric  acid  frequently  crys- 
tallizes. It  is  a  combination  of  an  oblique  rhombic  prism  t  with 
the  terminal  planes  ii  and  the  two  hemi-prisms  -\-i  and  — i. 
On  these  crystals  there  are  four  solid  angles,  e,  which  are  evi- 
dently similar,  and  we  should  therefore  expect  that  they  would 
in  any  case  be  similarly  modified.  But  on  the  crystal  of  the 
variety  of  tartaric  acid  which  rotates  the  plane  of  polarization 
of  light  to  the  right,  we  find  only  the  two  front  planes,  as  on 
Fig.  166 ;  and  on  the  crystals  of  the  variety  of  tartaric  acid  which 
rotate  the  plane  of  polarization  of  light  to  the  left,  only  two 
back  planes,  as  on  Fig.  167.  These  two  forms  are  evidently  re- 
lated to  each  other  in  the  same  way  as  the  two  forms  of  Figs. 


168  CHEMICAL   PHYSICS. 

149,  150,  and  cannot   be   made  to  coincide  by  any  change   of 
position. 

Such  hemihedral  modifications  occur  chiefly  on  crystals  of  sub- 
stances which  have  the  power  of  rotating1  the  plane  of  polariza- 
tion of  light.  Common  cane-sugar  has  this  property,  and  on  its 
crystals  we  find  the  two  back  planes  of  the  klinodiagonal  prism, 
without  the  corresponding  front  planes.  Fig.  168  represents  the 
common  form  of  the  crystals  of  this  substance.  They  have  all 


Fig.  168.  Fig.  169. 


the  planes  of  Fig.  169,  with  the  addition  of  the  planes  of  the  pos- 
itive hemi-prism  +  (oo  a  :  b  :  c),  and  the  two  back  planes  of 
the  klinodiagonal  prism  a  :  b  : 


CO  C. 


TRICLINIC  SYSTEM. 

In   the   triclinic  system,  a  simple  form  consists  of  only  two 
opposite  parallel  planes.     These  planes  may  have  any  position 
towards   the   three   axes,  and  these  axes  may  have   any  incli- 
nation towards  each  other,  and  any  relative 
lengths.     In  all  crystals  of  the  same  sub- 
stance, however,  the  axes  have  always  the 
same  relative  length,  and   are  inclined  to 
each  other  at  the  same  angles.    Moreover,  of 
the  possible  positions  in  which  the  two  paral- 
lel planes  of  a  simple  form  may  be  placed 
towards  the  axes,  only  a  very  few  are  ever 
observed ;  the  most  frequently  seen  are  those 
in  which  the  planes  are  parallel  either  to  one 
or  to  two  of  the  axes. 
Fig.  170  represents  an  octahedron  belonging  to  this  system, 
and  formed  by  uniting  the  ends  of  the  axes  by  planes.     It  is  com- 


THE   THREE    STATES    OF   MATTER. 


169 


fig  17L 


Fig.  172. 


posed  of  four  simple  forms  :  first,  the  form  consisting  of  the  plane 
ABC  and  its  opposite,  which  has  the  symbol  a  :  b  :  c,  or  a' :  b' :  c' ; 
secondly,  the  form  consisting  of  the  plane  ABC'  and  its  oppo- 
site, which  has  the  symbol  a  :  b  :  c',  or  a'  :  b'  :  c  ;  thirdly,  the 
form  consisting  of  the  plane  A  B'  C  and  its  opposite,  which  has 
the  symbol  a  :  b'  :  c,  or  a'  :  b  :  c' ;  fourthly,  the  form  consisting 
of  the  plane  A  B'  C'  and  its  opposite, 
which  has  the  symbol  a  :  b'  :  c',  or 
a'  :  b  :  c.  Fig.  171  represents  an  ob- 
lique prism  belonging  to  this  system,  in 
which  the  axes  have  the  same  position 
as  in  Fig.  170.  It  is  composed  of 
three  forms  :  first,  the  form  consisting 
of  the  plane  A  B  C  D  and  its  opposite, 
which  has  the  symbol  a  :  oo  b  :  c,  or 
a'  :  oo  &'  :  c';  secondly,  the  form  consisting  of  the  plane  A  A'  BE' 
and  its  opposite,  which  has  the  symbol  a  :  oo  b  :  c',  or  a' :  oo  b' :  c ; 
thirdly,  the  form  consisting  of  the  plane 
B  B'  C  C  and  its  opposite,  which  has  the 
symbol  oo  a  :  b  :  oo  c,  or  oo  a' :  b' :  oo  c'. 
Since,  however,  the  relative  lengths  and 
inclinations  of  the  axes  in  this  system 
may  have  any  possible  values,  it  is  evi- 
dent that  we  may  suppose  the  axes  of 
this  oblique  prism  to  unite  the  centres 
of  opposite  planes,  as  in  Fig.  172,  or  in 
fact  to  have  any  other  position  whatso- 
ever. Indeed,  the  position  of  the  axes 
in  the  crystals  of  any  given  substance 
is  in  a  great  measure  arbitrary,  and  we 
assign  such  a  position  in  every  case  as 
will  render  the  symbols  of  the  observed 
forms  of  the  substance  as  simple  as 
possible.  Fig.  173  represents  a  crystal 
of  sulphate  of  copper,  and  the  symbols 
below  the  figure  indicate  the  position 
of  each  pair  of  parallel  faces  towards 
the  three  lines  which  have  been  assumed 
as  the  axes  of  the  crystals  of  this  substance.  The  relative 
lengths  of  these  axes  are  a  :  b  :  c  =  1  :  0.974  :  1.768  and  the 
15 


Fig.  i:a 


170  CHEMICAL  PHYSICS. 

angles   of    inclination  are    a  =  82°   21',    ft  =  77°   87',    y  = 
73°  10'. 

(93.)  Irregularities  of  Crystals.  —  The  crystalline  forms, 
which  we  have  studied  in  the  last  section,  have  been  perfect  and 
regular.  Not  only  the  similar  angles  have  been  equal,  but  also 
the  similar  faces  and  the  other  similar  dimensions  of  the  crystals 
have  been  in  like  manner  equal.  Such,  however,  is  very  seldom 
the  case  with  the  crystals  which  we  find  in  nature  or  form  in  our 
laboratories  ;  indeed,  this  perfection  and  equality  are  so  uncom- 
mon, that  the  figures  which  we  have  studied  can  hardly  be  con- 
sidered other  than  as  ideal.  Crystals  are  very  generally  distorted, 
and  often  their  forms  are  so  much  disguised,  that  an  intimate  fa- 
miliarity with  the  possible  irregularities  is  required  in  order  to 
unravel  their  complexities. 

Crystals  are  rarely  terminated  on  all  sides,  one  or  more  of  the 
faces  being  obliterated  where  the  crystal  is  implanted  on  the 
rock,  or  where  it  is  merged  in  other  crystals.  Frequently,  also, 
some  of  the  faces  have  been  disproportionately  developed,  and  so 
much  so  as  to  change  entirely  the  general  aspect  of  the  crystal ; 
but  in  all  such  cases  the  relative  directions  of  the  faces  remain 
constant,  and  we  can  always  easily  construct  the  ideal  form  which 
corresponds  to  the  imperfect  crystal,  by  projecting  it  on  paper, 
and  placing  all  the  similar  faces  at  equal  distances  from  the 
centre  of  the  crystal,  taking  care  to  preserve  their  relative  di- 
rection. 

A  few  examples  will  give  an  idea  of  the  nature  and  extent  of 
these  irregularities. 

The  common  form  of  alum  is  the  octahedron  of  the  mono- 
metric  system,  and  we  sometimes  find  perfect  octahedrons  among 
the  minute  crystals  which  have  been  formed 
freely  in  the  midst  of  a  solution  of  the  salt ; 
as,  for  example,  at  the  end  of  a  thread  sus- 
pended in  the  liquid.     The  crystals  which 
form  against  the  sides  of  a  vessel  are  always 
more  or  less  united  with  each  other,  so  that 
only  a  few  of  their  faces,  and  sometimes  only 
FJg  17*.  portions  of  these  faces,  are  free.     Fig.  175 

represents  a  group  of  alum  crystals,  such  as  is  found  in  the 
large  Tats  in  which   the   salt  is  crystallized,  and  will   give  an 


THE   THREE   STATES   OF   MATTER. 


171 


Fig.  175. 

idea  of  f.ie  mode  in  which  the  individual  crystals  are  grouped 
together. 

If  a  small  and  perfect  crystal  of  alum  is  placed  on  the  bottom 
of  a  vessel  filled  with  a  saturated  solution  of  this  substance,  the 
crystal  will  gradually  enlarge,  and  in  a 
regular  manner,  on  all  sides  except  on  that 
on  which  it  rests.  Fig.  1TG  represents  a 
crystal  which  has  been  thus  formed ;  the 
shaded  face,  m  n  p  q  r  s,  being  the  one 
which  rested  on  the  bottom  of  the  vessel. 
And  it  will  be  noticed  that  the  form  is  pre- 
cisely the  same  as  would  be  obtained  by 
removing  from  the  regular  octahedron  a 
slice  parallel  to  one  of  its  faces. 

Frequently  the  growth  of  the  crystal, 
under  such  circumstances,  is  much  greater 
in  a  horizontal  direction  than  it  is  in  the 
direction  perpendicular  to  the  face  on 
which  it  rests  ;  and  the  crystal  then  pre- 
sents an  appearance  similar  to  Fig.  177, 
in  which  the  two  faces  which  were  hori- 
zontal in  the  solution  have  the  same  form. 

We  sometimes  meet  with  octahedrons  belonging  to  the  mono- 
metric  system,  which  have  the  form  of  Fig.  178.     Four  of  tho 


Fig.  176. 


Fig.  177. 


172 


CHEMICAL   PHYSICS. 


Fig  178. 


faces  of  this  octahedron  have 
been  abnormally  developed,  and 
so  much  so  that  we  might  even 
mistake  the  system  to  which 
the  crystal  belongs  ;  but  on 
measuring  the  interfacial  an- 
gles, we  should  find  that  they 
were  all  equal  to  109°  287, 
which  is  the  angle  of  the  octa- 
hedron. 

Fig.  179  represents  a  compound  form,  already  described,  con- 
sisting of  an  octahedron  and  a  cube,  a  form  in  which  the  sul- 
phide of  lead,  galena,  frequently  crystallizes.  We  sometimes, 

also,  find  crystals  of  this  min- 
eral, having  the  form  repre- 
sented in  Fig.  180,  which  we 
might  mistake  for  a  form  of 
the  dimetric  system.  It  is, 
however,  the  same  form  as 
that  of  Fig.  179,  only  abnor- 
mally developed  in  the  direc- 
tion of  one  of  the  axes,  as 
could  easily  be  proved  by 
measuring  the  interfacial  angle 

between  any  two  faces,  o,  which  would  be  found  in  every  case 
to  be  109°  28'. 

The  common  form  of  quartz  is  a  hexagonal  prism,  terminated 
by  a  hexagonal  pyramid.  The  interfacial  angle  between  any  two 
consecutive  prismatic  faces  is  120° ;  that  between  any  two  con- 
secutive pyramidal  faces,  133°  40'.  Fig.  181  represents  a  perfect 


Fig.  179. 


Fig.  180. 


Fig.  182. 


Fig.  183. 


Fig.  184. 


THE   THREE   STATES   OF   MATTER. 


173 


crystal  of  this  form  ;  but  it  is  very  rarely  that  we  find  crystals 
so  perfect,  unless  they  are  very  minute.  One  or  more  of  the 
faces  are  usually  abnormally  developed,  and  forms  like  those 
represented  by  Figs.  182,  183,  184  are  the  results.  Here,  as  in 
the  other  case,  it  would  be  found,  on  measuring  the  interfacial 
angles,  that  they  are  the  same  as  those  between  the  faces  of  the 
regular  form. 

In  the  oblique  system,  the  irregular  development  of  faces  pro- 
duces even  greater  changes  in  the  general  aspect  of  the  crystal 
than   those  which  have  been 
noticed.     Figs.  185  and   186 
represent  two  crystals  of  fel- 
spar belonging  to  the  mono- 
clinic  system,  which  have  ex- 
actly the  same  faces,  but  very 
differently  developed. 

Most  of  the  difficulties  in  the 
study  of  crystals   arise  from 
similar    distortions    to    those 
which  have   been    described, 
and  it  requires  practice  to  be 
able  to  unravel  the  complex- 
ities which   they  present.      This  practice  is   best  acquired  by 
studying  actual  specimens  whose  form  is  known,  and  comparing 
them  with  the  perfect  models  of  the  same  forms. 

(94.)  Groups  of  Crystals.  —  We  frequently  find  two  or  more 
crystals  imited  in  such  a  way  as  to  produce  a  symmetrical  com- 
bination. These  collections  of  crystals,  when  consisting  of  only 
two  individuals,  are  called  twin  crystals.  They  have  regular 
faces,  and  the  same  perfection  of  outline  and  angles  as  simple 
crystals,  for  which  they  might  sometimes  be  mistaken  by  un- 
practised observers.  There  is,  however,  a  simple  criterion  by 
which  they  can  be  generally  distinguished.  Simple  crystals 
never  have  re-entering  angles  ;  so  that,  whenever  such  angles 
occur,  there  must  be  present  on  the  specimen  two  or  more  indi- 
vidual crystals. 

Fig.  187  represents  a  twin  crystal,  consisting  of  portions  of 
two  octahedrons  united  at  the  plane  m  n  p  tf,  which  is  parallel 
to  an  octahedral  face.     It  may  be  formed  from  the  regular  octa- 
hedron (Fig.  188),  by  cutting  it  into  two  equal  parts  by  the 
15* 


Fig.  186. 


Fig.  186. 


174 


CHEMICAL   PHYSICS. 


Fig.  187. 


Fig.  188. 


plane  m  n  p  q  r  s,  and 
then  revolving  one  half 
on  the  axis  uniting  the 
centres  of  the  two  oc- 
tahedral faces  through 
an  angle  of  60°  or  180°, 
and  then  uniting  the 
two  halves  again  hy 
the  surfaces  at  which 
they  were  separated. 

Fig.  189  represents  a  common  form  of  the  crystals  of  gypsum 
(sulphate  of  lime).  It  consists,  as  the  re-entering  angle  shows, 
of  parts  of  two  crystals,  and  may  he 
formed  by  cutting  a  complete  crystal 
(Fig.  190)  into  two  equal  parts  by  the 
plane  p  q  r  m  n  o,  and  revolving  one 
half  of  the  crystal  through  an  angle 
of  185°,  on  an  axis  at  right  angles  to 
the  plane  of  section,  and  then  again 
uniting  the  two  halves.  Twin  crys- 
tals like  these  are  called  hemitropes. 
We  may  suppose  that  such  crystals 
were  formed  from  two  nuclei,  which 
became  originally  united,  one  being  in  an  inverted  position  as 
regards  the  other,  and  that  one  grew  only  in  one  direction,  and 
the  other  in  the  opposite  direction. 

In  the  trimet- 
ric  system,  cruci- 
form crystals,  like 
those  represented 
in  Figs.  191,  192, 
are  very  common. 
The  crystals  rep- 
resented in  the 
figures  consist,  in 
each  case,  of  four 
simple  crystals.  For  a  fuller  development  of  this  subject,  we 
refer  the  student  to  Dana's  "  System  of  Mineralogy,"  Vol.  I. 
p.  127. 

(95~.)  Determination  of  Crystals.  —  In  order  to  determine  a 


Fig.  189. 


Fig.  190. 


Fig.  191. 


Fig  192. 


THE   THREE    STATES    OP   MATTER.  175 

crystal,  it  is  essential  to  ascertain  two  points :  first,  the  crystal- 
line system  to  which  it  belongs,  and,  if  not  of  the  monometric 
system,  the  relative  lengths  and  inclinations  of  the  axes  ;  sec- 
ondly, the  simple  forms  of  which  it  consists. 

When  the  crystal  has  been  regularly  formed,  a  simple  in- 
spection is  generally  sufficient  to  determine  the  crystalline  sys- 
tem to  which  it  belongs  ;  but  when,  as  is  most  generally  the 
case,  the  crystal  is  more  or  less  distorted  by  the  enlargement 
of  a  portion  of  the  planes  at  the  expense  of  others,  the  deter- 
mination of  the  crystalline  system  is  frequently  very  difficult. 
In  studying  out  the  crystalline  system  in  such  cases,  it  is,  first 
of  all,  important  to  distinguish  the  different  sets  of  similar  planes, 
each  of  which  constitutes  a  simple  form.  The  following  indica- 
tions give  important  aid  in  this  respect. 

1.  Similar  planes  are  alike  in  lustre,  hardness,  strise,  what- 
ever may  be  the  variations  in  size.     For  example,  if  a  cubical 
crystal  has  like  striae  on  all  its  six  faces,  these  faces  are  all  simi- 
lar, and  the  form  belongs  to  the  monometric  system. 

2.  Most  crystals  may  be  split  (cleaved)  with  more  or  less  read- 
iness parallel  to  certain  of  their  faces.     This  property,  which  will 
be  considered  in  a  future  section,  frequently  enables  us  to  distin- 
guish similar  planes  when  the  crystallization  is  very  imperfect ; 
for  we  find  that  cleavage  is  obtained  with  equal  ease  or  difficulty 
parallel  to  similar  faces,  and  with  unequal  ease  or  difficulty  par- 
allel to  dissimilar  faces  ;  and  again,  that  cleavage  parallel  to 
similar  planes  affords  planes  of  similar  lustre  and  appearance, 
and  the  converse. 

3.  Planes  equally  inclined  to  the  same  plane  are  similar,  and 
planes  equally  inclined  to  similar  planes  are  similar. 

Having,  by  means  of  these  indications,  studied  out  the  simi- 
lar planes  of  the  crystal,  the  student  will  very  probably  be  able 
to  recognize  the  crystalline  system  at  once  ;  but  if  not,  he  will 
generally  find  an  unerring  guide  to  the  system  of  crystallization 
in  the  modifications  of  the  crystal.  The  law  which  governs  these 
modifications  has  already  been  stated  (91),  and  the  mode  of  ap- 
plying it  is  evident.  If,  for  example,  we  find  a  cubical  crystal 
whose  basal  edges  are  differently  modified  from  the  lateral  edges, 
we  know  that  these  edges  are  not  similar,  and  hence  that  the 
crystal  does  not  belong  to  the  monometric  system.  If  the  basal 
edges  are  all  modified  alike,  the  crystal  belongs  to  the  dimetric 


1T6 


CHEMICAL   PHYSICS. 


system ;  but  if  only  the  opposite  basal  edges  are  modified  alike, 
it  belongs  to  the  trimetric  system.  The  following  table,  for  which 
I  am  indebted  to  Professor  Dana,*  will  aid  the  student  in  the 
examination  of  crystals. 


MONOMETRIC 

System. 


Two  adjacent  or  ' 
two       approximate  ( 
sim.  pi.  impossible.  , 

Two  adjacent  or 
two       approximate 
sim.  pi.  possible. 

TRICLINIC 
System. 

MONOCLIN- 
IC 

1      System. 

1.  All  edges  modified  alike. 

2.  Angles  truncated  or  replaced 
by  3  or  6  similar  planes. 

^Number  of  similar  planes  at  extremities  )  HEXAGONAL 
some  multiple  of  3.  \      System. 

The  superior 
basal  modifica- 
tions in  front 
not  similar  to 
the  correspond- 
ing inferior  in 
front  or  supe- 
rior behind. 

N.  B.  The  right  rhomboidal  prism  on  its  rhom- 
boidal  base  may  be  distinguished  from  the  other 
right  prism  by  the  dissimilar  modifications  of  its  lat- 
eral and  basal  edges  and  angles. 

1.  Similar  planes 
at  each  base  either 
4  or  8  in  number. 
The  superior         2.  All  lat.  edires 
basal  modifica- 
tions   in   front 
similar  to   the 
corresponding 
inferior  in  front 
or  superior  be- 
hind. 


Number  of  si 

of  crystal  3  or 

1 

.  All  edges 

not  modified 

alike. 

Number  of 

!.    Two  f     or 
none   of   the  • 
angles  trunc. 
or  repl.  by  3 
or  6  similar 
planes. 

similar  planes 
at  extremities 
of  crystal  nei- 
ther 3  nor  a 
multiple  of  3. 

(if  modified)  simil. 
trunc.  or  bevelled.J 


DIMETRIO 
System. 


1.  Similar  planes 
at  each  base  either 
2  or  4  in  number. 

2.  All  lat.  edges 
(if    modified)    not 
simil.  truncated  or 
bevelled.  J 


TRIMETRIC 

System. 


The  study  of  the  modifications  of  crystals  may  sometimes 
correct  deductions  from  measurements.  The  interfaeial  angles 
of  crystals  are  liable  to  slight  variations,  not  generally  exceed- 
ing a  few  minutes,'but  in  extraordinary  cases  amounting  to  one 
or  two  degrees.  For  example,  cubes  of  common  salt  have  been 
observed  with  angles  of  92°  or  93°,  and  might  be  mistaken  for 
rhombohedrons,  were  it  not  that  the  distribution  of  modifying 
planes  indicated  the  perfect  similarity  of  the  edges  and  angles. 

Having  determined  the  system  of  crystallization,  it  is  next  im- 
portant, if  the  system  is  not  the  monometric,  to  determine  tho 


*  Dana's  System  of  Mineralogy,  Vol.  I.  p.  123. 

t  The  rhombohedron  is  the  only  solid  included  in  tbis  division,  any  of  wbose  angles 
admit  of  a  truncation  or  replacement  by  three  or  six  planes. 

I  The  terminal  edges  of  the  octahedrons  are  here  termed  lateral,  in  order  that  these 
statements  may  be  generally  applicable  both  to  prisms  and  octahedrons. 


THE   THREE   STATES   OP   MATTER.  177 

relative  lengths  and  inclinations  of  the  axes.  There  is  obviously 
a  direct  relation  between  these  values  and  the  interfacial  angles, 
and  this  relation  can  be  expressed  mathematically,  so  that  the 
one  can  be  calculated  from  the  other.  It  is  the  especial  object 
of  works  on  the  subject  of  Mathematical  Crystallography  to  ex- 
plain these  relations,  and  to  develop  the  formulae  by  which  the 
calculations  can  be  made. 

The  last  point  in  the  determination  of  a  crystal  is  to  ascertain 
the  simple  forms  of  which  it  is  composed,  so  as  to  give  the  sym- 
bol, that  is,  the  parameters  of  each  set  of  similar  planes.  In 
many  cases,  the  forms  may  be  discovered  by  inspection  ;  but  in 
other  cases  the  exact  parameters  of  any  one  form  can  only  be 
ascertained  by  calculation  from  the  value  of  the  interfacial  an- 
gles, or  from  the  parameters  of  other  forms  already  known.  The 
method  of  making  these  calculations  is  also  explained  in  the 
works  on  Mathematical  Crystallography. 

(96.)  Use  of  Goniometers.  —  It  is  evident,  from  the  last  sec- 
tion, that  the  interfacial  angles  are  the  most  important  elements 
in  the  determination  of  crystals.  These  angles  are  measured  by 
means  of  instruments  called  Goniometers.  The  simplest  of  these 
instruments,  called  the  Common  or  Application  Goniometer,  is 
represented  by  Fig.  193.  It 
consists  of  a  semicircular 
arc,  graduated  to  half-de- 
grees, and  of  two  arms,  ar- 
ranged as  represented  in  the 
figure.  The  first  of  these 
arms,  a  b,  is  fixed  at  the  ze- 
ro division ;  but  the  second, 
d  /,  turns  on  c,  the  centre  "e~^^  Fig.  193. 

of  the  arc,  as  an  axis,  and 

indicates  on  the  limb  the  angle  of  the  crystal.  In  using  the  in- 
strument, the  faces  whose  inclination  is  to  be  measured  are 
applied  between  the  arms,  which  are  opened  until  they  just  admit 
the  angle,  taking  care  that  the  edge  made  by  the  two  faces  is 
perpendicular  to  the  plane  of  the  instrument.  It  is  easy  to  de- 
termine when  the  arms  are  closely  applied  to  the  faces  of  the 
crystal,  by  holding  the  instrument  between  the  eye  and  the  light, 
and  observing  that  no  light  passes  between  the  arms  and  the  faces 
of  the  crystal.  The  two  arms,  a  b  and  df,  slide  in  the  slits  i  k, 


178 


CHEMICAL  PHYSICS. 


g  A,  /  #i,  and  can  be  shortened  at  pleasure,  a  provision  which  is 
frequently  important  in  the  case  of  small  crystals.  Moreover, 
for  measuring  crystals  partially  imbedded,  the  arc  is  jointed  at  £, 
so  that  the  part  a  t  may  be  folded  back  on  the  other  quadrant. 
Sometimes  the  arms  admit  of  being  separated  from  the  arc,  an 
arrangement  which  is  more  convenient  than  the  one  represented 
in  the  figure. 

When  a  regular  goniometer  is  not  at  hand,  approximate  results 
may  be  obtained  by  means  of  an  extemporaneous  pair  of  arms 
made  of  thin  sheet-metal,  mica,  or  even  of  card.  The  arms  are 
first  applied  to  the  faces  of  the  crystal,  as  already  described  ; 
then,  carefully  retained  in  their  relative  position,  they  are  placed 
on  a  sheet  of  paper,  and  the  angle  is  laid  off  by  drawing  lines 
with  a  pencil  and  ruler  parallel  with,  or  in  the  direction  of,  each 
of  the  arms.  This  angle  may  then  be  measured  by  means  of  a 
common  protractor,  or  a  scale  of  cords. 

The  common  goniometer  is  at  best  a  rough  instrument ;  for, 
even  when  delicately  used,  it  seldom  furnishes  results  within  a 
quarter  of  a  degree  of  the  truth.*  For  polished  crystals  we  have 
a  much  superior  instrument,  called  the  Reflective  Goniometer. 
There  are  several  varieties  of  this  instrument,  but  we  shall  only 
describe  the  one  which  is  most  generally  used.  This  was  origi- 
nally devised  by  Wollaston,  and  is  called  by  his  name. 

The  principle  of  all  reflective  goniometers  is  illustrated  by 
Fig.  194.  Let  a  b  c  be  the  section  of  a  crystal  made  by  a  plane 

perpendicular  to  the  edge 
formed  by  the  intersection 
of  the  two  faces  whose 
angle  we  wish  to  meas- 
ure, and  a  b,  a  c,  the  sec- 
tions of  the  two  faces. 
The  angle  required  is  ev- 
idently the  same  as  the 
plane  angle  b  a  c.  Let 
S  S  and  MM  be  two  ob- 
jects at  some  distance  from  the  crystal,  which  may  be  used  as 
signals.  The  eye  of  an  observer  at  O,  looking  at  the  face  of  the 


Fig.  194. 


*  A  more  accurate  form  of  the  Application  Goniometer,  devised  by  Adelmann,  is 
described  in  Dufrenoy's  "  Traite  de  Mineralogie,"  Vol.  I.  This  instrument  may  also 
be  used  as  a  Reflective  Goniometer. 


THE   THREE   STATES   OF   MATTER.  179 

crystal,  sees  a  reflected  image  of  the  upper  signal  in  the  direction 
O  My  and  coinciding  with  the  lower  signal,  seen  by  direct  vision. 
If,  now,  the  crystal  is  revolved  on  the  edge  whose  projection  is 
the  point  a,  until  it  assumes  the  position  a'  b'  c1',  it  is  evident 
that  the  reflected  image  of  the  upper  signal  will  again  be  seen 
in  coincidence  with  the  lower  signal.  But  in  order  to  bring  the 
crystal  to  the  second  position,  it  is  obviously  necessary  to  revolve 
the  face  a  c  through  the  arc  m  np,  which  is  the  supplement  of 
the  required  angle.  If,  then,  we  can  measure  the  angle  through 
which  the  crystal  must  be  turned  in  order  to  reproduce  the  coin- 
cidence, we  can  easily  calculate  the  angle  of  the  crystal.  This 
object  is  readily  accomplished  by  the  goniometer  of  Wollaston. 

The  instrument  consists  of  a  vertical  brass  circle,  L  Z/,  Fig. 
195,  about  twelve  centimetres  in  diameter,  whose  axis  is  mounted 


Fig.  195. 

on  a  firm  support,  p  q  r.  The  circle  is  graduated  on  its  rim  to 
half-degrees,  and  may  be  revolved  by  means  of  the  milled  head 
v,  which  is  fastened  to  one  end  of  the  axis.  A  vernier,*  w,  per- 
manently attached  to  the  support  at  w,  indicates  the  angle  through 
which  the  circle  is  revolved,  and  also  subdivides  the  half-degrees 
into  minutes.  The  axis  on  which  the  circle  revolves  is  hollow, 

*  The  vernier  will  be  described  in  the  chapter  on  Weighing  and  Measuring. 


180  CHEMICAL   PHYSICS. 

and  through  it  passes,  with  slight  friction,  an  interior  axis,  a  c. 
At  one  end  of  this  interior  axis  is  fastened  the  milled  head  s,  by 
means  of  which  it  may  be  revolved,  and  at  the  other  end  the 
contrivances  for  supporting  and  adjusting  the  crystal,  z,  which  is 
fastened  with  wax  to  a  thin  metallic  plate,  d  c.  From  this  con- 
struction it  is  evident  that,  if  we  turn  the  milled  head  v,  the 
circle  and  crystal  will  both  revolve  ;  but  if  we  turn  the  milled 
head  5,  the  crystal  may  be  revolved  independently  of  the  circle. 
Any  distinct  horizontal  line,  such  as  the  bar  of  a  window,  may  be 
used  for  the  upper  signal ;  and  for  the  lower  signal,  a  black  line 
drawn  on  white  paper,  placed  several  feet  below,  and  adjusted 
parallel  to  the  first. 

In  use,  the  instrument  is  placed  on  a  table  about  ten  or  twelve 
feet  in  front  of  the  signals,  and  adjusted  by  means  of  the  level- 
ling-screws,  until  its  axis  is  perfectly  horizontal  and  parallel  with 
the  lines  forming  the  signals.  The  crystal,  which  has  been  pre- 
viously attached  to  the  movable  plate  d  c,  is  next  adjusted,  so 
that  the  edge  of  the  interfacial  angle  to  be  measured  shall  exactly 
coincide  with  the  axis  of  the  instrument  produced.  This  is  the 
most  difficult  adjustment,  and  requires  some  skill.  The  crystal 
should  first  be  brought  into  place  as  nearly  as  possible  by  the 
eye,  either  by  shifting  its  position  on  the  plate  dc,  or  by  changing 
the  position  of  the  plate  by  means  of  the  axis  b  d  and  the  joint  g*. 
When  apparently  adjusted,  the  eye  should  be  brought  as  near  the 
crystal  as  possible,  and  directed  towards  the  lower  signal.  The 
milled  head  s  should  next  be  turned  until  the  image-'of  the  upper 
signal  is  seen  reflected  from  one  of  the  faces,  which  includes  the 
angle  to  be  measured.  If  the  crystal  is  perfectly  adjusted,  the 
image  will  appear  horizontal,  and  may  be  brought  into  perfect 
coincidence  with  the  lower  signal,  seen  by  direct  vision.  If  there 
is  not  a  perfect  coincidence,  the  adjustment  must  be  altered  until 
it  is  obtained.  The  milled  head  is  next  revolved  until  the  reflec- 
tion of  the  upper  signal  is  seen  in  the  second  face,  and  if  this 
image  also  coincides  with  the  lower  signal,  seen  in  direct  view, 
the  adjustment  is  complete  ;  if  not,  the  adjustment  must  be 
made  perfect,  by  altering  the  position  of  the  plate  d  c,  and  the 
first  face  again  tried.  A  few  successive  trials  of  the  two  faces 
will  enable  the  observer  to  obtain  a  perfect  adjustment.  When 
the  two  images  are  perfectly  horizontal,  the  edge  formed  by  the 
intersection  of  the  two  faces  must  be  parallel  to  the  axis  of  the 


THE   THREE   STATES   OP   MATTER.  181 

circle,  but  it  will  not  necessarily  coincide  with  it.  A  slight  vari- 
ation from  exact  centring  in  the  position  of  the  edge  is  not, 
however,  of  importance,  when  the  goniometer  is  placed  ten  or 
twelve  feet  distant  from  the  signals,  so  that  this  adjustment  may 
be  made  sufficiently  near  by  the  eye.  The  method  of  adjustment 
which  has  been  described  depends  on  the  laws  of  reflection,  which 
will  be  explained  in  the  chapter  on  Light.* 

The  crystal  thus  adjusted,  the  angle  is  very  easily  measured. 
The  zero  division  of  the  limb  is  first  made  to  coincide  with  the 
zero  division  of  the  vernier.  The  eye  is  then  brought  as  near 
to  the  crystal  as  possible,  and  directed  towards  the  lower  sig- 
nal. The  crystal  is  then  revolved  by  the  milled  head  s  until 
the  image  of  the  upper  signal,  reflected  from  one  of  the  faces 
enclosing  the  required  angle,  coincides  with  the  lower  signal  seen 
by  direct  vision.  This  coincidence  obtained,  the  circle  and 
crystal  are  turned  together  by  means  of  the  milled  head  v, 
taking  care  to  keep  the  eye  in  exactly  the  same  position  until 
the  same  coincidence  is  observed  with  the  second  face.  The  angle 
through  which  the  circle  has  been  turned  may  now  be  read  off 
by  means  of  the  vernier  ;  and  this,  as  we  have  seen,  is  the  sup- 
plement of  the  angle  of  the  crystal.  When  the  faces  of  a  crystal 
are  highly  polished,  we  can  determine  its  angles  by  means  of  the 
Wollaston  goniometer  within  a  few  minutes,  f  Unfortunately, 
however,  the  faces  of  most  crystals  are  not  sufficiently  polished 
to  give,  under  ordinary  circumstances,  a  distinct  image  of  the 
signal.  In  many  such  cases,  good  results  can  be  obtained  by 
making  the  measurements  in  a  partially  darkened  room,  and 
using  as  the  upper  signal  a  narrow  slit  in  the  screen  covering  one 
of  the  windows,  and  as  the  lower  signal,  a  horizontal  black  line 
drawn  on  the  casement  below.  The  slit  is  best  made  by  covering 
a  rectangular  aperture  in  the  screen  with  a  parallel  ruler,  which 


*  Another  method  of  adjusting  the  goniometer  and  the  crystal  is  described  by  Pro- 
fessor W.  H.  Miller,  of  Cambridge,  England,  in  his  work  on  Crystallography,  and  also 
in  the  last  edition  of  Phillips's  Mineralogy,  London,  1852.  This  method  is  preferable 
to  the  one  described  in  the  text  in  most  cases,  and  especially  when  the  crystals  are  mi- 
nute or  the  lustre  of  the  faces  dim. 

t  For  the  methods  of  rectifying  the  instrument  and  of  determining  the  probable 
errors  of  measurement,  the  student  may  consult  Naumann,  Lehrbuch  der  reinen  und 
angewandten  Krystallographie,  Leipzig,  1830,  Band  II  ;  Neumann,  Das  Krystallsys- 
tem  des  Alhites  ( Abhandlungen  der  koniglicheu  Akademic  der  Wissenschaften  in 
Berlin,  vom  Jahre  1830). 

16 


182  CHEMICAL   PHYSICS. 

may  be  opened  more  or  less,  as  circumstances  require.  When 
the  faces  are  very  dull,  the  slit  may  be  illuminated  by  means  oi 
a  heliostat.  In  such  cases,  when  we  can  see  no  image,  we  can 
sometimes  get  an  impression  of  light  imperfectly  reflected  from 
the  faces  of  the  crystal,  and  this  enables  us  to  measure  the  angle 
within  ten  or  twelve  minutes.  We  can  sometimes  render  the 
faces  of  crystals  reflecting,  by  fastening  on  them  very  thin  pieces 
of  mica  by  means  of  some  interposed  liquid,  such  as  water  or  oil 
of  turpentine. 

The  Wollaston  goniometer  has  been  modified  by  Rudberg* 
and  Mitscherlich,  f  and  the  instrument,  as  thus  improved,  is  con- 
structed by  Oertling,  of  Berlin.  The  modifications  consist 
chiefly,  —  First,  in  an  improved  apparatus  for  centring  and 
adjusting  the  crystal.  Secondly,  in  substituting  for  the  distant 
signals  cross-wires  at  the  focus  of  the  eye-piece  of  a  telescope 
which  is  firmly  attached  to  the  stand  of  the  instrument.  The 
object-glass,  which  is  directed  towards  the  crystal,  is  so  adjusted 
that  the  rays  of  light  emanating  from  a  lamp  placed  before  the 
eye-piece  and  illuminating  the  cross-wires  are  rendered  parallel 
before  they  strike  upon  the  face  of  the  crystal,  and  thus  produce 
the  same  effect  as  if  they  emanated  from  a  signal  ten  or  twelve 
feet  distant.  Thirdly,  in  directing  the  eye  by  means  of  a  second 
telescope,  furnished  with  cross-wires,  whose  optical  axis  is  in  the 
same  plane  as  that  of  the  first  telescope,  and  is  parallel  to  the 
plane  of  the  graduated  circle.  In  using  this  instrument,  the 
crystal  is  first  carefully  adjusted,  and  then  turned  until  the  re- 
flected image  of  the  cross-wires  of  the  first  telescope  is  seen  to 
coincide  with  those  of  the  second,  seen  by  direct  vision.  The 
whole  circle  is  then  turned  until  the  same  coincidence  is  obtained 
with  the  image  reflected  from  the  second  face.  The  angle  is  then 
read  off  on  the  graduated  limb,  which,  in  the  large  goniometer 
constructed  by  Oertling,  is  divided  into  sixths  of  a  degree,  and 
each  of  these  divisions  subdivided  by  a  vernier  into  sixths  of  a 
minute.  This  goniometer  gives  very  accurate  measurements; 
but  on  account  of  the  loss  of  light  produced  by  the  lenses,  it  can 
only  be  used  with  crystals  whose  faces  are  highly  polished.  In- 

*  Vorschlag  zu  einem  verbesserten  Reflexionsgoniometer  (Annalen  der  Phys.  und 
Chem.  von  Poggendorf,  IX.  s.  517). 

t  Abh.  der  kon.  Akad.  der  Wiss.,  Berlin,  1825,  1839.  Also  Dufrenoy,  Traite'  de 
Mineralogie,  Vol.  I. 


THE   THREE   STATES   OP   MATTER.  183 

deed,  it  is  seldom  that  such  nicety  is  required,  since  the  angles 
of  crystals  are  liable  to  accidental  variations  amounting  to  several 
minutes,  and  the  ordinary  Wollaston  goniometer  will  in  most  cases 
measure  the  angles  as  accurately  as  they  are  formed  by  nature. 

For  descriptions  of  the  various  forms  of  reflective  and  other 
goniometers,  which  have  been  proposed  by  Babinet,*  Haidinger,f 
and  others,  J  the  student  is  referred  to  the  original  memoirs. 

(97.)  Identity  of  Crystalline  Form.  —  It  was  stated  in  (79), 
that,  with  certain  limitations,  the  crystalline  form  is  always  the 
same  for  the  same  substance,  and  we  are  now  prepared  to  under- 
stand what  the  limitations  are.  It  is  not  true,  in  the  ordinary 
acceptation  of  the  word,  that  the  same  substance  always  crystal- 
lizes in  the  same  form ;  but  the  same  substance,  with  the  excep- 
tions hereafter  to  be  noticed,  always  crystallizes  in  the  same 
system.  Common  salt,  for  example,  usually  crystallizes  in  cubes  ; 
but  when  it  is  crystallized  from  a  solution  containing  urea,  it 
takes  the  form  of  the  regular  octahedron,  or  else  a  compound 
form,  on  which  the  cube  and  octahedron  are  united.  Both  of 
these  forms  belong  to  the  Monometric  System.  So  also,  M.  le 
Comte  de  Bournon,  in  a  monograph  of  two  volumes,  has  de- 
scribed eight  hundred  different  forms  of  the  mineral  calcite  ;  but 
all  of  these  belong  to  the  Hexagonal  System.  When  a  substance 
crystallizes  in  the  Monometric  System,  the  relative  lengths  of  the 
axes  of  the  different  forms  must  necessarily  be  the  same  ;  but  in 
the  other  systems,  the  relative  lengths  of  the  axes  of  the  different 
forms  of  the  same  substance  may  be  different.  We  have  seen, 
however,  that  these  lengths  always  bear  to  each  other  a  very  sim- 
ple numerical  ratio  (compare  pages  143, 147, 159,  and  104),  and 
that  in  the  oblique  systems  the  axes  of  the  different  forms  of  the 
same  substance  have  always  the  same  relative  inclinations  (com- 
pare pages  164  and  168).  It  follows,  therefore,  that  when  we  say 
that  a  substance  always  crystallizes  in  the  same  form,  we  only 
mean  that  it  crystallizes  in  forms  belonging  to  the  same  system. 
The  number  of  possible  forms  in  which  a  given  substance  may 
crystallize  (although  it  is  restricted  to  forms  of  one  system)  is, 

*  Dufre'noy,  Traite  de  Mineralogie,  Vol.  I. 

t  Sitzungsberichte  der  mathem.-naturw.  Classe  der  kais.  Akademie  der  Wissen- 
schaftcn  zu  Wien.  Novemberhefte  des  Jahrganges  1855. 

t  Suckow,  Vorschlag  zu  einem  Goniometer  (Journal  fur  praktische  Chemie  von 
Erdmann,  Band  II.).  Gilbert's  Annalen  der  Physik,  Jahrgang  1820.  Also  Kolinati, 
Elemente  der  Krystallogrnphie,  Brunn,  1855. 


184  CHEMICAL  PHYSICS. 

of  course,  infinite ;  but  the  number  of  actual  forms  in  which  it 
is  observed  to  crystallize  is  generally  very  limited,  —  seldom  ex- 
ceeding two  or  three.  Under  similar  circumstances,  a  given 
substance  almost  invariably  takes  the  same  form;  so  that  this 
form  is  one  of  the  most  characteristic  properties  by  which  a 
substance  may  be  recognized.  Moreover,  we  also  find  that  in 
any  given  system  the  possible  forms  of  a  substance  are  limited 
to  either  holohedral  or  hemihedral  forms.  For  example,  we 
always  find  iron  pyrites  crystallized  in  the  parallel  hemihedral 
forms  of  the  Monometric  System,  and  gray  copper  in  the  oblique 
hemihedral  forms  of  the  same  system. 

(98.)  Dimorphism  and  Polymorphism.  —  There  are  several 
substances,  which,  under  widely  different  conditions,  may  be 
made  to  crystallize  in  the  forms  of  two  systems,  and  a  few 
which  may  be  made  to  crystallize  in  those  of  three  systems. 
Such  substances  are  said  to  be  dimorphous  or  polymorphous. 
Sulphur,  for  example,  at  the  ordinary  temperature  of  the  air, 
crystallizes  in  the  forms  of  the  Trimetric  System  ;  but  at  the  tem- 
perature of  113°  C.  it  crystallizes  in  the  forms  of  the  Monoclinic 
System.  Carbon,  also,  is  found  in  nature  as  diamond,  whose 
crystals  belong  to  the  Monometric  System,  and  as  graphite,  whose 
crystals  belong  to  the  Hexagonal  System.  Again,  carbonate  of 
lime  occurs  in  forms  of  the  Hexagonal  System,  when  it  is  called 
calcite  ;  and  in  forms  of  the  Trimetric  System,  when  it  is  called 
arragonite.  Lastly,  titanic  acid  crystallizes  in  the  forms  of  the 
Dimetric  System,  in  which  a  :  b  =  1  :  0.6442  (rutile)  ;  in  forms 
of  the  same  system,  in  which  a  :  b  =  1  :  1.7723  (antase)  ;  and 
also  in  forms  of  the  Trimetric  System  (brookite). 

When,  however,  a  substance  crystallizes  in  the  forms  of  differ- 
ent systems,  we  find  that  in  the  several  states  its  other  properties 
differ  as  widely  as  the  forms ;  and  so  much  so,  that  it  may  be 
questioned  whether  they  can  properly  be  regarded  as  the  same 
substances.  No  two  substances  could  differ  more  widely  than 
the  two  states  of  carbon  (diamond  and  graphite)  ;  and  similar 
differences,  although  not  quite  so  striking,  exist  between  the 
different  states  of  other  substances.  It  becomes,  then,  a  question 
of  considerable  interest,  whether  these  states  can  properly  be  re- 
garded as  the  same  substance.  But  this  discussion  must  be  re- 
served for  another  portion  of  this  work. 


THE   THREE   STATES   OF  MATTER. 


185 


Elasticity. 

(99.)  Elasticity  of  Solids.  —  Having  considered  the  effect  of 
cohesion  in  retaining  the  molecules  of  solids  in  a  determinate  po- 
sition with  reference  to  each  other  (79),  we  come  next  to  consider 
the  effect  of  this  molecular  force  in  determining  phenomena  of 
elasticity.  It  has  been  stated  (77),  that  the  phenomena  of  elas- 
ticity could  be  developed  in  all  matter  by  compression,  and  that  in 
solid  matter  they  could  also  be  developed  by  tension,  by  flexure, 
and  by  torsion.  The  laws  of  elasticity  in  solid  bodies  may,  for  the- 
most  part,  be  developed  both  by  mathematical  analysis  and  by 
experiment ;  but  we  shall  be  obliged  to  confine  ourselves,  in  this 
work,  to  a  simple  enunciation  of  them,  referring  the  student  to 
the  works  on  Physics  which  have  been  previously  cited,  for  a 
full  development  of  the  subject. 

(100.)  Elasticity  of  Tension.  —  In  experimenting  on  the  elas- 
ticity developed  in  solids  by  tension,  we  suspend  the  rod  or  wire 
by  its  upper  extremity  to  a 
firm  support,  and  attach  to  its 
lower  extremity  a  pan  to  re- 
ceive weight  (Fig.  196).  The 
elongation  caused  by  the  addi- 
tion of  weight  to  the  pan  can 
then  be  measured  by  means  of 
a  cathetoraeter.*  If  the  elon- 
gation does  not  exceed  a  cer- 
tain amount  for  any  given 
rod,  and  the  experiment  is  not 
continued  too  long,  the  rod 
will  resume  its  original  length 
when  the  weight  is  removed. 
If,  however,  the  elongation 
exceeds  the  limit  of  elastici- 
ty, or  if  the  strain  is  contin- 
ued beyond  a  limited  time,  a 
permanent  change  of  length 
and  bulk  will  ensue.  When 
the  limits  of  elasticity  are  Fig  196 


*  This  instrument  will  be  described  in  the  chapter  on  Weighing  and  Measuring. 

16* 


186  CHEMICAL   PHYSICS. 

not  exceeded,  it  will  be  found  that  the  following  laws  will  hold 
true  in  all  experiments  of  this  kind. 

1.  The  elongation  caused  by  an  increase  of  tension  is  the  same 
for  the  same  subtance,  whatever  may  have  been  the  original  ten- 
sion.    For  example,  if  we  are  experimenting  on  a  rod  of  iron, 
we  shall  find  that  the  elongation  caused  by  the  addition  of  one 
kilogramme  to  the  pan  is  the  same,  whether  the  pan  was  before 
empty,  or  was  loaded  with  fifty  kilogrammes  or  any  other  amount 
of  weight. 

2.  The  elongation  is  proportional  to  the  increase  of  tension. 
If  the  rod  is  elongated  one  millimetre  by  one  kilogramme,  it  will 
be  elongated  ten  millimetres  by  ten  kilogrammes,  and  so  on. 

3.  The  elongation  is  proportional  to  the  length  of  the  rod. 
A.  rod  of  the  same  substance,  of  the  same  size,  but  twice  as  long 
as  another,  will  be  elongated  twice  as  much  by  the  same  increase 
of  weight. 

4.  The  elongation  is  inversely  proportional  to  the  area  of  the 
*  section  made  at  right  angles  to  the  length  of  the  rod.     If,  for 

example,  two  rods  of  the  same  substance  have  the  same  length, 
and  if  the  area  of  the  section  of  the  first  is  twice  as  great  as  that 
of  the  second,  it  will  only  be  elongated  one  half  as  much  by  the 
same  strain. 

(101.)  Coefficient  of  Elasticity.  —  It  follows  from  these  laws, 
that  the  elongation  of  a  given  rod,  which  we  will  represent  by  /, 
is  proportional,  first,  to  a  constant  quantity,  (7,  depending  on  the 
nature  of  its  substance  ;  secondly,  to  the  weight,  to,  by  which  it 
is  stretched  ;  thirdly,  to  its  length,  L  ;  and,  fourthly,  is  inversely 
proportional  to  the  area  of  the  section,  S.  This,  expressed  in 
mathematical  language,  is 

I  =  C .  to  .  L  .  1  ; 
hence, 

/_  q^L  r        C  =    l  S 

If  in  these  equations  we  put  K  =  ^-,  they  will  become, 

i  to  L  rr    L  to 

I  = -g  ^~- ,          or          K==  -j-£» 

This  quantity,  JT,  is  called  the  coefficient  of  elasticity.  If  in  the 
last  equation  we  put  /  =  L,  that  is,  if  we  suppose  the  elongation 


THE  THREE  STATES  OF   MATTER.  187 

to  be  equal  to  the  original  length,  and  also  make  S  =  1  m.  m.*, 
the  equation  becomes  K  =  tP  ;  which  shows  that  the  coefficient 
of  elasticity  of  any  homogeneous  substance  is  equal  to  the  abso- 
lute weight  required  to  double  the  length  of  a  bar  of  that  sub- 
stance, whose  section  is  equal  to  one  square  millimetre,  supposing 
such  an  increase  of  length  were  possible,  which  is  not  the  case 
except  with  threads  of  India-rubber.  The  following  table  gives 
the  coefficients  of  elasticity  of  a  number  of  metals,  as  deter- 
mined by  M.  Wertheim. 

Coefficients  of  Elasticity  of  Annealed  Metals  at  different  Temperatures. 

150  to  20o.  10(P.  2000. 

Lead,      .  .        .     1,727  1,630  .    . 

Gold,  .         .  .        5,584  5,408  5,482 

Silver,    .  .         .     7,140  7,274  6,374 

Copper,       .  .      10,519  9,827  7,862 

Platinum,  .         .  15,518  14,178  12,964 

Iron,  .         .  .       20,794  21,877  17,700 

Cast-Steel,  .         .  19,561  19,014  17,926 

English  Steel,  .       17,278  21,292  19,278 

It  appears  from  this  table,  that,  as  a  general  rule,  the  coeffi- 
cients diminish  as  the  temperature  rises  from  15°  to  200°. 

M.  Wertheim  has  also  made  experiments  on  metals  which  have 
been  submitted  to  various  mechanical  agencies,  and  has  found 
that  all  circumstances  which  increase  the  density  increase  also 
the  coefficient  of  elasticity,  and  the  reverse. 

The  coefficient  of  an  alloy  is  sensibly  the  mean  of  the  coeffi- 
cients of  the  metals  which  enter  into  its  composition,  even  when 
a  change  of  volume  accompanies  the  formation  of  the  alloy.  A 
current  of  electricity  diminishes  momentarily  the  elasticity,  inde- 
pendently of  the  diminution  caused  by  the  elevation  of  temper- 
ature which  it  produces. 

(102.)  Elasticity  of  Compression.  —  If  a  bar  is  compressed 
in  the  direction  of  its  length  by  a  force  acting  at  the  extremities, 
it  is  found  that  the  amount  by  which  it  is  shortened  is  exactly 
equal  to  the  amount  by  which  it  would  be  lengthened,  were  the 
force  applied  so  as  to  stretch  it.  It  follows,  from  this  equality  in 
the  effects  produced,  that  the  laws  of  elasticity  developed  by  com- 
pression are  the  same  as  the  laws  of  the  elasticity  of  tension. 

(103.)  Elasticity  of  Flexure.  —  The  simplest  case  of  elas- 
ticity developed  by  flexure  is  illustrated  by  Fig.  197.  It  repre- 


188  CHEMICAL  PHYSICS.  , 

sents  a  rectangular  bar,  A  B, 
fastened  at  one  of  its  extremi- 
ties in  a  horizontal  position. 
If,  now,  we  press  upon  the  free 
extremity  of  the  bar  at  JS,  so 
,.  197t  as  to  curve  it  a  little,  the  bar 

will  tend  to  return  to  its  first 

position,  in  consequence  of  the  elasticity  developed  by  the  flex- 
ure ;  and  if  left  to  itself,  will  resume  the  horizontal  position  after 
a  few  oscillations. 

The  elasticity  of  flexure  is,  in  great  measure,  a  mixed  effect  of 
the  elasticity  of  compression  and  tension.  Since,  by  the  bending 
of  the  bar,  the  particles  of  the  convex  surface  A  B'  are  drawn 
apart,  while  those  of  the  concave  surface  CD'  are  forced  to- 
gether, and  it  is  in  consequence  of  the  elasticity  thus  developed 
that  the  bar  tends  to  return  to  its  original  position.  But,  more- 
over, the  particles  of  the  bar  have  changed  their  position,  inde- 
pendently of  the  change  of  their  relative  distances  apart,  since 
the  particles,  which  were  previously  situated  on  a  straight  line, 
are  now  on  a  curved  line  ;  and  we  know  that  such  a  change 
of  position  must  be  accompanied  with  a  development  of  elas- 
ticity. 

Starting  from  these  data,  the  laws  of  elasticity  of  flexure  can 
be  deduced  by  mathematical  analysis.  They  are  comprised  in 
the  formula, 

a==to£s  or          to  =  ~a-3-        T67] 

in  which  L  is  the  length  of  the  bar ;  tD,  the  weight  acting  per- 
pendicularly, and  tending  to  bend  it ;  6,  the  breadth  of  the  bar 
measured  perpendicularly  to  the  direction  of  this  force  ;  e,  the 
thickness  of  the  bar  ;  a,  the  arc  described  B  B' ;  and  K,  a  con- 
stant quantity  depending  on  its  substance.  If  in  [67]  we  put 
L  =  1  m.,  b  =  1  c.  m.,  e  =  1  c.  m.,  a  =  1  c.  m.,  it  becomes 
tO  =  K.  The  number  K  is  called  the  coefficient  of  the  elas- 
ticity of  flexure,  and  it  is  evidently  equal  to  the  weight  which 
will  bend  a  bar  of  a  given  substance  one  metre  long  and  one 
centimetre  square  through  an  arc  of  one  centimetre.  When  the 
values-  of  a,  6,  e,  and  L  have  been  determined  by  experiment  in 
the  case  of  any  substance,  the  value  of  K  for  this  substance  can 
easily  be  calculated. 


THE   THREE   STATES   OF   MATTER.  189 

Equation  [67]  shows  that  the  flexure  of  the  bar,  or  a,  is  pro- 
portional to  the  force  tD.  It  follows  from  this,  that,  as  the  rod  is 
bent,  it  tends  to  restore  itself  to  the  position  of  equilibrium  with 
a  force  which  increases  with  the  distance  of  each  of  its  points 
from  their  position  of  equilibrium.  Now  it  can  be  proved  that, 
when  this  condition  exists,  the  oscillations  which  the  bar  makes 
in  returning  to  the  position  of  equilibrium  will  be  isochronous, 
whatever  may  be  their  amplitude.  Hence  reciprocally  it  will 
follow,  that,  if  the  oscillations  of  such  a  bar  are  isochronous,  the 
condition  under  consideration  must  exist.  It  is  easy  to  verify  the 
isochronism  of  the  oscillations  experimentally,  because,  being  very 
rapid,  they  produce  a  sound  whose  pitch  depends  on  the  number 
of  oscillations  in  a  second,  and  hence  in  any  case  would  vary,  if 
the  isochronism  were  not  preserved.  Now  it  is  well  known  that 
this  pitch  is  constant  for  a  given  bar,  whatever  may  be  the  ampli- 
tude of  the  oscillations  ;  and  thus  this  is  at  once  a  consequence 
and  a  proof  of  the  law,  that  the  flexure  is  proportional  to  the 
force. 

It  has  been  assumed  in  this  discussion,  that  the  section  of  the 
bar  is  a  rectangle,  and  that  the  force  is  applied  in  a  direction  per- 
pendicular to  one  of  its  sides.  When  these  conditions  are  not 
fulfilled,  the  formulae  [67]  no  longer  hold  true.  It  has  been  also 
assumed  that  the  bar  returns  exactly  to  its  first  position  when  it 
is  freed,  or,  in  other  words,  that  the  flexure  does  not  exceed  the 
limit  of  elasticity. 

(104.)  Applications.  —  Almost  all  springs  —  for  example, 
watch-springs  and  carriage-springs  —  are  appli- 
cations of  the  elasticity  of  flexure.  The  bow 
is  another  example.  The  elasticity  of  a  hair 
cushion  is  due  to  the  elasticity  of  flexure  devel- 
oped in  the  single  hairs.  The  spring  balance, 
Fig.  198,  which  has  been  already  described  (71), 
is  an  application  of  the  law  that  the  flexure  is 
proportional  to  the  weight. 

The  elasticity  of  flexure  has  been  applied  by 
Bourdon  in  the  construction  of  a  metallic  ma- 
nometer and  barometer,  which  bear  his  name. 
It  is  a  familiar  fact,  that,  if  we  force  air  into  Fig  198 

a  flexible   tube,  closed   at   one   end,  which   is 
flattened  and  coiled  up  on  its  flat  side,  the  pressure  tends  to 


190 


CHEMICAL   PHYSICS. 


0 


Fig.  199. 


uncoil  it ;  and,  on  the  other  hand,  that,  if  we  exhaust  the 
air,  the  exterior  pressure  tends  to  coil  it  still  further.  If  the 
tube  is  also  elastic,  it  is  evident  that,  when  the  pressure  is  re- 
moved or  restored,  it  will 
return  to  its  former  condi- 
tion, provided  that  the  lim- 
its of  elasticity  are  not 
passed.  These  facts  are 
the  basis  of  the  two  instru- 
ments represented  in  Figs. 
199  and  200. 

The  chief  object  of  the 
manometer  (Fig.  199)  is  to 
measure  the  pressure  exert- 
ed by  confined  steam,  al- 
though it  might  be  used  for 
any  similar  purpose.  It 
consists  of  an  elastic  tube, 
a  ft,  made  of  brass,  and 
coiled  as  represented  in  the 

figure.     A  section  of  this  tube  is  represented  at  S.     The  end  of 
the  tube,  #,  is  firmly  fastened  to  the  stopcock,  w,  by  which  it 
connects  with  the  steam-boiler.     To  the  closed  end  of  the  tube, 
ft,  is  attached  a  hand,  e,  which 
moves  over  an   index.     As  the 
pressure  of  the  steam  on  the  inte- 
rior surface  of  the  tube  increases, 
it  gradually  uncoils,  arid  the  hand 
points  to  the  number  of  atmos- 
pheres of  pressure.     When  the 
pressure   is   removed,  the   tube, 
in  virtue  of  its  elasticity,  resumes 
its  original  position,  and  the  hand 
points  to  the  first  division  of  the 
scale. 

The  barometer  (Fig.  200)  is  a 
more   delicate  instrument,   con- 
structed on  the  same  principle. 
The  tube  is  here  closed  at  both  ends,  and  when  the  pressure  of 
the  atmosphere  is  just  equal  to  the  tension  of  the  confined  air,  it 


Fig.  200. 


THE   THREE    STATES    OF    MATTER. 


191 


is  in  the  condition  of  equilibrium.  When,  however,  the  pressure 
of  the  atmosphere  diminishes,  there  is  an  excess  of  pressure  on  the 
interior  surface  of  the  tube,  and  it  tends  to  uncoil ;  on  the  other 
hand,  when  the  atmospheric  pressure  increases,  there  is  an  ex- 
cess of  pressure  on  the  exterior  surface,  and  the  tube  tends  to 
coil  still  more.  As  constructed,  the  air  is  partially  exhausted 
from  the  tube,  and  hence  the  pressure  of  the  atmosphere  always 
tends  to  coil  it  more  or  less,  as  compared  with  the  condition  of 
equilibrium.  The  tube  is  fastened,  at  the  middle  of  its  length,  to 
the  upper  part  of  the  instrument,  and  its  free  ends  are  connected, 
by  the  metallic  threads  a,  ft,  with  the  hand,  which  serves  to  mul- 
tiply the  motion,  while  a  small  spiral  spring,  c,  causes  the  needle 
to  follow  with  accuracy  any  change  of  position  in  the  ends  of  the 
tube.  The  arc  is  graduated  to  correspond  with  a  mercurial  ba- 
rometer, and  denotes  the  number  of  centimetres  of  mercury  to 
which  the  atmospheric  pressure  corresponds. 

(105.)  Elasticity  of  Torsion.  —  It  is  a  fact  of  frequent  obser- 
vation, that,  when  a  metallic  wire,  a  b  (Fig.  201),  fastened  at  one 
end,  is  twisted  by  a  force  applied  at  the 
other,  it  strives  to  return  to  its  original 
position,  and  when  free  returns  to  this  po- 
sition, after  having  made  a  number  of  os- 
cillations.    This  of  course  supposes  that 
the  strain  has  not  exceeded  the  limit  of 
elasticity. 

•  It  is  easy  to  see  how  elasticity  is  devel- 
oped in  a  wire  by  torsion.     Suppose  m  n, 
Fig.  201,  to  be  a  line  of  particles  parallel 
to  the  axis  of  the  wire  when  in  a  state  of 
equilibrium.     It  is  evident  that,  when  the 
wire  is  twisted,  these  particles  will  be  dis- 
tributed on  the  helix  m  ri ;  but  in  order  to 
assume  this  position,  the  distances  between 
the  successive  molecules  must  be  increased, 
which  will  develop  the  elasticity  of  tension, 
ticity  is  also  developed  by  the  fact  that  the  particles  resist  any 
change  of  position,  even  when  the  relative  distances  are  pre- 
served. 

The  angle  a,  through  which  a  radius  of  the  lower  base  of  the 
wire  is  turned,  is  termed  the  angle  of  torsion.     The  force  which, 


Fig  201. 

Besides,  this  elas- 


192  CHEMICAL  PHYSICS. 

applied  at  the  extremity  of  a  lever  equal  to  the  unit  of  length 
and  perpendicular  to  the  wire,  will  maintain  it  in  a  position 
which  corresponds  to  a  certain  angle  of  torsion,  is  called  the 
force  of  torsion.  And  when  the  angle  of  torsion  is  such  that  the 
arc  described  by  the  extremity  of  the  lever  is  also  equal  to  unity, 
the  force  of  torsion  is  called  the  coefficient  of  torsion. 

The  laws  of  the  elasticity  of  torsion  were  investigated  by  Cou- 
lomb, and  are  expressed  in  the  following  formulae .:  — 

4  -rr    *>  W  I~£Q    1 

t  =  n  r  __ ,  bo. 

'Vi  9  7r 

or 


which  apply  to  the  case  represented  in  Fig.  201,  of  a  cylindrical 
weight  suspended  by  a  cylindrical  wire  to  a  fixed  support,  a,  so 
that  the  axis  of  the  cylinder  and  the  wire  correspond.  In  this 
case,  W  represents  the  weight  of  the  cylinder  ;  r,  its  radius ;  g+ 
the  force  of  gravity ;  F,  the  coefficient  of  torsion  of  the  wire ; 
and  t,  the  time  of  the  oscillations  which  the  cylinder  makes  on 
its  axis,  in  returning  to  the  state  of  rest  after  the  wire  has  been 
twisted.  The  laws  of  torsion  discovered  by  Coulomb  are  as 
follows. 

1.  The  force  of  torsion  is  proportional  to  the  angle  of  torsion. 
In  order  to  establish  this  law,  Coulomb  made  experiments  on  the 
oscillations  of  the  weight  W  on  its  axis  caused  by  the  torsion  of 
the  wire,  using  wires  of  different  substances,  and  loading  them 
with  different  weights.     He  found  that  in  each  case  the  times  of 
the  oscillations  were  independent  of  the  amplitudes,  or,  in  other 
words,  that  they  were  isochronous ;  and  it  can  readily  be  shown, 
by  the  same  course  of  reasoning  used  in  (103),  in  regard  to  the 
elasticity  of  flexion,  that  the  law  is  a  necessary  consequence  of 
this  fact. 

The  isochronism  of  the  oscillations  caused  by  torsion  is  ex- 
pressed by  [68],  since  the  value  of  the  second  member  of  the 
equation  is  independent  of  the  amplitude. 

2.  The  force  of  torsion  is  independent  of  the  tension  of  the 
wire.    It  has  been  proved  by  experiment,  that  the  square  of  the 
time  of  oscillation  is  proportional  to  the  weight,  W9  or,  in  other 

W 
words,  that  -3-  is  a  constant  quantity ;  and  hence  it  follows,  that 


THE    THREE   STATES    OP   MATTER. 


193 


the  value  of  F  [69]  is  not  changed  by  any  variation   of  the 
weight. 

The  coefficient  of  torsion  depends  upon  the  substance  of  the 
wire,  and  also  upon  its  diameter  and  its  length,  it  being  inversely 
proportional  to  the  length  and  directly  proportional  to  the  fourth 
power  of  the  diameter  of  the  wire. 

(106.)  Applications  of  the  Elasticity  of  Torsion.  —  One  of 
the  most  beautiful  applications  of  the  laws  of  torsion  is  the  tor- 
sion-balance, contrived  for  measuring 
the  intensity  of  feeble  attractive  and 
repulsive  forces.  One  form  of  this 
balance,  which  is  used  for  measuring 
the  intensity  of  the  attractive  or  repul- 
sive force  between  electrified  bodies,  is 
represented  in  Fig.  202.  The  general 
structure  of  the  apparatus  is  evident 
from  the  figure,  and  does  not  require 
description.  The  most  essential  part 
of  it  is  a  fine  silver  wire,  attached, 
at  its  upper  end,  to  the  brass  circle 
e,  and  from  the  lower  end  of  which 
is  suspended  a  shellac  needle.  The 
circle  e  is  movable,  and  turns  on  the 
cap,  which  is  cemented  to  the  glass 
tube  d.  This  circle  is  graduated  on 
the  exterior  rim  into  degrees,  and  the  index-mark  at  a,  which  is 
fastened  to  the  cap,  indicates  the  angle  through  which  the  circle  e 
has  been  turned.  The  glass  tube  also  turns  in  a  brass  socket, 
which  is  cemented  to  the  glass  cover  of  the  apparatus.  The  re- 
pulsive or  attractive  force  between  the  two  electrified  balls  m  and 
w,  is  measured  by  the  angle  through  which  it  is  necessary  to  twist 
the  wire  (by  turning  the  circle  e),  in  order  to  balance  it,  the  force 
exerted  being  always  proportional  to  the  angle  of  torsion.  A 
modification  of  the  torsion-balance  was  employed  by  Cavendish, 
and  subsequently  by  Bayly,  in  the  determination  of  the  density 
of  the  earth. 

(107.)  Limit  of  Elasticity.  —  It  has  been  several  times  stated 

in  the  previous  sections,  that  the  laws  of  elasticity  only  hold  true 

so  long  as  the  strain  does  not  exceed  the  limit  of  elasticity ',  and 

it  was  stated  in  section  (77),  that,  within  more  or  less  narrow 

17 


Fig.  202. 


194  CHEMICAL  PHYSICS. 

limits,  all  solids  were  perfectly  elastic.  The  phenomena  of  elas- 
ticity may  be  developed  by  torsion  in  those  substances  which  seem 
the  most  destitute  of  this  property.  Thus,  if  we  take  a  leaden 
wire  two  millimetres  in  diameter  and  three  metres  long,  fix  one 
end  of  it  firmly  to  the  ceiling,  and  fasten  an  index  to  the  other, 
it  will  be  found  that,  if  we  twist  the  wire  twice  round  and  let 
it  go,  it  will,  after  a  number  of  oscillations,  come  to  rest  in  its 
original  position  ;  showing  that  the  elasticity  in  this  leaden  wire 
is  perfect  up  to  the  point  mentioned.  But  if  we  twist  the  wire 
four  times  instead  of  two,  it  will  not  return  to  its  first  position, 
but  to  a  position  short  of  that  by  nearly  two  revolutions.  The 
particles  of  a  leaden  wire  of  this  length  and  thickness  will  bear 
a  displacement  measured  by  two  revolutions  of  the  index  ;  but 
the  displacement  occasioned  by  four  turns  is  more  than  its 
particles  can  bear,  and  they  remain  permanently  displaced, — 
the  wire  having  taken  what  is  technically  called  a  set.  So 
also,  a  thin  cylinder  of  pipe-clay  (which  is  generally  consid- 
ered as  destitute  of  elasticity  as  almost  any  substance  can  be) 
shows  the  existence  of  elasticity  as  perfect  as  can  be  found  in  the 
best-tempered  steel ;  but  here  again  the  limit  of  elasticity  is  soon 
reached.  A  steel  wire,  similar  to  the  lead  one  just  mentioned, 
might  be  twisted  a  great  many  times  before  its  particles  would 
receive  such  a  set  as  to  prevent  it  from  completely  untwisting 
again ;  but  after  it  had  been  twisted  a  certain  number  of  times, 
the  limit  of  its  elasticity  would  be  passed,  and  it  would  not  come 
to  rest  again  at  its  first  position. 

The  same  phenomena  appear  in  all  the  cases  we  have  studied. 
A  wire,  which,  when  stretched  by  a  light  weight,  will  resume  its 
original  length  when  the  weight  is  removed,  will  be  permanently 
lengthened  if  the  weight  exceeds  a  limited  amount.  So  also  a 
steel  spring,  if  bent  beyond  a  certain  point,  is  forced,  and  re- 
mains permanently  bent  to  a  greater  or  less  extent. 

It  is  a  remarkable  fact,  that  even  when  the  limit  of  elasticity 
has  been  exceeded,  so  that  the  particles  have  taken  a  permanent 
set,  the  elasticity  of  the  whole  mass  remains  the  same  as  before. 
Thus,  when  a  wire  has  been  permanently  lengthened  by  a  great 
strain,  it  is  as  perfectly  elastic  in  its  new  condition  as  before, 
readily  recovering  from  the  effects  of  smaller  degrees  of  exten- 
sion. So  also  it  was  found  by  Coulomb,  that,  after  he  had  given 
a  set  to  the  lead  wire  already  referred  to,  by  twisting  it  four 


THE   THREE   STATES   OF   MATTER. 


195 


times  round,  the  wire  was  as  elastic  in  its  new  condition  as  be- 
fore, requiring  the  same  force  to  give  it  a  further  twist,  and 
recovering  itself  as  completely  when  that  force  was  withdrawn. 

The  limits  of  elasticity  have  been  determined  only  in  the  case 
of  the  elasticity  of  tension.  The  method  of  experimenting  was 
to  take  wires  of  any  length,  but  whose  section  was  equal  to 
one  square  millimetre,  and  to  determine  the  amount  of  weight 
required  to  extend  them  permanently  0.05  m.  m.  for  each 
metre  of  length.  This  investigation  was  more  difficult  than 
would  appear,  on  account  of  the  fact  that  the  duration  of  the 
strain  has  an  important  influence  on  the  permanent  elongation 
which  results  ;  for,  when  once  commenced,  this  elongation  slowly 
increases,  and  although  it  may  not  be  sensible  at  the  end  of  a  few 
minutes,  yet  after  several  hours  it  may  become  very  evident. 
This  principle  is  illustrated  by  the  well-known  facts,  that  the  best 
springs  are  worn  out  with  long  use,  that  the  beams  of  floors  bend 
little  by  little,  and  that  buildings  settle  with  time.  The  limit  of 
elasticity  is  not,  therefore,  a  value  which  can  be  rigorously  de- 
termined, and  hence  the  numbers  in  the  following  table  must  be 
regarded  as  only  approximate. 


Metals. 

Limit  of  Elasticity. 

Tenacity. 

Lead,  .     .     . 

(  Drawn, 
l  Annealed, 

k. 
0.25 
0.20 

k. 
2.50 
1.80 

Tin 

(  Drawn,      . 

0.40 

2.45 

JL  111,        •         •         • 

(  Annealed, 

0.20 

1.70 

Gold,.     .     . 

(  Drawn,      . 
I  Annealed, 

13.00 
3.00 

27.00 
10.08 

Silver,     .     . 

(  Drawn, 
I  Annealed, 

11.00 
2.50 

29.00 
16.02 

Copper,  .     . 

(  Drawn,     . 

(  Annealed, 

12.00 
3.00 

40.30 
30.54 

Platinum,     . 

(  Drawn,     .        .       «/ 
(Annealed,      .    .    . 

26.00 
14.00 

34.10 
23.50 

Iron,   .     .     . 

(  Drawn,      .      .  .^  •./)•,.  , 
\  Annealed,      .        . 

32.50 
5.00 

61.10 

46.88 

Cast-Steel,   . 

(  Drawn,    V       i        , 

i  Annealed,      .      ;«.ri 

55.60 
5.00 

80.00 
65.70 

(108.)  Elasticity  of  Crystals.  —  In  most  crystalline  solids 
the  elasticity  is  not  the  same  in  all  directions,  as  is  shown  by  the 
phenomena  of  cleavage  (110).  By  a  beautiful  application  of  the 


. 

196  CHEMICAL  PHYSICS. 

principles  of  acoustics,  Savart*  has  determined  in  a  few  in- 
stances the  differences  of  elasticity  which  the  same  crystals 
present,  when  examined  on  different  lines  of  direction  with 
reference  to  their  crystalline  axes.  As  neither  the  methods  nor 
the  results  of  his  investigations  could  be  made  intelligible  in 
this  connection,  we  must  refer  the  student  to  the  memoirs  cited 
below.  These  differences  of  elasticity  in  crystals  give  rise  to 
some  of  the  most  beautiful  phenomena  of  optics,  and  we  shall 
have  occasion  to  refer  to  the  subject  again  in  that  connection. 

(109.)    Collision  of  Elastic  Bodies.  —  The  effects  of  collision, 
described  in  (41),  are  greatly  modified  when  the  bodies  are  elas- 

tic, and  in  a  way  which  it  is  im- 
portant to  study.  Let  us  then 
suppose,  in  order  to  make  the 
case  simple,  that  the  bodies  are 
two  elastic  spheres,  a  and  b, 
Fig.  203,  with  different  masses, 
Fig.  203.  M  and  M',  which  are  moving  in 

the  same  direction,  from  left  to 
right,  with  the  velocities  V  and  to'  re- 
spectively, to  being  greater  than  to'. 
When  the  balls  come  together,  they  will 
flatten  each  other  (Fig.  204),  until  the 
velocities  of  the  two  become  equal.  If 
the  bodies  are  soft,  this  flattening  will 
be  permanent,  and  the  balls  will  move 
on  together  with  a  velocity  which,  as  we  have  found,  [23,]  is 

r23, 

•' 


If  the  bodies,  on  the  contrary,  are  elastic,  and  the  limit  of  elas- 
ticity is  not  exceeded  during  the  impact,  we  have  the  same  result 
as  before  up  to  the  moment  of  greatest  flattening,  and  at  that 
moment  the  velocity  is  to",  as  given  above.  But  after  this  moment 
a  new  set  of  phenomena  appears.  The  two  balls  thus  flattened 
act  as  springs,  and  in  resuming  their  original  form  impart  recip- 
rocally to  each  other  as  much  momentum  as  was  expended  in 
producing  the  compression.  At  the  moment  of  greatest  com- 

*  Annales  de  Chimie  et  de  Physique,  2"  Serie,  Tom.  XL.    Also  Dufrenoy,  Traite 
de  Mineralogie,  Tom.  I.  p.  289. 


THE   THREE   STATES    OP   MATTER.  197 

pression,  it  is  evident  that  the  ball  a  has  lost  in  velocity  an 
amount  equal  to  b  —  D"  ;  and,  on  the  other  hand,  the  ball  b 
has  gained  in  velocity  an  amount  equal  to  b"  —  b'.  In  recover- 
ing its  form,  the  ball  b  tends  to  drive  a  to  the  left,  and  therefore 
to  retard  its  motion  ;  and,  on  the  other  hand,  the  ball  a  tends  to 
throw  b  forward,  and  therefore  to  accelerate  its  motion.  More- 
over, by  the  principle  just  stated,  this  retardation  and  accelera- 
tion will  be  just  the  same  as  that  caused  between  the  first  contact 
of  the  balls  and  the  moment  of  greatest  compression.  Hence, 
after  the  impact,  the  velocity  of  a  will  be  diminished  by  an 
amount  equal  to  2(b  —  I)"),  and  that  of  b  increased  by  an 
amount  equal  to  2  (b"  —  I)').  Representing,  then,  the  veloci- 
ties after  the  impact  by  bo  and  il,,  we  have 

t)d  =  t)  —  2(b  —  b"),     and     bl===b>  +  2(tr  —  b1)-    [70.] 

Subtracting  the  second  of  these  equations  from  the  first,  we  ob- 
tain 

b0  —  h  =  b'  —  b.  pi.] 

This  equation  shows  that  the  difference  of  velocity  is  the  same 
after  the  impact  that  it  was  before  ;  but  the  relation  has  been  re- 
versed, the  velocity  of  a  being  now  less  than  that  of  b.  Hence 
it  follows,  that,  after  the  impact,  the  two  balls  will  recede  from 
each  other  as  rapidly  as  they  approached  each  other  before  ;  and 
this  is  true  in  every  case  of  the  impact  of  two  spheres,  when 
both  are  perfectly  elastic.  In  order  to  find  the  actual  velocities 
after  impact,  we  have  only  to  substitute  in  [70]  the  value  of  b" 
given  by  [23],  when  we  obtain 

h    -  W—  M')  b 


and  [72.] 

h         (M1  —M)  b'  +  2  Jl/b 

M+M' 

In  obtaining  these  values,  we  have  supposed  that  both  balls  were 
moving  from  left  to  right,  the  mass  M,  whose  velocity  is  the 
greatest,  being  at  the  left  of  the  other.  The  same  formulae,  how- 
ever, hold  true  for  all  cases  of  direct  impact  ;  except  that,  when 
one  of  the  balls  is  moving  from  right  to  left,  the  sign  of  its  velocity 
must  be  changed.  A  few  examples  will  illustrate  the  application 
of  the  formulae. 

17* 


198  CHEMICAL  PHYSICS. 

Let  us  suppose,  then,  for  the  first  case,  that  the  masses  of  the 
two  balls  are  equal,  and  that  the  ball  b  is  at  rest.  We  shall 
then  have  M1  =  M,  and  b'  =  0.  Substituting  these  values  in 
[72],  we  have 

bo  =  0,  and  bi  =  b.  [73.] 

Hence,  after  the  impact,  the  ball  a  remains  at  rest,  and  the  ball 
b  moves  on  with  the  velocity  which  a  had  before  the  impact. 

Let  us  suppose,  as  the  second  case,  that  the  masses  are  equal, 
and  that  .the  motions  are  in  opposite  directions,  that  of  a  posi- 
tive, and  that  of  b  negative.  We  shall  then  have  M'  =  M,  and 
b'  =  —  b'.  Substituting,  we  obtain 

b0  =  —  b',  and  bl==b.  [74.] 

Here,  after  the  impact,  the  ball  a  will  move  from  right  to  left 
with  the  previous  velocity  of  &,  and  b  will  move  from  left  to  right 
with  the  previous  velocity  of  a  ;  and  in  general,  when  the  masses 
are  equal,  the  two  spheres  will  interchange  velocities. 

Let  us  suppose,  as  a  third  case,  that  the  velocities  are  equal,  and 
the  motions  in,  opposite  directions,  as  before  ;  and  further,  that 
the  mass  of  b  is  greater  than  that  of  a.  We  then  have  1)'  =  —  b, 
and  M1  >  M.  Substituting,  we  obtain 

(M—  3  M1)  b  «.         (3  M—  M1)  b 

=  —--       and     bl  =  —- 


In  this  case,  after  the  impact,  the  ball  a  must  always  move  from 
right  to  left,  when,  as  supposed,  M1  >  M,  '.  If  M'  <  3  M,  the 
ball  6,  after  the  impact,  will  move  from  left  to  right.  If,  how- 
ever, M'  >  3  M,  it  will  move  from  right  to  left.  When 
M  '  =  3  My  we  have 

b0  =  2b,  and  t)i  =  0  ;  [76.] 

that  is,  the  ball  a  will  move  from  right  to  left  with  twice  its  pre- 
vious velocity,  and  the  ball  b  will  remain  at  rest. 

We  can  also  apply  the  formula  to  the  case  where  an  elastic 
ball  strikes  vertically  on  a  fixed  obstacle,  as  when  an  India- 
rubber  ball  is  let  fall  on  the  ground.  In  this  case,  M1  =  oo, 
and  b'  =  0.  Substituting  these  values,  [72]  becomes  bo  =  — 
that  is,  the  body  moves,  after  impact,  with  the  same  velocity  as 
before,  but  in  an  opposite  direction.  Hence  the  India-rubber  ball 
should,  by  (22),  rebound  to  the  same  height  from  which  it  fell. 


THE   THREE   STATES   OF   MATTER. 


199 


Fig.  206. 


This  is  not  practically  true,  because  the  surface  on  which  it  falls 
is  never  perfectly  elastic,  and,  moreover,  because  the  ball  does 
not  recover  promptly  from  the  compression. 

Let  us  next  suppose  that  the  sphere  strikes  the  obstacle  in  an 
oblique  direction  (Fig.  205),  and  that  its  velocity  at  the  moment 
of  collision  is  represented  by  the 
line  i  a',  which  represents  also 
the  direction  of  the  motion.  This 
motion  is,  by  (24),  equivalent  to 
two  others,  one  in  a  direction 
which  is  tangent  to  the  surface, 
and  whose  velocity  at  the  mo- 
ment of  collision  is  represent- 
ed by  the  line  i  c,  and  another, 
which  is  normal  to  the  surface, 
and  whose  velocity  at  the  mo- 
ment of  collision  is  represented 
by  the  line  i  n'.  The  lines  i  c 
and  i  n'  are  sides  of  a  parallelo- 
gram, of  which  i  a1  is  the  diagonal.  The  first  motion  will  con- 
tinue, after  the  impact,  with  the  same  velocity,  without  changing 
its  direction.  The  second  motion,  as  we  have  just  seen,  will  be 
changed  by  the  impact  into  a  motion  in  the  opposite  direction, 
but  with  the  same  velocity.  In  order  to  find  the  resulting  path 
and  velocity  of  the  ball  after  the  impact,  we  need  only  to  combine 
these  two  motions.  For  this  purpose,  we  have  already  drawn 
the  line  t  c,  which  represents  the  velocity  and  the  direction  of  the 
first  component.  The  line  i  n,  drawn  equal  to  the  line  i  n',  and 
in  an  opposite  direction,  will  represent  the  velocity  and  direction 
of  the  second  component.  Completing  the  parallelogram  and 
drawing  its  diagonal,  we  find  that  the  body  moves,  after  the  im- 
pact, in  the  direction  i  6,  with  a  velocity  represented  by  the  length 
of  this  line.  Moreover,  since  the  parallelograms  c  n  and  c  n1  are 
equal,  their  diagonals  are  also  equal,  —  proving  that  the  velocity 
after  the  impact  is  the  same  that  it  was  before.  Further,  since 
i  n  is  in  the  same  plane  as  i  ri,  it  follows  that  the  diagonals 
must  be  in  the  same  plane,  which  shows  that  after  the  impact  the 
ball  moves  in  the  same  plane  in  which  it  moved  before.  Lastly, 
it  follows,  from  the  equality  of  the  parallelograms,  that  the  an- 
gles b  i  n  and  a1  i  n1  are  equal,  and  consequently  the  angles  bin 


200  CHEMICAL   PHYSICS. 

and  a  in  are  equal.  The  angle  a  i  n,  which  the  original  direc- 
tion of  the  motion  makes  with  the  normal  to  the  surface  of  the 
fixed  obstacle,  is  called  the  angle  of  incidence  ;  and  the  angle 
b  i  n,  formed  by  the  direction  of  the  motion  after  impact  with 
this  normal,  is  called  the  angle  of  re/lection.  Hence,  the  angle 
of  incidence  is  equal  to  the  angle  of  reflection. 

The  absolute  equality  of  the  angles  of  incidence  and  reflection 
is  only  realized  when  both  the  body  and  the  obstacle  are  perfectly 
elastic.  When  this  is  not  the  case,  the  component  t  n  is  less  than 
i  n'y  and  hence  the  angle  b  i  n  greater  than  a  i  n,  the  angle  of  re- 
flection becoming  greater  in  proportion  to  the  deficiency  of  elas- 
ticity ;  and  when  the  bodies  are  unelastic,  it  becomes  equal  to 
90°,  and  the  ball  moves,  after  the  impact,  in  the  direction  i  c. 
Compare  (41). 

Finally,  let  us  suppose  that  two  elastic  spheres,  A  and  .B,  Fig. 
206,  —  moving  in  the  same  plane  with  the  different  velocities  t) 

and  t)',  —  meet  each  other  obliquely. 
In  order  to  find  the  directions  and  ve- 
locities of  their  motions  after  impact, 
we  may  extend  the  method  adopted  in 
the  case  just  discussed.  We  first  de- 
compose the  velocity  of  J.,  repre- 
sented by  the  line  n  v,  into  two  com- 
ponents at  right  angles  to  each  other, 
n  £/==&,  and  n  V=b.  In  like  man- 
ner, we  decompose  the  velocity  of  B 
into  two  components,  n  U1  =  a',  and 

n  V  =  b'.  It  is  now  evident  that  the  effect  of  collision  will  not 
be  felt  in  the  directions  n  U  and  n  U',  since  the  balls  will  slide 
over  each  other  in  the  direction  of  these  components,  and  hence 
we  shall  obtain  for  the  two  velocities  after  contact  in  the  direc- 
tion n  U  or  n  U'  two  quantities,  aQ  and  a1?  equal  to  a  and  a'  re- 
spectively. It  is,  however,  entirely  different  with  the  other  two 
components.  The  velocities  in  the  directions  Vn  and  Vn  are 
reversed  and  changed  by  the  collision,  and  we  therefore  seek  by 
(72)  what  will  be  the  velocities  after  the  collision  in  the  direc- 
tions n  V  for  J.,  and  n  Ffor  B,  and  obtain  two  quantities,  b0  and 
bi.  Lastly,  by  combining  together  on  the  principle  of  the  com- 
position of  velocities  the  components  a0  and  50,  we  shall  obtain 
the  final  direction  and  velocity  of  A ;  and  by  combining  «i  and 


THE  THREE   STATES   OP  MATTER.  201 

b»  the  final  direction  and  velocity  of  B.  This  calculation  can 
easily  be  made  in  any  special  case,  and  does  not,  therefore,  re- 
quire further  illustration.  When  the  masses  of  the  two  spheres 
are  equal,  as  follows  from  [74],  they  exchange  velocities  in  the 
directions  n  V  and  n  V,  and,  the  velocities  in  the  directions 
n  U  and  n  V  being  the  same  as  before,  the  calculation  then 
becomes  quite  simple. 

The  laws  of  the  collision  of  elastic  bodies  may  be  illustrated 
in  a  great  variety  of  ways  ;  but  the  best  of  all  illustrations  is 
found  in  the  game  of  billiards,  which  is  based  almost  entirely 
upon  them.  This  game  is  played  with  balls  of  ivory,  which  are 
in  themselves  elastic,  and  on  a  table  whose  raised  edges  are  cov- 
ered with  elastic  cushions.  The  object  of  the  game  is  to  hit 
one  ball  with  another,  set  in  motion  with  a  stick  moved  by  the 
hand,  so  that  one  or  both  shall  afterwards  move  toward  a  certain 
point  or  points.  To  effect  this,  in  the  various  positions  of  the 
balls,  requires  an  empirical  knowledge  of  the  laws  of  the  col- 
lision of  elastic  bodies,  and  great  skill  in  their  application.  The 
results  obtained  in  this  game  do  not  conform  exactly  to  the 
theory,  on  account  of  the  imperfect  elasticity  of  the  balls  and 
cushions.  Thus  we  have  seen  [73]  that,  when  an  elastic  body 
encounters  another  of  the  same  mass  at  rest,  the  last  is  set  in 
motion,  and  the  former  remains  stationary.  This  is  not  generally 
the  case  with  billiard-balls,  for  usually  both  balls  move  after 
the  impact ;  but  nevertheless,  when  the  stroke  is  very  sharp,  this 
result  does  at  times  occur.  This  is  probably  owing  to  the  fact, 
that  the  friction  of  the  ball  on  the  cloth  covering  of  the  table, 
the  imperfect  elasticity  of  ivory,  and  other  causes  of  disturbance, 
have  the  least  influence  when  the  ball  is  moving  with  a  powerful 
force.  So  also,  when  the  ball  rebounds  from  the  elastic  cushion, 
the  angles  of  incidence  and  reflection  are  not  exactly  equal, 
but  they  are  very  nearly  so  when  the  ball  is  driven  with  a 
powerful  stroke. 

Resistance  to  Rupture. 

(110.)  When  a  rod  is  stretched  in  the  direction  of  its  length, 
with  a  gradually  increasing  force,  it  finally  breaks,  the  force  re- 
quired to  break  it  depending  on  the  substance  of  the  rod,  and  its 
size.  The  smallest  weight  required  to  part  it  is  the  measure  of 


202 


CHEMICAL  PHYSICS. 


the  resistance  of  the  rod,  and  the  weight  required  to  part  a  rod 
of  any  substance,  whose  section  is  equal  to  one  square  millimetre, 
is  the  measure  of  the  tenacity  of  that  substance. 

The  resistance  to  rupture  can  be  conveniently  determined  by 
means  of  the  dynamometer,  represented  in  Fig.  207.     It  consists 


Fig  207. 

of  an  iron  frame,  P,  on  which  slide  two  carriages,  a  and  b.  The 
first  of  these  is  connected  with  a  powerful  spring,  contained  in 
the  box  H.  When  the  carriage  a  is  drawn  forward,  the  spring 
is  bent,  and  communicates  motion  to  the  index,  (7,  which  moves 
on  a  graduated  arc,  and  indicates  in  kilogrammes  the  inten- 
sity of  the  force.  The  second  carriage,  6,  is  united  with  the 
frame  at  A  by  means  of  the  screw  o,  and  may  be  moved  for- 
wards or  backwards  by  turning  the  handle  M.  The  rest  of  the 
apparatus  consists  of  a  train  of  wheels  and  pinions,  which  con- 
nect the  spring  with  the  fly-wheel  F,  and  prevent  it  from  flying 
back  too  suddenly  when  the  tension  is  removed. 

In  order  to  determine  the  resistance  to  rupture  of  a  given  wire 
by  means  of  this  apparatus,  the  two  ends  of  it  are  fastened  to  the 
carriages  by  means  of  the  vices  which  they  carry.  The  handle, 
M,  is  then  slowly  turned  until  the  wire  breaks,  when  the  needle, 
O,  indicates  in  kilogrammes  the  amount  of  force  which  has  pro- 
duced the  rupture. 

By  means  of  this  apparatus,  we  can  easily  establish  the  truth 
of  the  following  laws :  —  1.  The  force  required  to  produce 
rupture  is  proportional  to  the  section  of  the  bar.  2.  It  is  inde- 
pendent of  the  length  of  the  bar. 


THE   THREE   STATES   OF   MATTER.  203 

In  determining  the  resistance  of  bars  to  rupture,  we  meet 
with  the  same  difficulty  already  referred  to  in  connection  with 
the  determination  of  the  limit  of  elasticity.  Tlie  rupture  is  not 
caused  by  the  action  of  a  constant  force.  As. soon  as  the  strain 
exceeds  the  limit  of  elasticity,  the  rod  elongates  little  by  little, 
the  particles  are  at  first  slowly  displaced,  but  finally  they  sud- 
denly separate  and  the  rod  breaks  ;  so  that  a  moderate  force 
applied  for  a  long  time  will  frequently  cause  the  rupture  of  a  rod 
which  would  resist  a  much  greater  force  applied  for  a  short  time. 
This  slow  diminution  of  tenacity  is  a  fact  to  which  it  is  essential 
to  pay  regard  in  the  construction  of  buildings. 

(111.)  Tenacity.  —  The  tenacity  of  a  substance  is  the  resist- 
ance to  rupture,  measured  in  kilogrammes,  which  a  rod  will  ex- 
ert, whose  section  is  just  one  square  millimetre.  In  determining 
the  tenacity  of  solids,  we  may  obviously  experiment  on  rods  or 
wire  of  any  convenient  size,  the  area  of  whose  section  is  known, 
and  then  calculate  the  tenacity  by  the  principles  of  the  last  sec- 
tion. The  tenacity  of  the  different  metals  differs  very  greatly, 
between  that  of  lead,  in  which  it  is  very  feeble,  and  that  of  steel, 
which  has  the  greatest  tenacity  of  all,  as  will  be  seen  by  referring 
to  the  table  on'  page  195,  in  which  the  tenacity  of  the  useful 
metals  is  given  at  the  side  of  the  numbers  expressing  the  limit 
of  elasticity.  It  will  also  be  noticed,  that  there  is  a  very  great 
difference  between  the  tenacity  of  the  same  substance  when 
drawn  into  wire  and  when  annealed,  it  being  greatest  in  the 
first  condition.  The  process  of  drawing  wire  will  be  described 
in  (113).  The  change  of  form  which  it  produces  is  accompa- 
nied by  another  very  curious  result.  Although  the  particles  of 
the  wire  are  really  less  close  together  after  the  operation  of 
drawing  than  they  were  before,  yet  they  hold  together  more 
firmly,  so  that  the  tenacity  of  the  wire  is  greatly  increased. 
The  cohesion  of  iron  is  increased,  in  drawing,  to  a  very  remark- 
able degree,  so  that  fine  iron  wire  is  the  most  tenacious  of  all 
materials.  "  Thus  a  bar  one  inch  square  of  the  best  cast-iron 
may  be  extended  by  a  weight  of  nine  tons  and  three  quarters ; 
a  bar  of  the  same  size  of  the  best  wrought-iron  will  sustain  a 
weight  of  thirty  tons  ;  a  bundle  of  wires  one  tenth  of  an  inch  in 
diameter,  of  such  size  as  to  have  the  same  quantity  of  material, 
will  sustain  a  weight  of  from  thirty-six  to  forty  tons  ;  and  if  the 
wire  be  drawn  more  finely,  so  as  to  have  a  diameter  of  only  one 


204  CHEMICAL  PHYSICS. 

twentieth  or  one  thirtieth  of  an  inch,  a  bundle  containing  the 
same  quantity  of  material  will  sustain  a  weight  of  from  sixty  to 
ninety  tons."  Hence  cables  made  of  fine  iron  wire  twisted  to- 
gether will  sustain,  a  far  greater  weight  than  chains  containing 
the  same  quantity  of  iron.  The  cables  of  suspension  bridges  are 
usually  made  in  this  way. 

(112.)  Cleavage.  —  In  crystalline  bodies,  the  resistance  to 
rupture  is  not  equally  great  in  all  directions.  Most  crystallized 
bodies  are  found  to  break  most  readily  in  certain  planes  affording 
a  more  or  less  smooth  fracture  or  cleavage,  while,  if  they  are 
broken  in  any  other  direction,  the  fracture  is  rough  and  jagged. 
These  planes  are  called  planes  of  cleavage.  They  are  always 
parallel  either  to  actual  faces  on  the  crystal,  or  to  possible  faces. 
Cleavage  can  generally  be  reproduced  on  the  same  crystal  to  an 
indefinite  extent,  in  planes  parallel  to  each  other,  thus  dividing 
the  crystal  into  a  series  of  thin  laminae.  Generally  the  same 
crystal  may  be  cleaved  in  several  directions,  and  the  union  of  the 
several  planes  of  cleavage  forms  what  is  called  a  solid  of  cleav- 
age, which  is  constant  for  the  same  substance,  and  is  always  one 
of  the  simple  forms  of  the  system  to  which  the  crystal  belongs. 
Compare  (93). 

Crystals  differ  very  greatly  from  each  other  in  the  facility  with 
which  they  may  be  cleaved.  In  some  cases,  the  laminae  can  be 
separated  by  the  fingers.  This  is  the  case  with  mica  and  several 
other  minerals.  At  other  times,  a  slight  blow  of  the  hammer  is 
required,  as,  for  example,  with  galena  and  calc-spar ;  while  not 
unfrequently  cleavage  can  be  obtained  only  by  using  some  sharp 
cutting-tool  and  a  hammer.  When  other  means  fail,  it  can  some- 
times be  effected  by  heating  the  crystal  and  immersing  it  while 
hot  in  cold  water.  When  cleavage  is  easily  obtained,  it  is  said  to 
be  eminent. 

In  crystals  of  the  Monometric  System,  cleavage  is  obtained 
with  equal  ease  in  the  direction  of  any  one  of  the  planes  of  cleav- 
age ;  but  in  crystals  of  the  other  systems,  cleavage  is  obtained 
with  equal  ease  only  in  planes  which  are  parallel  to  the  similar 
planes  of  the  crystal.  The  cubic  crystals  of  galena,  for  example, 
which  belong  to  the  Monometric  System,  may  be  cleaved  with  equal 
readiness  in  either  of  the  three  directions  which  are  parallel  to 

*  Carpenter's  Mechanical  Philosophy. 


THE   THREE   STATES   OF   MATTER.  205 

the  faces  of  the  cube.  On  the  other  hand,  the  crystals  of  gypsum, 
which  belong  to  the  Monoclinic  System,  may  be  cleaved  with 
great  facility  in  one  direction,  less  readily  in  a  second,  and  only 
with  some  difficulty  in  a  third ;  in  thick  crystals,  the  last  two 
cleavages  are  scarcely  attainable. 

The  general  laws  with  respect  to  cleavage  are  stated  by  Pro- 
fessor Dana*  as  follows  :  — 

1.  Cleavage  in  crystals  of  the  same  species  yields  the  same 
form  and  angles. 

2.  Cleavage  is  obtained  with  equal  ease  or  difficulty  parallel 
to  similar  faces,  and  with  unequal  ease  or  difficulty  parallel  to 
dissimilar  faces. 

3.  Cleavage  parallel  to  similar  planes  affords  planes  of  similar 
lustre  and  appear ance,  and  the  converse. 

(113.)  Ductility  and  Malleability.  —  Some  substances  will 
not  allow  a  permanent  displacement  of  their  molecules,  and 
break  whenever  the  strain  exceeds  the  limit  of  elasticity.  Such 
substances  are  called  brittle  bodies,  and  to  this  class  belong 
glass,  tempered  steel,  marble,  sulphur,  and  many  others.  There 
are  other  substances,  on  the  contrary,  which,  when  submitted  to 
various  mechanical  processes,  allow  a  permanent  displacement, 
more  or  less  considerable,  of  their  molecules,  which  then  assume 
new  positions  of  equilibrium.  This  property  is  possessed  in  a 
high  degree  by  the  metals,  and  is  called  ductility  or  malleability, 
according  as  it  is  applied  in  drawing  out  wire,  or  in  reducing 
the  metal  to  sheets  and  leaves  in  a  rolling-mill  or  under  the 
hammer. 

The  machine  for  drawing  wire  consists  essentially  of  a  plate 
of  hardened  steel  pierced  with  a  number  of  conical  holes  of  dif- 
ferent sizes.  Through  one  of  these  holes  is  passed  the  end  of  a 
metallic  rod,  which  has  been  reduced  in  size  for  the  purpose. 
This  end  is  then  seized  with  a  pair  of  pliers  and  pulled  with  con- 
siderable force.  In  being  thus  forced  through  the  hole,  the  rod 
becomes  lengthened,  and  diminished  in  size.  It  is  then  passed 
in  like  manner  through  a  smaller  hole,  and  thus  successively, 
until  the-  wire  is  reduced  to  the  requisite  fineness.  Fig.  208 
is  a  representation  of  a  mill  used  for  drawing  iron  wire.  The 
coarser  wire  is  unwound  from  the  reel  F,  and,  after  having 


*  System  of  Mineralogy,  Vol.  I.  p.  103. 

18 


206 


CHEMICAL   PHYSICS. 


Fig.  208. 

passed  the  drawing-plate  A  B,  is  received  on  the  drum  (7,  to 
which  the  force  is  applied  through  the  cog-wheels  r  p,  n  q  (see 
Fig.  209). 

In  order  that  a  substance  should  read- 
ily yield  to  this  mechanical  action,  it  is 
evidently  essential,  not  only  that  its  par- 
ticles should  have  the  power  of  readily 
changing  their  position,  but  also  that  it 
should  be  endowed  with  great  tenacity. 
Hence  those  metals  whose  particles  ad- 
mit most  readily  of  change  of  position 
are  not  necessarily  the  most  ductile. 

A  rolling-mill  consists  of  two  steel 
rollers,  arranged  as  represented  in  Fig. 
210,  so  that  their  distance  apart  can  be 
varied  at  pleasure,  and  so  that  they  may 
be  turned  together  in  unison,  but  in  op- 
posite, directions.  The  plate  of  metal  is 
applied  between  the  two  rollers,  and  is  forced  to  accommodate  its 
thickness  to  the  distance  between  them,  which  is  adjusted  so  as 
to  be  a  little  less  than  the  thickness  of  the  plate.  This  distance 
may  then  be  diminished,  and  the  process  repeated  until  the  thick- 
ness of  the  plate  is  reduced  to  the  desired  amount. 

Many  of  the  metals  can  be  reduced  to  leaves  of  exceeding  te- 
nuity under  the  hammer.  It  is  in  this  way  that  the  goldleaf 
used  in  gilding  is  prepared.  The  gold  plate  is  first  reduced  in 
a  rolling-mill  to  the  thickness  of  about  one  millimetre.  Several 


Fig.  209. 


THE   THREE    STATES    OP   MATTER. 


207 


Fig.  210. 

of  these  plates  are  now  piled  on  each  other,  and  spread  out  by 
beating  the  pile  with  a  heavy  mallet  until  they  are  reduced  to 
the  thickness  of  a  sheet  of  paper.  The  leaves  are  next  separated 
from  each  other  by  sheets  of  paper,  and  the  pile  beaten  again. 
Finally,  the  sheets  of  paper  are  replaced  by  others  made  of  gold- 
beaters' skin.  In  this,  as  in  all  similar  processes,  the  metal  be- 
comes brittle,  and  would  infallibly  break  or  tear  were  it  not 
frequently  reannealed.  The  process  of  annealing  consists  in 
heating  the  substance  to  a  high  temperature,  and  then  allow- 
ing it  to  cool  very  slowly. 

The  relative  malleability  of  the  metals  is  not  the  same  when 
hammered  as  when  rolled,  and  the  difference  appears  to  arise 
from  the  sudden  shocks  which  accompany  the  blows  of  the  ham- 
mer. In  the  following  table,  the  relative  malleability  of  the 
useful  metals  by  both  methods  is  given  side  by  side,  together 
with  the  relative  tenacity  and  ductility.  A  comparison  of  the 
columns  will  illustrate  what  has  been  stated  above. 


Tenacity. 

Iron 

Copper 

Platinum 

Silver 

Zinc 

Gold 

Lead 

Tin 


Ductility. 

Platinum 

Silver 

Iron 

Copper 

Gold 

Zinc 

Tin 

Lead 


Malleability 
under  the 

Ilrunmor. 

Lead 

Tin 

Gold 

Zinc 

Silver 

Copper 

Platinum 

Iron 


Malleability 

under  the 

Rolling-Mill. 

Gold 

Silver 

Copper 

Tin 

Lead 

Zinc 

Platinum 

Iron 


The  action  of  heat  modifies,  in  a  most  marked  manner,  both  the 
ductility  and  malleability  of  many  bodies.     Iron,  for  example,  is 


208  CHEMICAL  PHYSICS. 

very  malleable  at  a  red  heat,  and  in  this  condition  it  can  be  read- 
ily forged  or  rolled  into  sheets.  Glass,  again,  which  is  brittle  at 
the  ordinary  temperature,  is  both  malleable  and  ductile  to  the 
highest  degree  at  a  red  heat.  Copper,  on  the  other  hand,  is  most 
malleable  when  cold,  and  zinc  cannot  be  rolled  out  with  success 
except  between  the  temperatures  of  130°  and  150°  C.  Above 
this  last  temperature,  it  becomes  very  brittle. 

The  malleable  metals  are  capable  of  receiving  impressions  from 
blows  ;  a  property  which  is  continually  made  use  of  in  various 
processes  of  the  arts.  The  processes  of  stamping  coins  and  em- 
bossing figures  on  surfaces  of  various  kinds  are  an  illustration  of 
the  fact.  The  impression  is  made  by  means  of  a  die,  in  which  the 
design  is  sunk,  just  as  the  raised  impression  which  the  wax  is  to 
present  is  sunk  in  the  seal.  The  die,  which  is  made  of  the  hardest 
steel,  is  forced  down  upon  the  blank  coin  by  means  of  a  powerful 
screw  or  lever,  and  the  metal  of  the  coin,  being  comparatively 
soft,  is  driven  with  great  force  into  the  cavities  of  the  die,  and 
retains  the  impression. 

Hardness. 

(114.)  Scale  of  Hardness.  —  Hardness  is  the  resistance  which 
bodies  oppose  to  being  scratched  or  worn  by  other  bodies.  Of 
two  substances,  that  one  is  said  to  be  the  hardest  which  will 
scratch  the  other.  The  hardness  of  a  body  is  closely  related 
to  its  ductility  and  tenacity,  all  circumstances  which  increase 
the  ductility  or  diminish  the  tenacity  rendering  the  body  softer, 
and  the  reverse.  In  order  to  distinguish  a  harder  body  from  a 
softer,  we  either  attempt  to  scratch  the  one  with  the  other,  or  we 
try  each  with  a  file.  The  last  method  is  generally  to  be  pre- 
ferred ;  but  both  should  be  employed  when  practicable,  since 
some  bodies  "  give  a  low  hardness  under  the  file,  owing  either  to 
impurities  or  imperfect  aggregation  of  the  particles,  while  they 
scratch  a  harder  species,  —  showing  that  the  particles  are  hard, 
although  loosely  aggregated."  * 

Hardness  is  an  important  character  of  a  substance,  and  is 
much  used  by  mineralogists  as  a  means  of  distinguishing  between 
mineral  species.  In  order  to  fix  a  common  standard  of  compari- 
son, the  distinguished  German  mineralogist,  Mohs,  introduced  a 

*  Dana's  System  of  Mineralogy,  Vol.  I.  p.  130. 


THE   THREE   STATES    OF   MATTER.  209 

scale  of  hardness.  This  scale  consisted  of  ten  minerals,  which 
gradually  increase  in  hardness,  marked  from  1  to  10.  It  has 
been  since  modified  by  Breithaupt,  who  has  introduced  two  ad- 
ditional degrees  of  hardness,  one  between  2  and  3,  the  other 
between  5  and  6,  as  these  intervals  were  larger  than  the  rest. 
The  numbers  of  Mohs,  however,  have  been  retained.  The  scale 
is  as  follows  :  — 

1.  Talc  ;  common  laminated,  light-green  variety. 

2.  Gypsum  ;  a  crystallized  variety. 
2.5.  Mica;  variety  from  Zinnwald. 

3.  Calcite  ;  transparent  variety. 

4.  Fluor-  Spar ;  crystalline  variety. 

5.  Apatite ;  transparent  variety. 
5.5.  Scapolite ;  crystalline  variety. 

6.  Felspar  (orthoclase)  ;  white,  cleavable  variety. 

7.  Quartz;  transparent. 

8.  Topaz;  transparent. 

9.  Sapphire ;  cleavable  varieties. 
10.     Diamond. 

In  determining  the  hardness  of  a  mineral,  we  draw  a  file  over 
it  with  considerable  pressure.  If  the  file  abrades  the  mineral 
with  the  same  ease  as  No.  4,  and  produces  an  equal  depth  of 
abrasion  with  the  same  force,  the  hardness  is  said  to  be  4  ;  if  less 
readily  than  4,  but  more  readily  than  5,  it  is  said  to  be  between 
4  and  5  (written  4  -  5)  ;  or  we  may  determine  it  with  more  accu- 
racy as  4.25  or  4.50.  Several  successive  trials  should  be  made, 
in  order  to  insure  accuracy,  and  the  student  should  practise  him- 
self in  the  use  of  the  file  with  specimens  of  known  hardness, 
until  he  can  obtain  constant  results.* 

(115.)  Sclerometer. — In  testing  the  hardness  of  the  dissim- 
ilar faces  of  the  crystal,  very  marked  differences  are  frequently 
observed.  Differences  may  also  be  perceived  on  the  same  face 
when  examined  in  different  directions.  For  the  purpose  of 
measuring  with  great  accuracy  the  differences  in  hardness  which 
the  faces  of  a  crystal  present,  an  apparatus  has  been  contrived 
by  Grailichf  and  Pekarek,  called  a  sclerometer.  It  consists 

*  Boxes  containing  the  twelve  minerals  of  the  Mohs  scale  can  be  procured  from 
the  dealers  in  philosophical  apparatus. 

t  Sitzungsberichte  der  mathem.-naturw.  Classe  der  kais.  Akad.  der  Wissen.,  (Wien, 
1854,)  Band  XIII.  s.  410. 

18* 


210  CHEMICAL  PHYSICS. 

essentially  of  a  hard  steel  point  attached  to  the  under  side,  at 
one  end,  of  a  balance  beam,  which  is  carefully  poised  on  its 
knife-edge.  Above  the  point,  and  on  the  upper  side  of  the  beam, 
there  is  a  pan  to  receive  weights,  by  which  the  steel  point  may 
be  pressed  down  upon  the  face  of  a  crystal  with  a  regulated 
force.  At  the  other  end  of  the  beam  there  is  fastened  a  spirit- 
level,  and  the  whole  is  so  adjusted  that  the  beam  —  with  the 
point  and  pan  at  one  end,  and  with  the  spirit-level  at  the  other 
—  is  just  in  equilibrium. 

By  means  of  the  sclerometer,  it  appears,  for  example,  that  the 
rhombohedral  faces  of  crystals  of  calcite,  r  (Fig.  211),  are  softer 


Pig.  211.  Fig.  212. 

than  the  end  faces,  a.  It  has  also  been  found  that  the  hardness 
is  not  the  same  in  all  directions  on  the  rhombohedral  face.  From 
a  series  of  determinations  made  by  Grailich  and  Pekarek  with 
theft  sclerometer,  it  appears  that  the  greatest  hardness  is  in  the 
direction  of  the  shorter  diagonal  of  the  face,  from  C  to  E  (Fig. 
212),  and  the  least  hardness  in  the  opposite  direction,  from  E  to 
C  on  the  same  diagonal.  The  weights  required  in  the  pan  above 
the  hard  point,  in  order  to  scratch  the  face  in  various  directions, 
were  as  follows  :  — 

Angle.*  Weight. 

0°  Shorter  diagonal  from  C  to  E,  285  centigrammes. 

39°  Perpendicular  to  edge  ar,  250  " 

51°  Parallel  to  edge  z,  213  " 

90°  Longer  diagonal  from  E  to  C,  152  " 

129°  Parallel  to  edge  x,  135  " 

141°  Perpendicular  to  edge  z,  126  " 

180°  Shorter  diagonal  from  E  to  C,  96  " 

These  numbers  are  in  each  case  the  mean  of  several  observa- 
tions.    Similar  differences  have  been  observed  on  a  large  number 

*  These  angles  are  those  made  by  the  given  direction  with  the  shorter  diagonal. 


THE   THREE   STATES   OP   MATTER.  211 

of  other  crystals,  and  they  lead  to  the  following  general  con- 
clusions :  — 

1.  That  the  hardest  planes  of  a  crystal  are  those  which  are 
perpendicular  to  the  plane  of  most  perfect  cleavage.* 

2.  That  on  a  given  plane  the  direction  of  greatest  hardness  is 
that  which   is   most   inclined   to   the  direction  of  most  perfect 
cleavage. 

(116.)  Annealing  and  Tempering.  —  The  hardness  of  many 
substances  may  be  greatly  modified  by  the  action  of  heat,  and  by 
various  mechanical  processes.  The  effects  of  change  of  tempera- 
ture in  varying  the  degree  of  hardness  are  most  important  in  re- 
gard to  steel,  since  it  is  on  this  influence  that  the  application  of 
steel  to  so  great  a  variety  of  useful  purposes  depends.  If  steel 
is  heated  to  a  red  heat,  and  then  very  slowly  cooled,  it  becomes 
ductile,  flexible,  soft,  and  comparatively  unelastic.*  This  pro- 
cess is  called  annealing,  and,  when  thus  annealed,  steel  can  read- 
ily be  drawn  into  wire,  rolled  into  sheets,  or  manufactured  into 
its  numerous  useful  forms.  If,  however,  the  articles  thus  manu- 
factured are  heated  to  a  white  heat,  and  then  suddenly  cooled  by 
plunging  them  into  water  or  mercury,  the  steel  becomes  very 
hard,  brittle,  highly  elastic,  and  less  dense. 

In  its  state  of  greatest  hardness,  steel  is  scarcely  fit  for  any 
purposes  in  the  arts,  since  it  is  so  brittle  that  its  points  or  edges 
are  broken  by  a  very  slight  resistance.  But  by  reheating  it  to  a 
lower  temperature,  and  then  slowly  cooling  it,  this  extreme 
hardness  may  be  reduced,  and  the  flexibility  of  the  steel  propor- 
tionally increased.  The  amount  of  the  reduction  is  greater,  the 
higher  the  temperature  to  which  the  articles  are  heated,  and  if 
heated  to  a  red  heat,  they  again  become  soft. 

This  process  of  reheating  is  termed  letting  down  or  tempering, 
and  the  workman  is  guided  to  the  effects  he  wishes  to  produce  by 
the  changes  of  color  which  the  surface  of  polished  steel  exhibits 
at  different  temperatures.  The  tints  which  correspond  approxi- 
matively  to  the  different  temperatures  are  as  follows  :  — 

Light  straw,       220°         Violet-yellow,  265°         Blue,  293° 

Golden-yellow,  230°         Purple-violet,  277°         Deep  Blue,  317° 
Orange-yellow,  240°         Feeble  blue,     288°         Sea-green,    330° 


*  Lehrbuch  der  Krystallographie  von  Miller  ubersetzt  und  erweitert  durch  Dr.  J. 
Grailich,  (Wien,  1856,)  Seite  229. 


212  CHEMICAL   PHYSICS. 

The  hardest  steel  is  used  for  little  else  than  the  making  of  dies 
for  coining.  The  steel  of  the  hardest  files  is  but  little  let  down. 
The  first  shade  of  yellow  indicates  that  the  reheating  has  been 
carried  sufficiently  far  for  lancet  and  other  small  surgeons'  instru- 
ments, on  which  the  keenest  edge  is  required.  Razor  and  pen- 
knife blades  are  heated  until  they  exhibit  a  light  straw-color. 
Scissors,  shears,  and  chisels,  in  which  a  greater  tenacity  is  required, 
are  tempered  at  the  first  shade  of  orange.  Table  cutlery,  in  which 
flexibility  is  more  desirable  than  the  hardness,  which  would  give  a 
fine  but  brittle  edge,  are  heated  to  the  violet.  Watch-springs  are 
heated  to  a  full  blue,  and  coach-springs  to  a  deep  blue.  In  many 
manufactories  the  temper  is  given  by  immersing  the  hardened 
steel  articles  in  a  bath  of  mercury  or  oil,  the  heat  of  which  can 
be  exactly  regulated  by  a  thermometer.  The  bath  is  heated  up 
to  the  required  temperature,  and  then  allowed  to  cool  slowly. 
In  this  way,  any  number  of  articles  which  are  to  receive  the 
same  temper  may  be  equably  heated  and  gradually  cooled. 

Most  other  metals  are  acted  upon  by  heat  and  cold  in  some- 
what the  same  manner,  although  to  a  much  less  degree.  Copper, 
however,  is  a  remarkable  exception  to  the  rule,  its  properties 
being  exactly  the  reverse  of  those  of  steel ;  for  when  cooled 
slowly  it  becomes  hard  and  brittle,  but  when  cooled  rapidly,  soft 
and  malleable.  This  same  property  is  possessed  to  a  still  higher 
degree  by  bronze,  which  is  an  alloy  of  copper  and  tin. 

Glass  undergoes,  from  the  action  of  heat  and  cold,  the  same 
changes  as  steel.  When  heated  to  a  red  heat,  and  suddenly 
cooled,  it  becomes  more  brittle,  harder,  and  less  dense  than  in  its 
annealed  condition.  When  a  glass  vessel  is  first  blown,  it  cools 
rapidly  and  irregularly,  and  the  varying  hardness  of  its  different 
parts  gives  to  it  such  a  degree  of  brittleness,  that  the  slightest 
shock  or  a  small  change  of  temperature  would  break  it.  In 
order  to  prevent  this,  it  is  annealed,  by  passing  it  through  a  long 
furnace,  of  which  the  heat  is  very  great  at  one  end  and  slowly 
diminishes  towards  the  other,  and  it  is  thus  cooled  gradually  and 
equably. 

,          The  properties  of  unannealed  glass  are  illustrated 

Y  by  Prince  Rupert's  drops.     These  are  made  by  drop- 

//  ping  melted  glass  into  water,  which  of  course  cools 

ll  them  suddenly,  and  gives  to  the  glass  a  high  degree  of 

Fig  213.       hardness  and  a  proportionate  brittleness.    They  have  a 


THE   THREE   STATES   OP   MATTER.  213 

long  oval  form,  tapering  to  a  point  at  one  end  (Fig.  213).  The 
body  of  the  drop  is  so  hard  that  it  will  bear  a  smart  stroke ;  but 
if  a  portion  be  broken  off  from  the  small  end,  the  whole  imme- 
diately flies  into  minute  particles  with  a  loud  snap. 

The  cause  of  the  changes  in  hardness  produced  by  the  action 
of  heat  has  not  been  as  yet  satisfactorily  explained.  The  expla- 
nation usually  given  is  this.  When  a  bar  of  steel  highly  heated, 
and  hence  greatly  expanded,  is  immersed  in  cold  water,  the  ex- 
terior layers  suddenly  contract,  and  are  compelled  to  adapt  them- 
selves, by  a  permanent  displacement  of  their  molecules,  to  the 
core,  which  is  still  in  an  expanded  state  within.  Subsequently, 
when  the  interior  of  the  mass  cools,  its  particles  cannot  approach 
each  other  freely,  because  they  are  more  or  less  united  to  the  ex- 
ternal crust,  which  has  been  already  fixed  in  position.  Hence, 
these  particles  remain  in  a  state  of  tension,  and  this  is  supposed 
to  give  rise  to  the  peculiar  change  of  properties. 

Were  this  explanation  correct,  the  effects  of  a  sudden  change 
of  temperature  ought  to  be  greatest  on  thick  bars  of  steel,  but  in 
fact  the  reverse  is  the  case.  The  change  is  most  probably  con- 
nected with  the  phenomena  of  dimorphism  (98),  but  in  what  way 
is  not  yet  understood. 

Most  metals  are  hardened,  not  only  by  sudden  cooling,  but  also 
by  such  mechanical  processes  as  tend  to  condense  them  perma- 
nently, and  thus  increase  their  density.  The  processes  of  stamp- 
ing coin,  of  wire-drawing,  of  rolling  out  metallic  plates,  and  of 
hammering,  are  all  evidently  of  this  nature.  This  change  is 
usually  called  hammer-hardening,  and  its  effects  are  the  same  on 
almost  all  ductile  bodies.  They  become  denser,  more  tenacious, 
harder,  more  brittle,  and  more  elastic.  All  these  effects  can  be 
removed  by  annealing ;  and  hence  the  necessity  of  continually 
reannealing  the  metals,  during  the  processes  just  mentioned. 

PROBLEMS. 
Elasticity  of  Tension. 

91.  A  rectangular  iron  bar  2  m.  in  length,  and  whose  section  is  equal 
to  2  c.  m.2,  is  suspended  by  its  upper  extremity  to  a  firm  support,  and  to 
its  lower  extremity  is  attached  a  weight  of  1,000  kilog.     How  much  is  it 
temporarily  elongated  by  the  strain,  when  the  temperature  is  15°  ? 

92.  An  annealed  iron  wire  2  m.  m.  in  diameter  and  2.25  m.  in  length  is 
suspended  as  in  the  last  example.     How  much  weight  is  required  to  elon- 
gate it  0.25  m.  m.,  when  the  temperature  is  15°  ? 


214  CHEMICAL  PHYSICS. 

93.  A  silver  wire  0.75  m.  m.  in  diameter  and  5  m.  long  is  elongated  by 
a  weight  0.25  m.  m.     How  great  is  this  weight  when  the  temperature  is 
15°? 

Tenacity. 

94.  "With  how  much  weight  in  kilogrammes  must  a  copper  wire  be 
loaded,  in  order  to  part  it,  when  the  diameter  of  the  wire  is  equal  to 
1  m.  m.  ?     Calculate  both  for  annealed  and  unannealed  wire. 

95.  In  a  pendulum  experiment,  it  is  required  to  suspend  a  weight  of 
50  kilog.  by  a  copper  wire.     What  must  be  the  diameter  of  the  wire, 
allowing  -g$  for  security  beyond  the  diameter  absolutely  essential  ?     Cal- 
culate both  for  annealed  and  unannealed  wire. 

Collision  of  Perfectly  Elastic  Bodies. 

In  the  following  problems  marked  with  a  ( *  ),  the  masses  and  velocities  of  the  two  balls  are 
indicated  as  described  in  (109).  The  motion  is  from  left  to  right,  unless  the  reverse  is  indi- 
cated by  a  negative  sign.  In  each  problem  it  is  required  to  jind  the  velocities  of  the  two  balls 
after  the  impact,  and  also  the  direction  of  the  motion. 

*96.  M  =  6.  t)  =  3  m.  M1  =  17.  ft'  =  1  m. 

*97.  Jf=10.  t)  =  5m.  M'  =  20.  t)'  =  2.5  m. 

*98.  M  =  10.  fa  =  10  m.  M'  =  100.  6'  =  0  m. 

*99.  M  =  20.  fa  =  10  m.  M1  =  10.  ()'  =  —  5  m. 

•100.  M=15.  6  — 16m.  M'=W.  \)>  =  —  32m. 

101.  A  ball  whose  mass  is  M,  with  a  velocity  ft,  meets  a  second  ball 
moving  in  the  same  direction,  whose  mass  is  M'.     What  must  be  the 
velocity  of  the  second  ball,  when  the  first  ball  remains  at  rest  after  the 
collision  ? 

102.  A  ball  strikes  on  a  plane  making  an  angle  of  incidence  equal  to 
60°.     What  will  be  the  angle  of  reflection  when,  in  consequence  of  the 
imperfection  of  the  elasticity  both  of  the  plane  and  the  body,  one  third  of 
the  vertical  velocity  is  lost  by  the  impact  ?     Solve  the  same  problem,  sup- 
posing that  one  fourth  of  the  velocity  is  lost. 

103.  An  elastic  ball  falls  from  the  height  of  2  m.     How  high  will  it  re- 
bound, supposing  that  one  fifth  of  the  final  velocity  is  lost  at  the  impact,  in 
consequence  of  imperfect  elasticity  ? 

104.  Two  perfectly  elastic  balls,  moving  in  the  same  plane,  meet  each 
other  obliquely.     The  angles  made  by  the  two  directions  of  their  motions 
with  the  line  n  £7" (Fig.  206),  lying  in  the  same  plane  and  tangent  to  both 
balls  at  the  point  of  contact,  are  «  =  60°  and  /?  =  30°.     The  masses 
are  M  =  10  and  M'=  5  ;  the  velocities  are  fa  =  2.5  and  {)'  =  5.     It 
is  required  to  find  the  velocities  of  the  two  balls  after  collision,  and  the 
angles  which  the  directions  of  their  motions  make  with  the  given  line. 

105.  Solve  the  same  problem  for  the  following  values  :  — 

«  =  40°.         =  30°.     M  =  5.     M>  =  10.     t)  =  4  m.     t)'  =  6  m. 


THE   THREE   STATES   OF   MATTER.  215 


II.    CHARACTERISTIC  PROPERTIES  OP  LIQUIDS. 

(117.)  Mechanical  Condition  of  Liquids.  Fluidity.  —  The 
liquid  has  not,  like  the  solid  (79),  a  definite  form;  but  it  takes 
the  form  of  the  vessel  in  which  it  is  placed.  Its  particles  are  in 
a  condition  of  equilibrium  between  the  attractive  and  repulsive 
forces  (78),  and  instead  of  being  bound  together,  as  in  a  solid, 
they  possess  a  perfect  freedom  of  motion  ;  and  under  the  influ- 
ence of  the  slightest  force,  they  move  among  each  other  without 
friction  and  without  disturbing  the  general  equilibrium.  This 
mechanical  condition  of  matter  is  termed  fluidity,  and  belongs 
both  to  liquids  and  gases.  Liquids  are  not,  however,  perfect 
fluids,  for  there  always  exists  between  their  particles  a  certain 
amount  of  adhesion,  owing  to  an  excess  of  attractive  force  which 
renders  them  more  or  less  viscous.  Between  an  almost  perfect 
fluid,  like  water,  and  a  condition  like  dough,  we  have  every  grade 
of  fluidity.  This  is  illustrated  by  the  well-known  series  of  or- 
ganic acids,  commencing  with  formic  acid  and  ending  with  me- 
lissic  acid.  The  series  consists  of  over  twenty  members,  and  pre- 
sents every  grade  of  condition.  Formic  acid  is  as  fluid  as  water  ; 
but  as  we  descend  in  the  series,  the  numbers  are  found  to  be 
more  and  more  viscous,  becoming  first  oily,  then  soft  fats,  next 
hard  fats,  and  finally  solids,  like  wax. 

(118.)  Elasticity  of  Liquids.  —  It  has  already  been  stated 
(76),  that  liquids  are  compressible,  and,  moreover,  that  they- re- 
sume exactly  their  original  volume  as  soon  as  the  pressure  by 
which  this  was  diminished  is  removed.  It  follows  from  these 
facts,  that  liquids  are  perfectly  elastic,  and  that  this  elasticity  is 
unlimited  in  extent. 

In  the  early  experiments  on  compressibility  made  by  Oersted, 
it  was  assumed  that  the  capacity  of  the  bulb  A,  of  the  appara- 
tus already  described  (Fig.  214),  remained  invariable.  This  as- 
sumption was  based  on  the  fact,  that  the  walls  of  this  reservoir 
were  equally  pressed  by  the  fluid  on  both  sides.  It  is  easy, 
however,  to  see  that  this  assumption  is  incorrect  ;  for  if  we 
suppose  the  interior  of  the  bulb  to  be  filled  with  solid  glass,  it  is 
evident  that  the  volume  of  the  interior  core,  and  hence  that  of 
the  bulb,  would  be  diminished  by  the  exact  amount  that  this 
glass  core  would  be  compressed  by  the  given  pressure.  In  such 
a  case,  the  pressure  on  the  exterior  surface  of  the  bulb  would  be 


216 


CHEMICAL   PHYSICS. 


exactly  balanced  by  the  reaction  of  the  glass  core.  If,  now,  the 
place  of  the  glass  core  is  supplied  by  water,  the  pressure  on  the 
exterior  surface  remaining  the  same,  it  is  evident  that  the  reac- 
tion of  the  water  core  must  be  exactly  the  same  as  that  exerted 
by  the  glass  core  ;  for  otherwise  the  law  of  action  and  reaction 
(41)  would  not  be  obeyed.  The  conditions,  then,  with  respect  to 
the  bulb,  are  not  changed,  and  it  is  evident  that  its  volume  will 
be  just  as  much  reduced  when  filled  with  water  as  when  filled 
with  glass  ;  that  is,  by  the  amount  to  which  a  glass  core  just  fill- 
ing it  would  be  compressed  by  the  given  force. 

It  follows  from  this,  that  the  apparent  condensation  of  any  fluid 
tinder  a  given  pressure,  when  determined  by  the  apparatus  repre- 
sented in  Fig.  214,  is  not  so  great  as  the 
real  condensation,  and  that  it  is  neces- 
sary to  correct  the  determinations  thus 
made  by  adding  to  the  observed  compres- 
sion an  amount  equal  to  the  compres- 
sion, under  a  given  pressure,  of  a  glass 
core  which  would  just  fill  the  interior 
of  the  bulb.     This  amount  can  in  any 
case  be  calculated  from  data  furnished 
by  experiments   on   the  elongation  of 
glass  rods  by  tension,  since,  according 
to  M.  Wertheim,  the  diminution,  under 
a   given    pressure,  of  one  cubic   cen- 
timetre of  glass,  in  fractions  of  a  cubic 
centimetre,  is  just  equal  to  the  elonga- 
tion of  a  glass  rod  one  centimetre  long, 
in  fractions  of  a  centimetre,  under  an 
equivalent    tension.      M.    Grassi    has 
carefully  redetermined  the  compressi- 
bility of  several  liquids,  making  use  of 
an   improved   apparatus   contrived  by 
Regnault,  and  correcting  his  observa- 
tions for  the  compressibility  of  the  reservoir  used  according  to  the 
formulae  of  Wertheim.     He  has  also  studied  the  influence  of  a 
variation  of  temperature  on  the  compressibility,  as  well  as  the 
influence  of  different  pressures.     The  most  important  results  ob- 
tained -  by  M.  Grassi  are  given  in  the  following  table.     In  every 
case,  the   numbers   expressing  the   compressibility  of  a   liquid 


Fig.  214. 


THE   THREE   STATES    OF   MATTER. 


217 


indicate  the  fraction  of  its  volume  by  which  it  is  condensed  when 
submitted  to  a  pressure  of  one  atmosphere. 

Table  of  the  Coefficients  of  Compressibility* 


Liquid. 

Temperature. 

Compressibility. 

Pressure  in  Atmos- 
pheres, from  which 
the  Compressibility 
was  determined. 

o 

Mercury,      .... 

0.0 

0.00000295 

.    . 

Water,     .... 

0.0 

0.0000503 

.    . 

M 

1.5 

0.0000515 

.    . 

(( 

4.1 

0.0000499 

.    . 

« 

10.8 

0.0000480 

.    . 

M 

13.4 

0.0000477 

.    . 

"                    .... 

18.0 

0.0000463 

.    . 

(« 

u 

0.0000460 

.    . 

« 

25.0 

0.0000456 

.    . 

U 

34.5 

0.0000453 

.    . 

if 

43.0 

0.0000442 

.    . 

t( 

53.0 

0.0000-141 

.    . 

Ether,          .... 

0.0 

0.000111 

3.408 

0.0 

0.000131 

7.820 

n 

14.0 

0.000140 

1.580 

u 

13.8 

0.000153 

8.362 

Ethylic  Alcohol,  . 

7.3 

0.0000828 

2.302 

«               u 

7.3 

0.0000853 

9.450 

"              " 

13.1 

0.0000904 

1.570 

u               « 

13.1 

0.0000991 

8.97 

Methylic  Alcohol, 

13.5 

0.0000913 

.    . 

Chloroform,      . 

8.5 

0.0000625 

.    . 

"          .... 

12.0 

0.0000648 

1.309 

« 

12.5 

0.0000763 

9.2 

In  the  case  of  water,  it  was  found  that  the  amount  of  condensa- 
tion was  proportional  to  the  pressure,  and  that  it  diminished 
when  the  temperature  was  increased.  On  the  other  hand,  it 
appeared  that  the  compressibility  of  alcohol,  ether,  and  chloro- 
form increased  with  the  temperature,  and,  moreover,  that  the 
compressibility  of  these  fluids,  as  well  as  that  of  methylic  ether, 
increased  with  the  pressure. 

M.  Grassi  also  made  experiments  on  the  compressibility  of  sa- 
line solution,  and  found  that,  for  the  same  solution,  it  was  as 
constant  as  that  of  pure  water,  and  that  it  diminished  when  the 
amount  of  salt  in  solution  was  increased. 


*  Annales  de  Chimie  et  de  Physique,  3e  Serie,  Tom.  XXXI.  p.  437. 

19 


218  CHEMICAL   PHYSICS. 

Consequences  of  the  Mechanical  Condition  of  Liquids. 

(119.)  We  have  seen,  in  the  last  two  sections,  that  the  mole- 
cules of  a  liquid  are  in  a  condition  of  equilibrium,  and  also  that 
all  liquids  are  but  slightly  compressible  and  perfectly  elastic.  Of 
the  characteristic  properties  of  liquids,  we  shall  only  consider 
those  which  are  a  necessary  consequence  of  these  conditions. 
These  naturally  divide  themselves  into  two. classes:  first,  those 
which  are  independent  of  the  action  of  gravity ;  and,  secondly, 
those  which  depend  upon  it. 

(120.)  Liquids  transmit  Pressure  in  all  Directions.  —  This 
most  important  quality  of  liquids  was  first  clearly  stated  by  Blaise 
Pascal,  in  the  following  terms :  Liquids  transmit  equally  in  all 
directions  a  pressure  exerted  at  any  point  of  their  mass. 

We  may  illustrate  what  is  meant  by  this  statement  of  Pascal, 
by  means  of  Fig.  215,  which  represents  the  section  of  a  vessel 
— which  may  be  of  any  shape  —  filled  with 
water,  on  the  sides  of  which  are  several 
apertures  closed  by  movable  pistons.     Let 
us  suppose  that  the  two  pistons  d  and  c 
present  the  same  surface  ;   and,  further, 
that  the  piston  a  presents  twice,  and  the 
piston  b  five  times,  the  area  of  c.    If,  now, 
we  press  in  the  piston  c  with  the  force  of  Fig.  215. 

one  kilogramme,  this  force  will  be  trans- 
mitted in  every  direction  to  the  sides  of  the  vessel,  and  every 
portion  of  the  interior  surface  whose  area  equals  that  of  the 
piston  will  be  pressed  upon  with  a  force  of  one  kilogramme; 
the  piston  d  will  be  pressed  out  with  a  force  of  one  kilogramme ; 
the  piston  a,  with  a  force  of  two  kilogrammes  ;  the  piston  £, 
with  a  force  of  five  kilogrammes.  And  so  will  it  be  with  any 
other  portion  of  surface,  either  on  the  side  of  the  vessel  or  im- 
mersed in  the  fluid ;  it  will  be  pressed  upon  with  a  force  as  many 
times  greater  than  one  kilogramme,  as  it  is  itself  greater  than 
the  surface  of  the  piston  c. 

It  is  easy  to  see  that  this  is  a  necessary  consequence  of  the 
constitution  of  liquids.  Since  fluids  are  compressible  and  elastic, 
it  follows  that,  on  pressing  in  the  piston  d,  the  liquid  is  very 
slightly  condensed,  and  the  elasticity  of  compression  developed  in 
its  particles.  Each  particle  at  once  becomes  like  a  bent  spring, 


THE  THREE   STATES   OP   MATTER.  219 

and  presses  in  all  directions.  If  the  particle  is  in  the  midst  of 
the  fluid  mass,  it  presses  against  the  neighboring  particles ;  if 
it  is  on  the  side  of  the  vessel,  it  presses  in  one  direction  against 
the  vessel,  but  in  all  others  against  similar  particles.  Since 
the  same  is  true  of  every  particle,  it  follows  that  the  pressure  ex- 
erted by  the  condensed  liquid  against  any  two  surfaces  will  be 
proportional  to  the  number  of  particles  in  contact  with  these  sur- 
faces ;  and  as  the  particles  have  the  same  size,  it  will  also  be 
proportional  to  the  area  of  the  surface.  Hence  the  pistons  d  and 
c  will  be  pressed  out  each  by  the  same  force,  the  piston  a  by  a 
force  twice  as  great,  and  the  piston  b  by  a  force  five  times  as 
great,  as  this.  From  the  principle  of  equality  between  action  and 
reaction,  it  follows  that  the  outward  pressure  on  the  piston  c  is 
exactly  equal  to  the  force  applied  to  press  it  in ;  so  that,  if  this 
piston  is  pressed  in  with  a  force  of  one  kilogramme,  the  piston 
d  is  pressed  out  with  the  same  force,  the  piston  a  with  a  force  of 
two  kilogrammes,  etc. ;  which  was  the  proposition  to  be  proved. 

Representing  the  area  of  any  portion  of  the  interior  surface  of 
a  vessel  by  S9  and  that  of  any  other  portion  by  S' ;  representing 
also  by  £  and  £'  the  pressure  exerted  against  these  surfaces  by  a 
confined  liquid,  in  consequence  of  any  compression  ;  we  have 

£  :  £ '  =  S  :  S'.  [77.] 

Moreover,  it  is  evident  from  the  principle  involved,  that  this 
equation  is  true,  not  only  for  the  surface  of  the  vessel  itself,  but 
also  for  that  of  any  solid  immersed  in  the  compressed  liquid,  or 
for  any  section  of  liquid  particles  whatsoever  in  the  vessel. 

(121.)  The  line  indicating  the  direction  of  the  pressure  ex- 
erted by  any  liquid  particle  against  the  surface  with  which  it  is 
in  contact,  is  always  a  perpendicular  to  this  surface  at  the  point 
of  contact.  If  the  surface  is  a  plane,  the  line  is  a  perpendicular 
to  this  plane ;  if  the  surface  is  curved,  the  line  is  a  normal  to  this 
curve.  The  truth  of  this  principle  will  be  seen,  if  we  consider 
what  must  be  the  result  if  the  direction  of  the  pressure  were 
oblique.  It  is  evident  that  such  oblique  pressure  would  be  re- 
solved into  two  forces  (35),  one  perpendicular  to  the  surface,  and 
the  other  tangent  to  it.  The  second  component  could  of  course 
exert  no  pressure  against  the  surface  ;  so  that  the  whole  pressure 
exerted  by  the  liquid  particle  would  be  that  of  the  first  compo- 
nent, which  is,  as  the  proposition  requires,  perpendicular  to  the 
surface  at  the  point  of  contact. 


220  CHEMICAL   PHYSICS. 

When  the  surface  is  plane,  the  directions  of  the  pressures  ex- 
erted by  the  particles  are  all  parallel.  It  is  then  always  possible, 
by  (39),  to  find  a  common  resultant  of  all  these  parallel  forces. 
The  point  of  application  of  this  resultant  is  called  the  centre  of 
pressure.  When  the  pressures  exerted  by  the  separate  particles 
are  all  equal,  the  centre  of  pressure  is  always  the  centre  of  figure 
of  the  surface.  In  the  case  of  the  pistons  (Fig.  215),  the  centre 
of  pressure  is  in  each  one  the  centre  of  the  circular  base,  and  in 
studying  its  mechanical  effects  we  may  regard  all  the  pressure  as 
concentrated  at  that  point.  Were  the  base  of  the  piston  con- 
cave, then  the  directions  of  the  pressures  exerted  by  the  separate 
particles  would  no  longer  be  parallel ;  since  the  lines  indicating 
these  directions  would  diverge  from  the  centres  of  curvature. 
Compare  (60) .  Moreover,  as  the  area  of  the  curved  surface  would 
be  greater  than  that  of  the  plane  surface,  it  is  evident  that  the 
total  amount  of  pressure  which  it  would  sustain  under  the  same 
circumstances  would  be  greater ;  but  it  can  be  proved  that  the 
pressure  available  in  moving  the  piston  would  be  the  same  as 
before.  For  this  purpose,  it  is  only  necessary  to  decompose  the 
pressure  exerted  by  each  particle  into  two  forces,  one  acting  in  a 
direction  which  is  parallel  to  the  axis  of  the  cylinder,  and  the 
other  at  right  angles  to  this  direction.  The  forces  acting  parallel 
to  the  axis  of  the  piston  are  obviously  the  only  ones  which  are 
available  in  moving  it ;  and  the  sum  of  these  forces  will  be  found 
to  be  the  same  as  the  total  pressure  which  would  be  exerted  if 
the  base  of  the  cylinder  were  a  plane. 

(122.)  Hydrostatic  Press.  —  This  most  beautiful  application 
of  the  equality  of  pressure  was  conceived  by  Pascal ;  but  the 
difficulty  of  avoiding  the  escape  of  water 
from  the  joints  of  pistons  prevented  him 
from  realizing  his  conception,  and  the 
press  was  first  constructed  by  Bramah,  in 
1796,  at  London. 

It  is  perfectly  evident  that  the  principle 
of  equality  of  pressures  deduced  in  the 
last  section  is  entirely  independent  of  the 
form  of  the  vessel,  and  we  may  therefore 
give  to  the  vessel  the  form  of  Fig.  216,  in 

which  the  area  of  the  piston  b  c  is  twenty  times  as  large  as  that 
of  the  piston  a.     Hence  it  follows,  that,  if  we  press  in  the  pis- 


THE   THREE   STATES   OP   MATTER. 


223 


ton  a  with  a  force  of  five  kilogrammes,  the  piston  b  will  be 
forced  out  with  twenty  times  as  much  force,  or  one  hundred  kilo- 
grammes ;  and,  on  the  other  hand,  if  we  press  in  the  piston  b  c 
with  a  force  of  one  hundred  kilogrammes,  the  piston  a  will  be 
forced  out  with  a  force  of  only  five  kilogrammes.  It  is  evidently 
unimportant  that  the  connection  between  the  piston  should  be  so 
direct  as  in  Fig.  216.  If  it  is  effected  by  a  long  and  narrow  tube, 
the  principle  will  still  hold  true,  provided  only  that  the  joints  are 
tight  and  the  material  of  the  vessel  unyielding. 

The  hydrostatic  press,  which  is  used  in  the  arts  for  producing 
great  pressure,  is  only  a  modification  of  the  apparatus  represented 
by  the  diagram,  Fig.  216.  One  of  the  most  usual  forms  of  this 
machine  is  represented  in  perspective  by  Fig.  217,  and  in  section 


Fig  217. 

by  Fig.  218.  The  same  parts  are  lettered  alike  on  the  two  figures. 
It  consists  of  two  cylinders,  A  and  J5,  connected  together  by  a  tube, 
K.  In  the  larger  cylinder  moves  the  large  piston  P,  which  is 
made  in  the  form  of  a  plunger,  touching  the  walls  of  the  cylinder 
only  at  the  top,  where  it  passes  through  a  water-tight  packing. 
On  the  top  of  this  piston  is  a  platform,  which  rises  and  falls  with 
19* 


222 


CHEMICAL   PHYSICS. 


it,  and  the  articles  to  be  submitted  to  pressure  are  placed  between 
this  and  a  second  platform,  Q,  which  is  firmly  fastened  to  the 
floor  by  means  of  four  iron  columns,  which  also  serve  to  guide 
the  motion  of  the  lower  platform.  The  small  piston  p  is  con- 


Fig.  218. 

structed  exactly  like  the  larger,  and  is  moved  up  and  down  in 
the  cylinder  by  the  pump-handle  M.  The  small  cylinder  acts 
as  a  force-pump.  It  connects  with  a  reservoir  of  water  below 
by  means  of  a  tube  terminating  with  a  rose,  a.  This  tube  is 
guarded  by  a  valve,  c,  which  allows  the  water  to  flow  up  into  the 
pump,  but  not  in  the  reverse  direction.  It  is  evident  from  this  de- 
scription, that,  on  working  the  handle  Jf,  water  will  be  alternately 
sucked  up  from  the  reservoir  and  forced  into  the  large  cylinder 
B,  through  the  pipe  K,  from  which  it  is  prevented  from  returning 
by  a  valve  at  o.  The  large  piston  will  thus  be  forced  up  by  a  pres- 
sure which  will  be  as  much  greater  than  that  exerted  on  the  small 
piston  as  the  area  of  its  section  is  greater.  If,  for  example,  it  is 
a  hundred  times  as  large,  it  will  be  pressed  up  with  a  force  one 
hundred  times  greater  than  that  exerted  on  p.  This  force  can 
be  so  much  increased  by  the  lever  M9  that  a  man  can  easily  exert 
a  downward  pressure  of  150  kilogrammes  on  />,  and  the  piston  P 
will  then  be  pressed  up  with  a  force  equal  to  15,000  kilogrammes. 
It  must  be  noticed,  however,  that  the  piston  P  will  rise  very 
slowly,  and  as  much  more  slowly  than  the  motion  of  p  as  the  area 
of  its  section  is  greater.  This  is  in  accordance  with  a  well-known 
principle  of  mechanics,  which  is  true  of  all  machines,  that  what  is 
gained  in  force  is  lost  in  velocity  (or  extent  of  motion).  In  the 
present  case,  in  order  to  raise  the  piston  P  one  metre  under  a  force 


THE   THREE   STATES   OF    MATTER.  223 

of  15,000  kilogrammes,  it  is  necessary  to  push  down  the  piston  p 
through  one  hundred  metres  with  a  force  of  150  kilogrammes. 
This  is  accomplished  by  repeated  motions  of  the  handle  M. 

The  tube  K  is  furnislved  with  a  safety-valve,  i  (Fig.  218),  kept 
in  place  by  a  weight  acting  on  it  through  a  lever  (Fig.  217). 
There  is  also  a  valve-cock  at  r,  by  which  the, water  in  the  cylinder 
B  may  be  vented  into  the  reservoir  H,  in  order  to  lower  the  pis- 
ton ;  and,  lastly,  a  third  valve-cock,  by  which  the  communication 
between  the  cylinders  may  be  closed  when  it  is  desirable  to  keep 
the  articles  under  pressure  for  some  time.  The  peculiar  form  of 
the  packing  at  n  is  also  deserving  of  notice.  It  is  made  of  thick 
leather  saturated  with  oil,  in  the  form  of  an  inverted  U,  and 
the  more  the  water  is  compressed,  the  more  firmly  the  leather  is 
pressed  against  the  sides  of  the  cylinder  and  piston. 

The  hydraulic  press  is  applied  in  the  arts  for  a  great  variety  of 
purposes,  such  as  packing  dry  goods  in  bales,  pressing  out  printed 
sheets,  extracting  oil  from  grains,  and  testing  steam-boilers.  It 
was  also  used  for  raising  the  iron  tubes  of  the  Britannia  Bridge 
over  the  Menai  Strait. 

(123.)  Pressure  exerted  by  Liquids  in  Consequence  of  their 
Weight.  —  In  the  first  place,  let  us  consider  what  will  be  the 
pressure  exerted  by  a  liquid  on  the  bottom 
of  the  containing  vessel.  Let  arm,  Fig.  219, 
be  a  conical  vessel,  which  we  will  suppose  filled 
with  water  to  the  point  o.  Let  us  suppose 
the  liquid  to  be  divided  into  a  number  of 
strata  by  the  planes  b  c,  e  d,  ig,  p  n,  which 
we  may  take  as  thin  as  we  wish,  and  only 
consider  in  each  stratum  the  cylindrical  mass 

,      ,.  T        .  .  Fig.  219. 

enclosed  in  dotted  lines.  It  is  now  evi- 
dent that  the  pressure  exerted  by  each  cylindrical  mass  on  its 
own  base  will  be  equal  to  its  own  weight.  Then,  from  the  prin- 
ciple of  Pascal,  the  pressure  exerted  by  the  weight  of  the  first 
mass  will  be  transmitted  to  the  whole  section  b  c,  so  that  this  will 
have  to  support  a  pressure  as  much  greater  than  the  weight  of  the 
first  mass  as  the  area  of  this  section  is  greater  than  the  area  of  the 
base  of  the  first  cylinder.  Hence  it  follows,  that  it  will  support 
a  pressure  equal  to  the  weight  of  a  column  of  water  whose  base 
equals  b  c,  and  whose  height  is  that  of  the  first  cylinder.  This 
pressure  will  then  be  added  to  the  weight  of  the  second  cylinder, 


224  CHEMICAL  PHYSICS. 

which,  on  the  same  principle,  will  be  transmitted  to  the  whole 
section  e  d\  and  hence  the  resulting  pressure  exerted  on  the  sec- 
tion e  d  is  equal  to  the  weight  of  a  column  of  water  whose  base 
equals  this  section,  and  whose  height  equals  the  sum  of  the 
heights  of  the  first  and  second  cylinders.  The  same  course  of 
reasoning  may  be  extended  to  the  sections  i  g*,  p  n,  and  also  to 
the  base,  r  m.  Hence  the  pressure  on  the  base,  r  m,  is  equal  to 
the  weight  of  a  column  of  water  whose  base  equals  this  base, 
and  whose  height  equals  the  sum  of  the  heights  of  all  the  cylin- 
ders, or  o  m. 

This  demonstration  is  evidently  independent  of  the  number  of 
strata,  and  must  therefore  hold  when  this  number  is  infinite  and 
the  vessel  conical.  It  is  also  evident  that  it  is  independent  of  the 
form  of  the  vessel.  It  would  hold  if  the  vessel,  remaining  conical, 
were  placed  in  an  inverted  position,  or  for  a  vessel  of  any  shape 
whatsoever.  We  may  therefore  conclude,  as  the  general  result 
of  this  discussion,  that  the  pressure  exerted  by  a  liquid  on  the 
horizontal  base  of  the  containing  vessel  is  equal  to  the  weight  of 
a  column  of  this  liquid  whose  base  equals  the  base  of  the  vessel, 
and  whose  height  equals  the  depth  of  the  liquid  in  the  vessel. 

The  fact,  that  the  pressure  exerted  by  a  liquid  on  the  bottom  of 
the  vessel  containing  it  is  independent  of  the  form  of  the  vessel, 
may  be  demonstrated  experimentally  by  means  of  the  apparatus 
represented  in  Fig.  220,  which  was  invented  by  Haldat,  and  is 
known  by  his  name.  It  consists  of  a  bent  glass  tube,  A  B  C,  at 
one  end  of  which,  J.,  is  a  brass  cap,  to  which  may  be  screwed  either 
of  the  glass  vessels  M  and  P.  There  is  also  a  cock  by  which  the 
liquid  in  the  vessel  may  be  drawn  off.  In  order  to  make  the  ex- 
periment, we  fill  the  bent  tube  with  mercury,  and  then  screw  into 
its  place  the  larger  of  the  two  vessels,  which  we  fill  with  water. 
This  presses  up  the  mercury  in  the  branch  (7,  and  we  mark  the 
level  to  which  it  rises  by  means  of  the  ring  a.  We  also  mark  the 
level  of  the  water  in  the  vessel  by  means  of  the  index-rod  c,  which 
we  push  down  until  it  just  touches  the  surface.  We  then  draw  off 
the  water,  and,  having  replaced  the  vessel  M  by  the  smaller  ves- 
sel P,  we  fill  this  with  water  to  the  same  height  as  marked  by  the 
index,  when  we  find  that  the  mercury  rises  in  the  branch  C  to 
precisely  the  same  level  as  before.  As  the  effect  produced  by  the 
pressure  of  the  water  in  the  two  cases  is  the  same,  we  have  a 
right  to  conclude  that  the  two  pressures  are  equal.  This  pres- 


THE   THREE   STATES   OP   MATTER. 


225 


Fig.  220. 

sure,  then,  is  independent  of  the  form  of  the  vessel  or  of  the 
quantity  of  water  ;  and,  since  the  base  of  the  vessel  is  the  same  in 
both  cases,  (that  is,  the  surface  of  the  mercury  in  the  tube  A,) 
and  the  height  of  the  liquid  also  the  same,  it  is  evident  that  the 
equality  of  pressure  is  a  necessary  result  of  the  principle  before 
proved. 

(124.)  Upward  Pressure.  —  If  we 
consider  any  given  section  of  liquid, 
as  p  n,  Fig.  219,  it  is  evident  that  the 
particles  on  this  section  are  com- 
pressed by  the  weight  of  the  liquid 
above  them,  and  hence  must  be  ex- 
erting pressure  in  every  direction, 
and  just  as  much  upward  pressure 
as  downward  pressure.  If,  then,  we 
immerse  in  the  liquid  a  cylindrical 
body,  such  as  c  d,  Fig.  221,  it  is  plain 
that  the  particles  of  water  in  contact 
with  the  base,  d,  of  the  cylinder,  be- 
ing in  a  compressed  condition,  must 
exert  an  upward  pressure  on  the  base 
of  the  cylinder  equal  to  the  pressure 
they  exert  on  the  section  of  liquid  next  below  them.  This 


226 


CHEMICAL   PHYSICS. 


pressure,  by  the  last  section,  is  equal  to  the  weight  of  a  column 
of  liquid  having  the  same  base  as  the  cylinder,  and  having  a 
height  equal  to  the  depth  of  the  section  below  the  surface  of  the 
liquid. 

(125.)  Pressure  on  the  Sides  of  a  Vessel.  —  This  same  course 
of  reasoning  may  also  be  extended  to  the  pressure  exerted  by  a 
liquid  against  the  sides  of  the  containing  vessel.  It  is  evident,  for 
example,  that  the  particles  of  the  liquid  in  contact  with  the 

piston  6,  Fig.  221,  are  in  a  state  of 
tension  caiised  by  the  pressure  of 
the  weight  of  liquid  above  them. 
They  are  therefore  exerting  pressure 
in  all  directions,  and  hence  also  against 
the  surface  of  the  piston  in  directions 
which  are  perpendicular  to  that  sur- 
face. Now  the  pressure  of  any  one 
particle  is,  by  the  principle  of  (123), 
equal  to  the  weight  of  a  column 
of  similar  particles  whose  height  is 
equal  to  the  depth  of  this  particle  be- 
low the  surface.  And  since  the  total 
pressure  against  the  piston  is  equal  to 
the  sum  of  the  pressures  of  the  sep- 
arate particles,  it  follows  that  the  total 
pressure  is  equal  to  the  weight  of  a 
column  of  liquid,  the  area  of  whose  base  is  equal  to  the  area  of  the 
surface  of  the  piston,  and  whose  height  is  equal  to  the  mean  depth 
of  the  various  particles  below  the  surface.  This  mean  depth,  in 
the  example  under  consideration,  is  evidently  the  depth  of  the 
centre  of  the  piston,  and  hence  e  g  is  a  column  of  liquid  whose 
weight  is  equal  to  the  pressure.  In  the  same  way,  the  pressure 
against  the  piston  a  is  equal  to  the  column  represented  by  h  i. 

It  is  easy  to  extend  this  demonstration  to  any  portion  of  the 
sides  of  a  vessel,  whether  plane  or  curved.  It  can  also  easily  be 
proved  that  the  mean  depth  of  the  various  particles  of  liquid  in 
contact  with  any  surface  is  in  every  case  equal  to  the  depth  of  the 
centre  of  gravity  of  these  particles. 

Were  the  pressure  exerted  by  each  of  the  particles  of  water  in 
contact  with  the  piston  (Fig.  221)  the  same,  the  centre  of  pres- 
sure (121)  would,  as  in  Fig.  215,  coincide  with  the  centre  01 


Fig.  221. 


THE   THREE   STATES   OF   MATTER.  227 

figure.  This,  however,  is  not  the  case  ;  the  particles  below 
the  level  of  the  centre  of  the  piston,  being  at  a  greater  depth, 
exert  a  greater  pressure  than  those  above  this  level.  Hence 
the  point  of  application  of  the  parallel  forces  which  they  ex- 
ert, (being  nearest  to  the  greater  forces  [20],)  must  be  below 
the  centre  of  figure.  In  any  similar  case,  the  position  of  the 
centre  of  pressure  is  below  the  centre  of  gravity  of  the  particles 
composing  the  section  against  which  the  pressure  is  exerted,  and 
it  can  always  be  found  by  calculation  when  the  form  of  the  sur- 
face is  known. 

(126.)  Generalization.  —  The  separate  results  at  which  we 
have  arrived  in  the  last  three  sections  may  be  generalized  as  fol- 
lows :  The  pressure  exerted  by  a  liquid  on  any  section  ivhatso- 
ever  is  equal  to  the  weight  of  a  column  of  the  liquid,  the  area  of 
ivhose  base  is  equal  to  the  area  of  the  section,  and  whose  height 
is  equal  to  the  depth  of  the  centre  of  gravity  of  the  section  below 
the  surface  of  the  liquid. 

(127.)  The  pressures  exerted  by  two  liquids  on  equal  sections 
at  equal  depths  are  proportional  to  the  specific  gravities  of  these 
liquids.  It  follows,  from  the  last  section,  that  the  two  pressures 
are  equal  to  the  weights  of  equal  columns  —  and  hence  of  equal 
volumes  —  of  the  two  liquids.  But  it  follows  from  (69),  that 
the  weights  of  equal  volumes  of  two  liquids  are  to  each  other  as 
their  specific  gravities,  and  hence  the  pressures  exerted  by 
them  on  equal  sections  at  equal  depths  must  be  in  the  same  pro- 
portion. 

If  we  represent  by  S  the  area  of  any  section  in  square  cen- 
timetres, by  H  the  depth  of  the  centre  of  gravity  in  centimetres, 
we  have,  by  geometry,  for  the  volume  of  the  column  of  liquid 
whose  weight  represents  the  pressure,  V=H.  S,  in  which  V 
stands  for  a  certain  number  of  cubic  centimetres.  But  we  know 
by  [56],  that  W=  V .  Sp.  Gr.,  and  hence,  if  we  represent  the 
pressure  exerted  on  any  section  by  f,  we  have 

$=  W=H.  S.  (Sp.Gr)  [78.] 

For  any  other  section,  having  the  same  area  and  at  the  same 
depth,  we  have 

f  =H.  S.  <iSp.Gr.y-,  [79.] 

and,  comparing, 

£  :  £ '  =  (  Sp.  Gr.)  :  (  Sp.  Gr.y.  [80.] 


228  CHEMICAL  PHYSICS. 

(128.)  Hydrostatic  Paradox.— It  is  evident  from  (123),  that 
the  pressure  of  a  liquid  on  the  bottom  of  the  containing  vessel 
may  be  very  much  greater  than  the  weight 
of  liquid  it  contains.  For  example,  the 
pressure  of  the  liquid  on  the  bottom  of  the 
vessel  D  <7,  Fig.  222,  is  the  same  as  if  its 
diameter  were  equal  throughout  to  that  of 
the  lower  part ;  and  from  this  it  would  seem 
to  follow,  that,  if  the  vessel  were  placed  in 
the  pan  of  a  balance,  M  N,  it  ought  to 
produce  the  same  effect  as  a  cylindrical 
vessel  of  the  same  weight,  containing  the 
same  height  of  water,  and  having  through- 
out the  diameter  of  the  part  D.  But  it  has 
been  shown,  that  the  liquid  presses  on  the  walls  n  o  as  well  as  on 
the  bottom,  and,  since  this  pressure  is  in  an  upward  direction,  it 
will  tend  to  make  the  vessel  rise,  while  the  pressure  on  the  bot- 
tom tends  to  make  it  fall.  The  difference  of  these  two  pressures 
is  all  that  is  exerted  on  the  pan  of  the  balance,  and  this  in  every 
case  is  just  equal  to  the  weight  of  the  vessel  and  that  of  the 
liquid  which  it  contains. 

This  fact  is  usually  called  the  Hydrostatic  Paradox.  It  is, 
however,  evidently  no  paradox,  but  only  a  necessary  consequence 
of  the  mechanical  condition  of  liquid  matter. 

Equilibrium  of  Liquids. 

(129.)  In  order  that  there  should  be  a  condition  of  equi- 
librium in  a  liquid  mass,  it  is  essential  that  each  particle  of  the 
liquid  should  be  pressed  on  all  sides  equally.  This  principle  — • 
the  first  statement  of  which  is  attributed  to  Archimedes  —  is  a 
necessary  consequence  of  the  mobility  of  liquid  particles.  For, 
suppose  that  any  one  particle  were  not  pressed  on  all  sides  equal- 
ly, it  is  evident  that,  being  free  to  move,  it  must  move  in  the 
direction  of  the  greatest  pressure,  and  there  would  not  be  an 
equilibrium  (28). 

When  a  liquid  mass  under  the  influence  of  gravity  is  sup- 
ported in  a  vessel,  it  is  essential,  in  order  that  each  particle  may 
be  pressed  on  all  sides  equally  (in  other  words,  in  order  that 
there  may  be  a  condition  of  equilibrium),  that  two  conditions 
should  be  fulfilled,  which  we  will  now  consider. 


THE   THREE   STATES   OP  MATTEB.  229 

1.  The  surface  of  the  liquid  must  be  perpendicular  at  each 
point  to  the  direction  of  gravity ;  that  is  to  say,  it  must  be  hori- 
zontal. 

To  prove  this,  let  us  suppose  that  the  surface  of  the  liquid 
has  any  other  form,  as  in  Fig.  223.  It  is  then  evident,  that 
the  force  of  gravity  acting  on  any  particle, 
m,  and  represented  by  the  line  mp  (31), 
will  be  decomposed  into  two  others  (35). 
One  of  these,  represented  by  m  q,  is  nor- 
mal to  the  surface  at  the  point  m,  and, 
being  balanced  by  the  resistance  of  the 

fluid  particles,  would  not  cause  motion.  The  second  compo- 
nent is  tangent  to  the  surface,  and,  not  being  balanced,  tends  to 
move  the  particles  in  the  direction  mf.  Hence,  under  these 
circumstances,  there  could  not  be  an  equilibrium.  If,  however, 
the  surface  is  horizontal,  the  tendency  of  the  force  of  gravity  is 
solely  to  sink  the  particles  under  the  surface,  and  since  all  the 
particles  at  the  surface  are  solicited  equally  by  this  force,  the 
equilibrium  is  maintained. 

It  follows  from  this,  that  the  surface  of  still  water  is  horizontal 
when  its  extent  is  so  limited  that  we  can  regard  the  directions  of 
the  forces  of  gravity  as  all  parallel  (44).  Such  is  not,  however, 
the  case  with  the  surface  of  the  ocean  when  at  rest,  or  of  a  large 
sea.  For  since  this  surface  must  be  perpendicular  at  every  point 
to  the  plumb-line,  and  since  all  plumb-lines,  if  extended,  pass  ap- 
proximatively  through  the  centre  of  the  earth,  it  follows  that  the 
surface  must  be  sensibly  spherical  (60). 

The  principle  just  illustrated  is  only  a  particular  case  of  a 
more  extended  principle,  which  may  be  thus  stated  :  — 

When  a  liquid  mass  is  in  equilibrium,  the  resultant  of  all  the 
forces  acting  at  any  point  of  its  surface  is  normal  to  the  surface 
at  that  point. 

2.  The  pressure  must   be  equal  over  the  whole   surface  of 
any  horizontal  section.     The  necessity  of  this  condition  is  easily 
shown.     For  suppose  this  not  to  be  the  case,  then  there  must  be 
somewhere  on  the  same  horizontal  section  —  for  example,  p  n, 
Fig.  219  —  two  adjacent  particles  which  are  not  equally  pressed 
by  the  superincumbent  liquid.     But  two  such  particles  must  ex- 
ert, in  consequence  of  their  elasticity,  an  unequal  pressure  on 
each  other,  a  condition  which  is  evidently  not  consistent  with  a 
state  of  equilibrium. 

20 


230  CHEMICAL  PHYSICS. 

At  the  surface  of  a  liquid  the  pressure  must  be  everywhere 
zero,  and  hence,  in  a  state  of  equilibrium,  the  surface  must  be 
horizontal ;  so  that  the  first  condition  may  be  regarded  as  a 
special  case  of  the  last. 

This  condition  is  also  a  particular  case  of  a  general  principle, 
which  may  be  thus  stated :  — 

Any  liquid  mass  in  equilibrium  may  be  regarded  as  consisting1 
of  an  infinite  number  of  lamince,  normal  at  each  point  of  their 
surface  to  the  resultant  of  all  the  forces  which  act  at  this  point, 
and  sustaining  at  every  point  exactly  the  same  pressure. 

It  is  a  consequence  of  this  principle,  that  any  liquid  mass,  which 
is  not  acted  upon  by  external  forces,  will  take  the  form  of  a  sphere 
in  consequence  of  the  mutual  attraction  of  its  own  particles.  In 
this  case,  the  infinitely  thin  laminae  are  concentric  spherical  sur- 
faces, and  the  resultant  of  all  the  forces  acting  on  any  particle 
in  every  case  passes  through  the  centre  of  the  sphere,  and  is  nor- 
mal to  the  spherical  surface  on  which  the  point  is  situated.  By 
no  other  form  than  the  sphere  would  the  conditions  of  equilibrium 
be  satisfied. 

Observation  confirms  this  result  of  theory.  Drops  of  water  or 
mercury,  so  small  as  not  to  be  sensibly  deformed  by  their  own 
weight,  take  a  spherical 'form  when  placed  on  surfaces  they  do 
not  wet.  The  rain-drop  also  is  spherical,  and  in  like  manner  the 
drops  of  melted  lead  become  spherical  while  falling  in  the  shot- 
towers.  But  the  theory  is  still  more  beautifully  illustrated  by  an 
experiment  devised  by  Plateau. 

By  mixing  alcohol  and  water,  a  liquid  can  be  obtained  having 
the  same  density  as  oil.  If,  now,  we  add  drops  of  oil  to  the  liquid, 
these  drops,  as  we  shall  soon  see,  are  in  the  same  condition  as 
if  they  had  no  weight,  and  in  conformity  with  the  theory  take 
a  spherical  form.  By  carefully  introducing  the  oil,  a  sphere  of 
considerable  size  can  be  formed,  suspended  in  the  alcoholic  fluid. 
Plateau  succeeded  in  giving  to  this  liquid  sphere  a  rotation  by 
means  of  very  simple  machinery,  and  found  that,  by  regulating 
the  velocity,  he  could  cause  it  to  become  flattened  at  the  poles,  to 
throw  off  rings  and  satellites,  and  thus  in  various  ways  illustrate 
the  nebular  hypothesis  of  Laplace. 

(130.)  A  liquid  when  in  equilibrium  always  maintains  the 
same  level, in  vessels  communicating  with  each  other.  —  This  fa- 
miliar fact  is  illustrated  by  Fig.  224,  which  represents  four  ves- 


THE   THREE   STATES   OF   MATTER. 


231 


sels,  A,  B,  Cy  Z>,  communicating  through  the  tube  m  n,  in  all  of 
which  the  liquid  stands  at  the  same  level.  That  this  must  neces- 
sarily be  the  case,  is  easily  shown.  Consider  any  vertical  section 
in  the  tube  m  n,  separating  the 
liquid  in  D  from  that  in  O, 
and  let  us  denote  the  area  of 
its  surface  by  S.  Now  it  is 
evident  that  this  section  can  be 
in  equilibrium  only  when  the 
pressures  on  its  two  faces  are 
equal.  The  pressure  on  the 
face  towards  D  is,  by  [78], 
f  =  S.H.(Sp.  Gr.) ,  in  which 
H  is  the  depth  of  the  centre  of 
gravity  of  the  section  below  the 
level  of  the  liquid  in  D.  The  "r  224 

pressure  on  the  face  towards  C 

is,  in  like  manner,  £  =  S  .  H '  .  (Sp.Gr.),  in  which  H'  equals 
the  depth  of  the  centre  of  gravity  below  the  level  of  the  liquid 
in  C.  Since  these  two  pressures  are  equal  when  there  is  an 
equilibrium,  it  follows  that  H=  H',  which  demonstrates  the  prin- 
ciple in  question. 

(131.)  When  two  vessels  communicating  together  are  filled 
with  different  liquids,  which  will  not  mix  or  combine  chemically 

with  each  other,  the  heights  of  the 
two  liquid  columns  when  in  equi- 
librium are  inversely  proportional 
to  the  specific  gravities  of  the 
liquids.  This  principle  may  be  il- 
lustrated by  means  of  the  apparatus 
represented  in  Fig.  225.  It  consists 
of  two  tubes,  m  and  w,  connected 
together  by  a  smaller  tube  below. 
The  lower  portion  of  both  tubes  is 
filled  with  mercury,  and  on  the 
surface  of  the  mercury  in  the  tube 
n  rests  a  column  of  water,  A  B.  If 
Fig.  225.  now  we  conceive  a  horizontal  line, 

B  C,  drawn,  across  the   apparatus 
from  the  surface  of  the  mercury  at  B,  it  is  evident,  from  the 


232 


CHEMICAL  PHYSICS. 


last  section,  that  the  liquid  below  this  line  is  in  equilibrium  ; 
and  hence  it  follows,  that  the  column  of  water  B  A  is  just  bal- 
anced by  the  column  of  mercury  D  C.  On  measuring  these  two 
heights,  it  will  be  found  that  D  C  is  thirteen  and  a  half  times 
smaller  than  A  B  ;  and  by  referring  to  the  table  of  specific  grav- 
ities, it  will  be  found  that  the  specific  gravity  of  mercury  is  thir- 
teen and  a  half  times  greater  than  that  of  water  ;  or,  in  other  words, 
the  heights  are  inversely  proportional  to  the  specific  gravities. 

The  truth  of  this  principle  can  easily  be  proved.  If  we 
represent  the  surface  of  the  mercury  at  B  by  £,  and  the 
height  of  the  column  of  water  B  A  by  H,  the  specific  gravity  of 
water  by  Sp.Gr.,  then  by  [78]  the  pressure  on  the  surface  is 
£  =  S  .  H  .  (Sp.Gr.).  In  the  same  way,  the  pressure  of  the 
column  of  mercury,  C  D,  is  £'  =  S'  .  H'  .  (  Sp.  Gr.y,  where  S1  is 
the  area  of  the  section  at  C,  H'  the  height  of  the  column  C  D, 
and  (Sp.Gr.y  the  specific  gravity  of  the  mercury.  Now,  it  fol- 
lows from  (120),  that  there  can  be  an  equilibrium  only  when  the 
pressures  exerted  on  the  two  surfaces  at  B  and  C  are  proportional 
to  the  area  of  these  surfaces,  or  when  £  :  £'  =  S  :  S'.  Substi- 
tuting the  value  of  £  and  4P,  we  find  that  when  this  is  the  case, 

H.  (Sp.Gr.)  ==  H'  .  (Sp.Gr.y, 

or  [81.] 

H:  H'*=(8p.Gr.y  :  (Sp.GrJ. 

Hence,  there  can  be  an  equilibrium  only  where  the  heights  of  the 

two  columns  are  inversely  as  the  specific  gravities  of  the  liquids. 

(132.)    Spirit-Level.  —  We  have  seen  that  the  surface  of  a 

liquid  at  rest  is  always  horizontal,  that  is  to  say,  perpendicular  to 

the  direction  of  gravity. 
We  have,  therefore,  in 
this  fact  a  ready  means 
of  determining  the  hor- 
izontal plane.  The  spir- 
it-level, which  is  used 
for  this  purpose,  con- 
sists of  a  tube  of  glass 
(Fig.  226)  very  slightly 
curved,  and  filled  with 
alcohol,*  leaving  only  a 


227. 


*  Alcohol  does  not  freeze  even  at  the  lowest  temperatures. 


THE   THREE    STATES   OP   MATTER. 


233 


small  bulb  of  air,  which  always  tends  to  occupy  the  highest  part. 
The  tube  is  hermetically  sealed,  and  mounted  on  a  brass  or 
wooden  stand,  D  (7,  Fig.  227,  the  base  of  which  is  carefully  ad- 
justed, so  that  when  it  rests  on  a  horizontal  plane,  P,  the  air- 
bubble,  Jf,  shall  rest  just  at  the  middle  of  the  tube. 

(133.)  Artesian  Wells.  —  The  tendency  of  water  to  seek  its 
own  level  is  illustrated  by  all  seas,  lakes,  springs,  and  rivers, 
which  are  so  many  vessels  connecting  with  each  other.  One  of 
the  most  remarkable  of  this  class  of  illustrations  is  the  Artesian 
well,  named  from  the  old  province  of  Artois,  in  France,  where 
these  wells  were  first  made.  They  are  narrow  tubes  sunk  in  the 
earth  to  various  depths,  in  which  the  water  frequently  rises  many 
feet  above  the  surface  of  the  ground. 

The  principle  of  the  Artesian  well  is  illustrated  by  Fig.  228. 
The  crust  of  our  globe  is  formed  of  numerous  strata,  some 


Fig.  228. 

of  which  are  permeable  to  water,  like  sand  and  gravel,  while 
others,  such  as  clay,  are  impermeable.  Let  us  suppose,  then, 
that  in  a  geological  basin  we  have  an  alternation  of  such  strata, 
for  example,  two  beds  of  clay-rock,  A  and  B,  enclosing  a  bed 
of  some  permeable  material,  Jf,  as  sand ;  and  let  us  also  suppose 
that  the  sand  bed  comes 
to  the  surface  at  some 
higher  level  (Fig.  229), 
where  it  will  receive  the 
rain-water.  This  water 
will  filter  through  the 
sand  and  collect  under 
the  geographical  basin, 
without  being  able  to  rise  to  the  surface,  on  account  of  the  clay 
bed  A.  But  if  we  sink  a  tube  through  this  bed,  it  is  evident 
.20* 


Fig.  229. 


234 


CHEMICAL   PHYSICS. 


that  the  water  will  rise  to  a  height  as  much  above  the  soil  as  is 
the  level  at  which  it  stands  in  the  peculiar  reservoir  formed  by 
the  clay  beds. 

These  wells  are  sunk  with  a  peculiar  form  of  auger,  which  is 
worked  within  an  iron  tube,  the  tube  be- 
ing driven  down  as  fast  as  the  auger  de- 
scends. One  of  the  most  remarkable  of 
these  wells  is  that  of  Grenelle,  on  the  out- 
skirts of  Paris.  It  is  548  metres  deep, 
and  yields  3,000  litres  of  water  each  min- 
ute. The  water  has  a  constant  tempera- 
of  27°  C. 

(134.)  Salt  Wells.  —  An  illustration 
of  the  principles  of  section  (131)  is  fur- 
nished by  the  mode  in  which  salt  wells  are 
worked  in  some  parts  of  Germany.  It  not 
unfrequently  happens,  that  beds  of  rock-salt 
occur  in  the  midst  of  impermeable  strata 
(see  Fig.  230).  It  can  then  be  extracted 


Fig.  230. 

in  the  following  way.  An  Artesian  well 
(Fig.  231)  is  first  sunk  to  about  the  mid- 
dle of  the  bed.  Within  this  well  is  en- 
closed a  smaller  tube  of  copper,  descend- 
ing to  the  bottom  of  the  bed  of  salt,  and 
therefore  considerably  lower  than  the  iron 
tube  forming  the  sides  of  the  well.  The 
lower  end  of  the  copper  tube  is  closed,  but 
it  is  perforated  with  little  holes  to  the 
height  of  a  few  metres,  which  allow  the 
water,  but  not  dirt,  to  enter.  From 
some  convenient  source  fresh  water  is  made  to  flow  into  the  well, 
and  descends  outside  of  the  copper  tube  to  the  salt  bed.  It 


Fig.  231. 


THE   THREE   STATES   OF   MATTER.  235 

dissolves  the  salt,  and  the  heavy  brine  sinks  to  the  bottom  of  the 
bed,  where  it  finds  the  lower  end  of  the  copper  tube.  This  tube 
then  fills  with  salt  water  ;  but  the  brine  does  not  rise  to  the  sur- 
face of  the  soil,  but  only  to  such  a  level  that  the  column  of  brine 
in  the  interior  copper  tube  shall  be  in  equilibrium  with  that  of 
water  in  the  annular  space  outside.  The  specific  gravity  of  sat- 
urated brine  is  about  1.20,  that  of  water  being  1 ;  hence,  if  we 
represent  the  heights  of  the  two  columns  by  H  and  U',  we  shall 
have  II:  H1  =  1.20  :  1.  If,  then,  the  depth  of  the  well  is  200 
metres,  the  brine  will  rise  ^  .  200  =  166,  and  consequently  to 
a  level  34  m.  below  the  surface  of  the  soil.  Through  this  dis- 
tance it  is  raised  by  a  pump. 

Buoyancy  of  Liquids. 

(135.)  Principle  of  Archimedes.  —  All  liquids  buoy  up  solids 
immersed  in  them  with  a  force  equal  to  the  weight  of  the  liquid 
displaced.  This  very  important  fact  was  discovered  by  Archime- 
des, and  is  generally  known  under  the  name  of  the  Principle  of 
Archimedes.  It  is  generally  stated  that  the  discovery  was  made 
by  this  renowned  philosopher  of  antiquity  while  reflecting  on  the 
buoyancy  of  the  water  on  his  own  body  when  he  was  bathing ;  and 
he  is  said  to  have  been  so  much  elated  by  the  discovery,  that  he 
rushed  from  the  bath  through  the  streets  of  Syracuse,  exclaiming, 
Evprjrca  !  evpyfca  ! 

The  principle  of  Archimedes  may  be  illustrated  by  means  of 
the  apparatus  represented  in  Fig.  232.  The  brass  cylinder  B 
is  made  so  as  to  fit  accurately  the  brass  cup  A.  In  experi- 
menting with  the  apparatus,  the  cylinder  and  cup,  having  been 
suspended  to  one  pan  of  a  balance  arranged  for  the  purpose, 
are  carefully  poised,  by  placing  weights  in  the  opposite  pan; 
the  cylinder  is  then  immersed  in  water,  as  represented  in  the 
figure.  In  consequence  of  the  buoyancy  of  the  liquid,  the  pan 
containing  the  weights  will  preponderate.  According  to  the  prin- 
ciple, this  buoyancy  is  equal  to  the  weight  of  the  water  which 
the  cylinder  has  displaced.  But  from  the  construction  of  the 
apparatus,  the  cup  A  will  hold  exactly  this  amount  of  water ; 
and  hence,  if  the  principle  is  correct,  the  equilibrium  will  be  re- 
stored on  filling  the  cup  A  with  water,  —  and  this  we  find  to  be 
the  case.  The  same  result  would  also  be  obtained  with  alcohol, 
or  with  any  other  liquid. 


23G 


CHEMICAL   PHYSICS. 


Fig  232. 

It  appears,  then,  that  the  cylinder  is  buoyed  up  by  a  force 
equal  to  the  weight  of  the  liquid  which  it  displaces.     But  this 

statement  expresses  only 
one  half  of  the  truth  ;  for 
it  is  a  necessary  result  of 
the  equality  of  action  and 
reaction,  that  the  upward 
pressure  of  the  water  on  the 
cylinder  must  be  accompa- 
nied by  an  equivalent  down- 
ward pressure  of  the  cylin- 
der on  the  water  ;  or,  in 
other  words,  not  only  that 
the  cylinder  loses  in  weight, 
but  also  that  the  water  gains 
the  weight  which  the  cyl- 
inder loses.  In  order  to  il- 
lustrate this  fact,  we  can 


THE   THREE   STATES   OF   MATTER. 


237 


arrange  the  experiment  as  represented  in  Fig.  233.  "We  first 
balance  the  vessel  of  water,  and  then  immerse  in  the  liquid  the 
brass  cylinder,  supported  as  represented  in  the  figure.  The 
water  will  be  found  to  have  gained  in  weight,  and  in  order  to 
restore  the  equilibrium  it  will  be  necessary  to  remove  from  the 
vessel  sufficient  water  to  just  fill  the  cylinder  A. 

(136.)  Demonstration.  —  The  principle  of  Archimedes  is  a 
necessary  consequence  of  the  law  enunciated  in  (126),  as  can 
easily  be  proved.  Let  us,  in  the  first 
place,  suppose  that  the  body  im- 
mersed in  the  liquid  is  a  right  cyl- 
inder, as  c  d,  Fig.  234,  suspended  so 
that  its  bases  shall  be  horizontal. 
Consider  now  the  pressure  exerted 
by  the  liquid  at  any  one  point  on  the 
side  of  this  cylinder.  By  (121)  the 
direction  of  this  pressure  is  normal 
to  the  surface  at  this  point.  But,  as 
is  well  known,  this  normal,  if  pro- 
duced, will  coincide  with  the  diam- 
eter of  the  circular  section  of  the 
cylinder  which  would  be  made  by 
a  horizontal  plane  cutting  the  cylin- 
der at  the  point  in  question.  Now, 
as  the  other  end  of  this  diameter  is 
in  contact  with  the  liquid,  and  at  the  same  depth  below  its  surface, 
it  is  evident  that  this  point  will  sustain  a  pressure  equal  in  amount 
and  opposite  in  direction  to  that  sustained  by  the  first  point. 
These  two  pressures  will  consequently  balance  each  other,  and, 
since  the  same  holds  true  of  every  other  similar  point,  it  follows 
that  the  whole  pressure  of  the  liquid  on  the  convex  surface  of  the 
cylinder  is  in  equilibrium. 

It  is  different,  however,  with  the  pressure  on  the  two  horizon- 
tal bases.  The  pressure  exerted  on  the  base  d  is,  by  (126),  equal 
to  the  weight  of  the  liquid  cylinder  represented  by  e  g-,  and  the 
pressure  on  the  base  c  to  the  weight  of  the  liquid  cylinder  h  i. 
There  is,  therefore,  an  excess  of  upward  pressure  equal  to  the 
weight  of  the  liquid  cylinder  /g-,  which  is  equal  in  size  to  the 
cylinder  c  d.  The  cylinder,  then,  is  buoyed  up  with  a  force  equal 
to  the  weight  of  liquid  displaced. 


Fig.  234. 


238  CHEMICAL  PHYSICS. 

(137.)  This  demonstration  may  readily  be  extended  to  a  body 
of  any  form  whatsoever.  Let  s  s'  s"  be  the  body,  and  o  x,  o  y, 
o  z  three  co-ordinate  axes  perpendicular  with  each  other,  to  which 
we  can  refer  position.  The  pressure  exerted  by  a  liquid  on  any 

infinitely  small  element  of  surface, 
5,  is  by  [78]  f  =  s.H.(Sp.Gr.'). 
This  pressure,  which  by  (121)  is  nor- 
mal to  the  surface,  may  be  resolved 
into  three  forces,  at  right  angles  to 
each  other  and  parallel  to  the  co-or- 
dinate axes.  Representing  the  nor- 
mal by  JP,  and  the  angles  which  it 

makes  with  x,  y,  z,  as  px  ,    p  ,    pz  , 
we  have,  for  the  three  components, 
4F  '  =  $  cos  px  ,  £  "  =  £  cos  p  ,  and 
Fig'235'  JF'"  =  f  cos  {  .     Substituting   for 

its  value  given  above,  the  three  components  become 


.  Or.)  .  s  cos  px  ;  [82.] 

.  GV.)  .  *  cos  ^  ;  [83.] 

o' 

IF'"  s=H  .(Sp.G.-)  .s  cos{  .  [84.] 


But  5  cos  -^  is  the  projection  of  the  surface  s  on  the  plane  of  y  z, 

and  this  projection  is  equal  to  the  right  section  of  an  infinitely 
small  cylinder  parallel  to  the  axis  of  x.  Representing  the  area 
of  this  section  by  r",  we  have,  for  the  value  of  the  first  compo- 
nent, £'  =  H  .  (Sp.Gr.)  r".  But  this  pressure  will  obviously 
be  balanced  by  the  pressure  exerted  on  the  element  of  surface,  s", 
which,  decomposed  in  the  same  way,  will  give  a  component  also 
equal  to  H  .  ($/?.  6rr.)  r",  and  parallel  to  the  axis  of  x,  but  act- 
ing in  the  opposite  direction.  It  can  easily  be  shown  that  the 
same  is  true  of  the  component  parallel  to  the  axis  of  z.  This 
will  be  balanced  by  an  opposite  and  equal  component  of  the 
pressure  exerted  on  the  element  s"1.  Let  us,  lastly,  consider 
what  will  be  the  effect  of  the  component  parallel  to  the  axis 

of  y.    In  the  value  of  £"   [83],  the  quantity  of  s  cos  *    is 

u 

the  projection  of  the  surface  s  on  the  plane  of  x  z.  This  pro- 
jection is  equal  to  the  right  section  of  the  vertical  cylinder  s  s'. 


THE   THREE   STATES   OF   MATTER.  2B9 

Representing  the  area  of  this  section  by  r',  we  have,  for  the  value 
of  the  vertical  component,  £"  =  H  (Sp. Gr.)  r',  a  force  which 
tends  to  raise  the  body.  This  force  is  in  part  balanced  by  the 
pressure  exerted  on  the  element  s'.  By  decomposing  this  force, 
it  will  be  found  that  the  vertical  component  which  exerts  a  down- 
ward pressure  in  the  direction  s'  s,  is  equal  to  £ 2  =  H1  (  Sp.  Gr.}  r'. 
The  vertical  cylinder  of  the  body  s  s'  is  then  buoyed  up  by 
a  force  equal  to  the  difference  of  these  two  values,  that  is, 
£"  —  jf2  =  (J/ — H')  (Sp.Gr.)  r',  which  is  the  weight  of  a 
column  of  liquid  of  the  same  volume  as  the  cylinder. 

By  extending  the  same  course  of  reasoning  to  each  of  the  in- 
finitely small  elements  of  surface  which  the  body  presents,  we 
should  decompose  the  body  into  an  infinite  number  of  vertical 
cylinders  similar  to  s  s',  each  of  which  is  buoyed  up  by  a  force 
equal  to  the  weight  of  its  own  volume  of  liquid.  The  whole 
body  is  of  course  buoyed  up  by  a  force  equal  to  the  sum  of  the 
forces  acting  on  the  elementary  cylinders,  that  is,  by  a  force 
equal  to  the  weight  of  the  liquid  which  it  displaces. 

(138.)  The  correctness  of  the  principle  of  Archimedes  can  be 
proved  in  another  way,  which  more  directly  connects  it  with  the 
condition  of  equilibrium  which  exists  among 
the  particles  of  all  liquids  when  at  rest. 
Consider,  for  example,  any  cubic  centimetre 
of  the  liquid  contained  in  the  vessel,  Fig. 
236,  such  as  A  B.  Since  the  liquid  is  at 
rest,  it  is  evident  that  this  liquid  cube  is  ex- 
actly sustained  in  its  position  by  the  pres- 
sure of  the  surrounding  particles.  But  the 
mass  of  liquid,  of  which  it  consists,  has 
weight  ;  and  it  is  therefore  also  evident, 
that  the  liquid  cube  is  sustained  because  it 
is  buoyed  up  by  a  force  which  is  just  equal 
to  its  weight.  Let  us  now  suppose  the 
liquid  cube  to  be  suddenly  solidified  without  changing  its  volume ; 
it  is  evident  that  it  will  be  buoyed  up  by  the  same  force  as  be- 
fore ;  for  no  change  has  taken  place  either  in  the  position  or  the 
conditions  of  the  surrounding  particles.  Whatever,  therefore, 
may  be  the  substance  or  weight  of  the  solid  cube,  it  will  be  buoyed 
up  by  a  force  equal  to  the  weight  of  one  cubic  centimetre  of  the 
liquid  in  which  it  is  immersed.  This  demonstration  can  evident- 
ly be  extended  to  any  other  body,  of  whatsoever  size  or  shape. 


240  CHEMICAL  PHYSICS. 

(139.)  Centre  of  Pressure.  —  It  has  been  proved  (45),  that 
the  resultant  of  all  the  forces  which  gravity  exerts  on  the  parti- 
cles of  a  body  is  a  single  force  —  represented  by  the  weight  of 
the  body  —  directed  vertically  downwards.  And  it  has  further 
been  proved  (46),  that  this  force  may  always  be  regarded  as  ap- 
plied at  the  centre  of  gravity,  whatever  position  the  body  may 
assume.  Now,  since  the  supposed  liquid 
cube  (Fig.  236)  is  exactly  supported,  it  fol- 
lows that  the  resultant  of  all  the  pressures 
which  it  receives  from  the  surrounding  par- 
ticles of  liquid  must  also  be  a  single  force 
equal  to  the  weight  of  the  cube,  but  di- 
rected vertically  upwards.  Moreover,  if  our 
ideal  cube  could  be  turned  in  the  liquid,  it 
would  evidently  still  remain  in  equilibrium, 
in  whatever  position  it  might  be  placed. 
Since  in  all  possible  positions  the  resultant 
°f  the  forces  of  gravity  may  be  regarded  as 
applied  at  the  centre  of  gravity,  it  follows 
that  in  the  different  positions  the  resultant  of  all  the  pressures 
may  also  be  regarded  as  applied  at  the  same  point.  The  same 
point,  then,  which  is  common  to  all  the  resultants  of  the  forces 
of  gravity  in  the  different  positions  which  a  body  may  assume,  is 
common,  also,  to  all  the  resultants  of  pressure  ;  in  other  words, 
the  centre  of  gravity  of  our  liquid  cube  is  also  the  centre  of 
pressure. 

If,  now,  we  replace  the  ideal  cube  of  liquid  with  a  cube  of  brass 
having  the  same  size  and  volume,  it  is  evident  that  the  conditions 
of  the  particles  exerting  the  pressure  have  not  been  changed. 
Hence  the  resultant  of  the  pressures  exerted  by  these  particles 
will  still  be  a  force  acting  vertically  upwards  ;  and,  further,  in 
any  position  which  the  brass  cube  may  assume,  the  direction  of 
this  resultant  will  pass  through  what  would  be  the  centre  of  grav- 
ity of  a  liquid  cube  of  the  same  form  and  volume.  This  com- 
mon point,  through  which  the  resultant  of  the  pressure  passes, 
in  any  position  of  the  brass  cube,  is  its  centre  of  pressure.  We 
have  made  use  of  a  brass  cube  in  this  discussion,  merely  to  give 
distinctness  to  our  conceptions  ;  but  it  is  evident  that  the  same 
reasoning  would  apply  to  a  body  of  any  shape  whatsoever.  In 
any  case,  the  centre  of  pressure  is  always  the  same  point  which 


THE   THREE   STATES   OF   MATTER.  241 

was  previously  the  centre  of  gravity  of  the  liquid  which  has  been 
displaced  by  the  body. 

If  the  body  is  homogeneous  and  entirely  immersed  in  water, 
the  centre  of  pressure  coincides  with  the  centre  of  gravity  of  the 
body.  If,  however,  the  body  is  not  homogeneous,  —  if,  for  ex- 
ample, it  is  loaded  on  one  side,  —  then  the  centre  of  gravity  will 
no  longer  coincide  with  the  centre  of  pressure  ;  because  it  will 
not  coincide  with  the  centre  of  gravity  of  a  liquid  body  of  the 
same  shape  and  volume. 

(140.)  Floating  Bodies.  —  If  the  weight  of  a  body  is  less 
than  that  of  the  liquid  which  it  displaces,  then,  the  buoyancy  be- 
ing greater  than  the  weight,  the  body  will  rise  to  the  surface  of 
the  liquid,  and  float.  On  the  other  hand,  if  the  weight  of  a  body 
is  greater  than  that  of  the  liquid  which  it  displaces,  it  will  sink. 
Moreover,  since  the  specific  gravities  of  any  two  substances  are 
to  each  other  as  the  weights  of  equal  volumes  of  these  substances, 
it  is  also  true  that  a  homogeneous  solid  will  float  when  its  spe- 
cific gravity  is  less  than  that  of  the  liquid,  and  that  it  will  sink 
when  these  conditions  are  reversed. 

An  iron  bar  sinks  in  water,  but  floats  in  mercury,  because  a 
given  volume  of  iron  weighs  less  than  the  same  volume  of  mer- 
cury, and  more  than  the  same  volume  of  water.  For  a  similar 
reason,  a  piece  of  boxwood  will  float  in  water,  but  sink  in  alco- 
hol. The  bar  of  iron,  however,  can  be  made  into  a  hollow  vessel, 
which  will  float  on  water ;  and,  in  the  same  manner,  boxwood 
can  be  made  to  float  on  alcohol.  The  volumes  of  the  bodies  will 
thus  be  increased  without  increasing  the  weight,  and  since  the 
weight  of  the  liquid  they  displace  is  now  greater  than  their  own 
weight,  they  will  float.  Steamships  are  frequently  made  of  iron, 
and  loaded  with  heavy  machinery  ;  but  nevertheless,  since  their 
whole  weight  is  less  than  that  of  the  water  which  they  displace, 
they  float.  The  specific  gravity  of  the  human  body  is  very  nearly 
the  same  as  that  of  water,  and  can  readily,  therefore,  by  a  little 
effort,  be  kept  at  the  surface  in  the  act  of  swimming.  By  in- 
creasing slightly  the  volume  of  water  displaced,  without  increas- 
ing sensibly  its  weight,  the  body  will  float  without  effort.  Most 
persons  can  expand  the  chest,  by  a  little  effort,  sufficiently  to  make 
the  specific  gravity  of  the  body  less  than  that  of  water,  and  it  is 
well  known  that  good  swimmers  can  float  their  bodies  by  lying 
back  on  the  surface  of  the  water  and  expanding  the  chest.  This  is 
21 


242  CHEMICAL  PHYSICS. 

also  the  theory  of  life-preservers,  which  are  bags  filled  with  air, 
or  pieces  of  cork  worn  under  the  arms.  They  so  far  increase  the 
volume  of  the  body  as  to  make  the  specific  gravity  of  the  life- 
preserver  and  the  body  together,  as  a  whole,  less  than  that  of 
water. 

The  large  floating  tanks,  called  camels,  which  are  used  to  lift 
large  vessels  over  the  sand-bars  that  obstruct  the  mouths  of  many 
harbors,  are  an  ingenious  application  of  the  same  principle.  These 
tanks,  which  are  closed  on  all  sides  and  water-tight,  having  been 
filled  with  water,  are  fastened  under  the  sides  of  the  vessel.  The 
water  is  then  pumped  out,  when  the  tanks  rise,  and  raise  the  ves- 
sel with  them.  A  similar  contrivance,  called  a  floating  dock,  is 
very  much  used  in  the  United  States  for  raising  ships  completely 
out  of  water,  for  repairs.  It  consists  of  a  large  platform,  on 
which  the  ship  is  to  rest,  beneath  which  are  hollow  and  water- 
tight tanks,  so  loaded  that,  when  full  of  water,  they  will  sink. 
The  platform  is,  in  the  first  place,  sunk  to  the  depth  of  several 
fathoms,  and  the  ship  to  be  raised  is  then  floated  over  it.  The 
water  is  now  pumped  out  of  the  tanks  beneath  the  platform, 
which  then  rises,  and  raises  the  vessel  with  it. 

(141.)  Equilibrium  of  Floating  Bodies.  —  When  a  body  is  at 
rest,  floating  on  the  surface  of  a  liquid,  there  must  be  an  equi- 
librium between  the  weight  of  the  body  and  the  buoyancy  of  the 
liquid.  Hence  it  follows,  from  (135),  that  the  weight  of  the 
liquid  actually  displaced  by  a  floating  body  is  equal  to  its  own 
weight.  We  can  always  determine  the  weight  of  a  ship  by 
measuring  the  volume  which  is  below  the  water-level,  and  mul- 
tiplying this  by  the  specific  gravity  of  the  liquid.  This  will,  by 
[56],  give  the  weight  of  water  displaced,  which,  as  we  have  just 
seen,  is  the  same  as  the  weight  of  the  ship.  We  can  also  deter- 
mine the  weight  of  the  cargo  by  determining  the  volume  of  water 
displaced  by  the  ship  both  before  and  after  loading.  The  differ- 
ence between  these  two  volumes,  multiplied  by  the  specific  gravity 
of  the  liquid,  will  give  the  weight  of  the  cargo. 

The  centre  of  pressure  of  a  floating  body  is,  by  (139),  the 
same  point  as  the  centre  of  gravity  of  the  fluid  it  displaces.  It 
is  obviously,  therefore,  an  entirely  different  point  from  the  centre 
of  gravity  of  the  body,  and  must  always  be  below  this  point  when 
the  body  is  a  homogeneous  solid.  For  example,  in  Fig.  237,  the 
centre  of  gravity  of  the  homogeneous  floating  body  a  b  c  d  is 


THE   THREE   STATES   OP   MATTER. 


243 


the  point  G.  The  centre  of  pressure,  P,  is  the  centre  of  gravity 
of  the  liquid  displaced,  and  this  is  obviously  below  the  centre  of 
gravity  of  the  whole  body.  When 
the  floating  body  is  not  homoge- 
neous, the  centre  of  gravity  may 
be  below  the  centre  of  pressure. 
For  example,  if  we  should  attach 
to  the  bottom  of  the  body  abed 
a  piece  of  lead,  this  would  sink 
the  body  still  deeper  in  the  water, 
and  thus  raise  the  centre  of  pres- 
sure, while  at  the  same  time  it 
would  lower  the  centre  of  gravity, 
and  thus  might  change  the  relative  position  of  the  two  points. 

In  order  that  a  floating  body  should  be  in  equilibrium,  it  is  not 
only  necessary  that  it  should  displace  its  own  weight  of  liquid, 
but  it  is  also  essential  that  the 
centres  of  gravity  and  pressure 
should  be  situated  on  the  same 
vertical.  If,  as  in  Fig.  238,  the 
two  points  are  not  situated  on  the 
same  vertical,  then  the  resultants 
of  the  forces  of  gravity  and  pres- 
sure will  be  represented  by  two 
opposite  vertical  forces,  as  P  q 
and  G  r.  Since  these  forces  are 
equal,  they  will  neither  tend  to 
raise  nor  depress  the  body  in  the  liquid ;  but  nevertheless,  as  the 
two  forces  form  a  couple  (38),  they  will  tend  to  rotate  the  body. 
Hence,  although  the  body  will  neither  rise  nor  fall,  it  will  turn  in 
the  liquid  until  the  centre  of  pressure  falls  in  the  same  vertical 
with  the  centre  of  gravity,  but  in  such  a  way  that  the  amount  of 
water  displaced  by  the  body  shall  be  always  the  same. 

(142.)  Stable  and  Unstable  Equilibrium.  —  When  the  cen- 
tres of  pressure  and  gravity  are  in  the  same  vertical,  there  will  be 
a  condition  of  equilibrium,  but  this  equilibrium  may  be  either 
stable,  unstable,  or  neutral.  The  equilibrium  is  said  to  be  stable 
when,  on  turning  the  floating  body  slightly  in  the  water,  it  tends 
to  return  to  its  first  position ;  it  is  said  to  be  unstable,  when, 
under  these  circumstances,  it  continues  to  turn  until  it  passes 


Fig.  238. 


244 


CHEMICAL   PHYSICS. 


into  a  new  condition  of  equilibrium ;  and  it  is  said  to  be  neutral, 
when  it  will  remain  at  rest  in  any  position  indifferently. 

The  condition  of  a  floating  body  is  always  stable  when  the 
centre  of  gravity  is  below  the  centre  of  pressure.  The  truth 
of  this  statement  is  an  immediate  consequence  of  the  princi- 
ples of  the  last  section.  The  centre  of  pressure  is  a  point 
at  which  the  whole  upward  pressure  of  the  liquid  may  be  re- 
garded as  concentrated.  It  may  therefore  be  considered  as  the 
point  of  support  of  the  floating  body  ;  and  it  has  already  been 
shown  (48),  that  the  condition  of  a  body  is  stable  when  the 
centre  of  gravity  is  below  the  point  of  support.  It  does  not  fql- 
low,  however,  that  the  condition  is  necessarily  unstable  when  the 
centre  of  gravity  is  above  the  point  of  support.  In  this  case,  the 
stability  of  the  body  depends  upon  the  position  of  a  variable  point, 
which  is  called  the  metacentre ;  and  the  equilibrium  is  still  stable, 
when  the  centre  of  gravity  is  below  this  point.  The  position  of 
the  metacentre  depends  on  the  form  and  position  of  the  body. 
"We  shall  only  be  able  to  point  out  its  position  in  the  case  of  one 
of  the  simplest  solids  ;  but  this  example  will  serve  to  illustrate 
the  general  principle. 

Let  us  suppose,  then,  that  the  floating  body  is  a  homogeneous 
rectangular  prism  (Fig.  239).  The  centre  of  gravity  will  then 


BiS.Ls 

"-*  ^i'.-His-fl 

--  :  i.~r^'=r=:=r%"=:S5=iiI||:5Ii5i  =  -  = 

"*!lal:a^i:!^*IIr 


Fig  239.  Fig.  240. 

be  the  same  as  the  centre  of  its  figure,  or  <2,  and  the  centre  of 
pressure  the  centre  of  gravity  of  the  part  immersed  in  the  liquid, 
a  variable  point,  depending  on  the  position  of  the  body.  If,  now, 
when  it  is  floating  on  its  broadest  side,  we  turn  it  through  the 
angle  e  o  c  (Fig.  240),  the  portion  represented  by  the  triangle 
e  o  c  is  raised  out  of  the  liquid,  and  that  represented  by  b'  of  sub- 
merged ;  and  since  the  quantity  of  water  displaced  must  be  the 


THE  THREE   STATES   OF   MATTER.  245 

same  in  every  position  of  the  body,  it  follows  that  the  portion  e  o  c 
is  equal  to  the  portion  b  of.  But  now  the  form  of  the  submerged 
portion  is  entirely  changed,  and  the  centre  of  gravity  of  the  sub- 
merged portion,  which  is  the  centre  of  pressure,  is  also  changed, 
and  moved  to  the  point  P.  If  in  this  position  we  draw  through 
the  point  P  a  perpendicular,  it  will  intersect  the  perpendicular 
drawn  through  the  point  P  in  the  previous  position,  namely,  O  #, 
at  a  point  #,  and  this  point  is  the  metacentre.  In  the  case  before 
us,  the  metacentre  is  above  the  centre  of  gravity  ;  and  it  is  evi- 
dent  from  the  figures,  that  the  couple  formed  by  the  resultants 
of  the  forces  of  gravity  and  of  the  pressure  tends  to  restore  the 
floating  body  to  its  first  position  (Fig.  239). 

Let  us  now  suppose  that  the  rectangular  prism  is  floating  on 
its  narrow  side,  as  in  Fig.  241 ;  and  that,  as  before,  we  turn  it  to 


a 


Fig.  241.  Fig.  242. 

the  right  through  a  small  angle.  The  centre  of  pressure  will 
then  be  shifted  to  a  new  position,  at  the  right  of  the  plane  of 
symmetry  (Fig.  242).  If,  now,  we  erect  a  perpendicular,  it  will 
intersect  the  perpendicular  drawn  through  the  centre  of  pressure 
in  the  previous  position,  at  a  point  q,  below  the  centre  of  gravity; 
and  it  can  easily  be  seen  that  the  couple  formed  by  the  force  of 
gravity  and  the  pressure  will  tend  to  turn  the  body  still  fur- 
ther, and  it  will  only  come  to  rest  when  it  falls  back  into  the 
position  of  stable  equilibrium,  floating  on  its  broad  side,  as  in 
Fig.  239. 

What  has  now  been  illustrated  in  the  case  of  a  rectangular 
prism,  is  true  of  all  floating  bodies.  In  general,  the  metacentre 
may  be  defined  as  the  point  ivhere  the  vertical  passing"  through 
the  centre  of  pressure  in  the  position  of  equilibrium,  meets  the 
vertical  drawn  through  the  new  centre  of  pressure  after  the  body 
21* 


246  CHEMICAL  PHYSICS. 

has  been  slightly  displaced  from  this  position.  A  floating  body 
is  in  a  stable  condition  when  the  metacentre  is  above  the  centre 
of  gravity,  and  unstable  when  this  condition  of  things  is  reversed. 
When  the  centre  of  gravity  is  below  the  centre  of  pressure,  the 
metacentre  must  evidently  always  be  above  the  centre  of  gravity, 
and,  as  before  shown,  this  condition  is  always  stable.  It  is  also 
evident,  from  the  above  discussion,  that  the  stability  of  a  floating 
body  is  the  greater  the  broader  the  submerged  part  and  the 
lower  the  position  of  the  centre  of  gravity. 

It  is  of  great  importance  to  pay  attention  to  the  conditions  of 
stable  equilibrium  in  the  construction  and  loading  of  ships. 
Vessels  which  are  used  to  transport  passengers  or  light  cargoes 
require  to  be  ballasted,  by  depositing  immediately  above  the  keel 
a  quantity  of  heavy  matter,  such  as  stones  or  pigs  of  iron.  The 
centre  of  gravity  may  thus  be  brought  so  low,  as  to  give  the 
vessel  such  stability  that  no  lateral  force  of  the  wind  acting  on 
its  sails  can  capsize  it.  So,  also,  the  heaviest  part  of  a  cargo 
should  always  be  deposited  in  the  lowest  possible  position,  in  or- 
der that  its  centre  of  gravity  may  be  immediately  over  the  keel. 
When  this  is  the  case,  any  inclination  of  the  vessel  causes  the 
centre  of  gravity  to  rise  ;  and  to  accomplish  this  requires  a  force 
proportional  to  the  weight  of  the  vessel,  and  to  the  height  through 
which  the  centre  is  elevated. 

The  equilibrium  of  a  boat  may  be  rendered  unstable  by  the 
passengers  standing  up  in  it ;  and  this  is  not  unfrequently  the 
cause  of  accidents  to  light  sail-boats. 

If  the  centre  of  gravity  of  a  vessel  be  not  directly  over  the 
keel,  the  vessel  will  incline  to  that  side  at  which  it  is  placed  ;  and 
if  this  displacement  is  considerable,  danger  may  ensue.  The 
rolling  of  a  vessel  in  a  storm  may  so  derange  the  ballast  or  cargo, 
as  to  throw  the  vessel  on  her  beam-ends. 

(143.)  Neutral  Equilibrium. — In  some  cases,  the  position  of 
the  centre  of  pressure  is  not  changed  by  any  change  of  position 
of  the  body  which  is  compatible  with  displacing  its  own  weight 
of  fluid.  In  such  a  case,  the  body  will  float  in  equilibrium  in 
any  position  indifferently,  and  is  said  to  be  in  a  condition  of  neu- 
tral equilibrium.  A  sphere  of  uniform  density  is  an  example  of 
this ;  for  in  whatever  position  it  floats,  the  part  immersed  is 
always  a  segment  of  the  sphere  of  precisely  the  same  magnitude 
and  shape,  so  that  the  centre  of  pressure  has  always  the  same  posi- 


THE   THREE   STATES   OP   MATTER.  247 

tion  with  reference  to  the  centre  of  gravity  of  the  sphere.  Con- 
sequently, the  sphere  will  float  indifferently  in  any  position  in 
which  it  may  be  placed. 

Methods  of  determining  Specific  Gravity. 

(144.)  The  specific  gravity  of  a  substance  has  been  defined 
as  the  ratio  of  its  weight  to  that  of  an  equal  volume  of  pure 
water  at  4°  C.,  —  the  temperature  at  which  the  volume  of  the 
solid  is  measured  being  0°  C.  'As  most  of  the  methods  used  for 
determining  specific  gravity  are  illustrations  of  the  principles  of 
hydrostatics,  we  will  briefly  describe  them  in  this  connection, 
reserving,  however,  for  the  chapter  on  Weighing  and  Measuring, 
the  practical  details  of  the  subject. 

(145.)  First  Method.     Specific- Gravity  Bottle.  —  The  most 
obvious  method  of  determining  the  specific  gravity  of  a  substance 
is  to  weigh  equal  volumes  of  the  substance  and  of  water,  and 
then  divide  the  first  weight  by  the  last.     When  the  substance  is 
a  liquid,  this  method  is  readily  applied.     We  use  for  the  purpose 
a  small  glass  bottle,  such  as  is  represented  in  Fig.  243.     The 
bottle  is  closed  by  a  perforated  ground-glass  stopper 
of  peculiar  construction,  terminating  in  a  fine  tube, 
on  which  is  marked,  with  a  file,  a  point  to  which 
the  bottle  is  to  be  filled  at  each  experiment.     The 
bottle,  whose  tare  has  been  previously  ascertained) 
is  first  of  all  filled  with  pure  water,  and  the  stopper 
inserted,  when  the  water  rises  in  the  glass  tube. 
The  excess  of  water  above  the  mark  is  now  removed 
with  a  piece  of  bibulous  paper,  and  the  bottle  care- 
fully weighed.     By  substracting  from  this  weight 
the  tare  of  the  bottle,  we  have  the  weight  of  a  given         rig.  243. 
volume  of  water,  which  is  thus  ascertained  once  for 
all.     If,  then,  we  wish  to  obtain  the  specific  gravity  of  any  other 
liquid,  we  fill  the  bottle  with  this  liquid  in  the  same  way  as  be- 
fore, and  weigh  it ;  then,  having  subtracted  the  weight  of  the 
bottle,  we  have  the  weight  of  a  volume  of  this  liquid  equal  to 
the  volume  of  the  water.     Representing  these  two  weights  by 
W  and  W9  we  have,  by  definition, 

($*Gr.)  =  -».  [85.] 


248 


CHEMICAL   PHYSICS. 


If  we  repeat  this  process  at  different  temperatures,  we  obtain 
different  results,  owing  to  the  expansion  both  of  the  liquids  and  of 
the  glass.  It  is,  therefore,  essential  to  observe  carefully  the  tem- 
perature of  the  liquids  at  the  time  of  filling  the  bottle,  and  then 
to  calculate,  by  means  of  tables  prepared  for  the  purpose,  what 
would  have  been  the  result  had  the  temperature  of  the  water 
been  at  4°  C.  and  that  of  the  substance  at  0°  C.  This  is  called 
reducing'  the  results  to  the  standard  temperature,  and  the  method 
of  making  the  reduction  will  be  described  in  the  chapter  just  re- 
ferred to. 

The  specific-gravity  bottle  may  also  be  applied  to  determin- 
ing the  specific  gravity  of  solids,  when  they  can  be  broken  into 
small  pieces.  For  this  purpose,  we  take  a  specific-gravity 
bottle  and  determine  the  weight  of  the  bottle  when  filled  with 
water,  as  before  described.  Call  this  weight  TF,.  We  then  in- 
troduce into  the  bottle  a  known  weight  of  the  solid,  W,  and  fill 
up  the  remainder  of  the  bottle  with  water.  The  weight  of  the 
bottle,  solid  and  water,  which  we  then  ascertain,  we  will  repre- 
sent by  W*.  It  is  then  evident  that  the  weight  of  water  dis- 
placed by  the  solid  is  W1  =  W:  -f-  W  —  W2 ,  and  hence  we  have 


W 


W— 


[86.] 


Fig.  244. 


Here,  as  before,  it  is  necessary  to  reduce 
the  results  obtained  to  the  standard  tem- 
perature. 

(146.)  Second  Method.  The  Hydro- 
static Balance. — We  suspend  the  body  by 
a  fine  thread  to  the  pan  of  a  balance  (Fig. 
244),  and,  having  equipoised  it  by  means 
of  a  tare  in  the  other  pan,  immerse  it 
in  water,  as  represented  in  the  figure. 
The  weight  which  it  loses,  being  exactly 
equal  to  that  of  the  water  which  it  dis- 
places, is  the  weight  of  a  volume  of 
water  equal  to  that  of  the  body  which 
we  wish  to  find.  Hence,  in  order  to  de- 
termine this  weight,  we  have  only  to  add 
weights  to  the  pan  from  which  the  body 
is  suspended,  until  the  equilibrium  is  es- 


THE   THREE   STATES   OF   MATTER.  249 

tablished.  It  is  evidently  essential  to  the  accuracy  of  this  meth- 
od, that  the  water  used  should  be  pure,  and  the  thread  so  fine 
that  we  can,  without  sensible  error,  neglect  the  weight  of  water 
which  it  itself  displaces. 

Representing  by  W  the  weight  of  the  body,  and  by  W  the 
weight  required  to  restore  the  equilibrium,  we  have,  by  defini- 
tion, 

(4*0%)  — ip-  [87.] 

The  value  thus  obtained  must  be  reduced  to  the  standard  tem- 
perature. 

This  method  may  also  be  applied  to  liquids  as  well  as  to  solids. 
For  this  purpose  we  prepare  a  closed  glass  tube,  and  enclose  in 
it  sufficient  mercury  to  sink  the  tube  beneath  any 
liquid,  with  the  exception  of  the  two  heaviest,  mer- 
cury and  bromine.  To  this  tube  we  attach  a  fine 
platinum  wire,  as  in  Fig.  245,  which  represents  the 
apparatus  of  its  full  size.  We  commence  by  deter- 
mining once  for  all,  by  the  method  just  described,  the 
weight  of  the  volume  of  water  at  4°  C.  which  the  glass 
tube  displaces.  This  we  may  call  C,  as  it  is  a  con- 
stant quantity  for  each  apparatus.  In  order,  now,  to 
determine  the  specific  gravity  of  a  liquid,  we  suspend 
the  tube  to  the  pan  of  a  balance,  and,  having  equi- 
poised it  by  placing  a  weight,  prepared  for  the  pur- 
pose, in  the  other  pan,  immerse  it  in  the  liquid.  The 
amount  of  weight  required  to  restore  the  equilibrium 
is  the  weight  of  the  volume  of  this  liquid  which  the 
tube  displaces,  and  the  weight  of  the  same  volume  of 
water  at  4°  C.  is  known  to  be  C.  Hence  the  specific 

gravity  of  the  liquid  is  -^ .     This  value  must  be  cor- 
rected for  the  temperature  at  which  the  experiment  is  made. 

(147.)  Third  Method.  Hydrometers.  —  In  this  method,  the 
balance  is  not  used,  but  its  place  is  supplied  by  floating  bodies  of 
peculiar  construction,  called  hydrometers.  A.  few  of  these  we 
will  now  describe.  They  may,  for  convenience,  be  divided  into 
two  classes,  —  Hydrometers  with  a  Constant  Volume,  and  Hy- 
drometers with  a  Constant  Weight. 


250 


CHEMICAL  PHYSICS. 


HYDROMETERS   WITH   A   CONSTANT   VOLUME. 

1.  Nicholson's  Hydrometer.  —  This  instrument  is  represent- 
ed in  Fig.  246.  It  consists  of  a  hollow,  cylindrical  vessel,  B, 
made  usually  of  sheet  brass  or  tinned  iron.  To  the  lower  end 
of  this  vessel  is  fastened  a  cone  filled  with  lead,  O,  the  base  of 
which  forms  a  pan  on  which  the  body  whose. specific  gravity  is  to 
be  determined  is  placed.  The  object  of 
the  lead  is  to  load  the  apparatus  so  that 
the  centre  of  gravity  may  be  below  the 
centre  of  pressure,  which,  as  we  have  seen 
(142),  is  a  condition  of  stable  equilibrium. 
To  the  top  of  the  vessel  is  fastened  a  wire, 
which  supports  the  pan  A,  and  on  this 
wire  is  marked  a  fixed  point,  o. 

In  using  this  apparatus,  we  commence 
by  determining  the  weight  which,  placed 
in  the  pan  A,  will  sink  the  hydrometer  to 
the  fixed  point  o.  This  is  a  constant 
quantity  for  the  same  apparatus,  and  may 
be  represented  by  (7.  Let  us  suppose  that 
in  any  given  case  it  is  125  grammes,  and 
that  it  is  required  to  determine  the  spe- 
cific gravity  of  sulphur.  We  take  a  piece 

of  sulphur,  weighing  less  than  125  grammes,  and  place  it  on 
the  pan  A,  and  then  add  weights  until  the  hydrometer  sinks 
again  to  the  fixed  point  o.  If  it  requires  55  grammes  to  sink 
it  to  the  fixed  point,  it  is  evident  that  the  weight  of  the  sul- 
phur is  125  —  55  =  70  grammes.  Having  determined  the 
weight  of  the  sulphur  in  the  air,  it  only  remains  to  determine 
the  weight  of  an  equal  volume  of  water.  For  this  purpose,  we 
raise  the  hydrometer,  and,  without  disturbing  the  weights,  shift 
the  piece  of  sulphur  to  the  pan  C,  and  replace  the  instrument  in 
the  water.  It  will  not,  of  course,  sink  to  the  fixed  point ;  be- 
cause the  piece  of  sulphur,  which  is  now  submerged,  is  buoyed 
up  by  a  force  equal  to  the  weight  of  its  volume  of  water.  If, 
now,  we  add  weights  to  the  pan  A,  until  the  hydrometer  again 
sinks  to  the  point  o,  we  shall  find  that  34.4  grammes  are  re- 
quired. This  is  then  the  weight  of  its  volume  of  water,  and  the 
specific  gravity  is  ^i  =  2.03.  Representing  the  successive 


Fig.  246. 


THE   THREE   STATES   OF   MATTER. 


251 


weights  described  above  by  (7,  TF,  and  W'9  we  have  in  every  case 

Q  _    JJ7" 

.  Gr.)  =  —  T^  —  .     If  the  instrument  is  to  be  used  for  sub- 


stances lighter  than  water,  a  perforated  cover  is  adapted  to  the 
pan  (7,  to  prevent  them  from  rising  to  the  surface  of  the  liquid. 

2.  Fahrenheit's  Hydrometer.  —  This  instrument  (Fig.  247)  is 
used  for  determining  the  specific  gravity  of  liquid,  and  differs 
from  the  one  just  described  only  in  being  made 
of  glass,  and  in  having  no  lower  pan.     In  using 
this  instrument,  we  commence  by  weighing  it 
in  a  balance.     Let  us  call  its  weight  C.     Then, 
having  placed  it  in  water,  we  determine  the 
amount  of  weight  required  to  sink  it  to  a  fixed 
point,  marked  on  the  stem,  which  we  will  rep- 
resent by  c.    The  sum  of  these  constant  weights, 
or  (7-f-  c,  is,  by  (141),  equal   to   the  weight 
of  the  water  displaced.     We  then  float  the  hy- 
drometer in  the   liquid  whose  specific  gravity 
we  wish  to  find,  and  determine  the  weight  re- 
quired to  sink  it  in  this  liquid  to  the  fixed  point. 
Call  this  weight  W.     Then  C  +  W  is  equal  to 
the  weight  of  the  liquid  displaced,  and   since 
C  -j-  c  and  C  -\-W  are  the  weights   of  the   same  volumes  of 
water  and  the  liquid,  the  specific  gravity  of  the  liquid  is  easily 
found  ;  since 

.] 


Fig.  247. 


HYDROMETERS   WITH   A   CONSTANT   WEIGHT. 

In  the  two  hydrometers  just  described,  the  volume  of  the 
instrument,  which  is  submerged,  remains  constant  during  the 
experiment,  and  the  specific  gravity  is  determined  from  the 
amount  of  weight  required  to  keep  the  volume  constant  under 
different  circumstances.  The  hydrometers  in  most  general  use 
are  constructed  on  a  different  principle.  In  these  the  weight  is 
constant,  and  the  specific  gravity  of  a  liquid  is  determined  by 
measuring  the  volume  of  this  liquid  which  the  instrument  dis- 
places when  floating  in  it.  The  weight  of  this  volume  is,  by 
(141),  the  same  as  the  weight  of  the  instrument.  If,  then,  we 
represent  by  V  the  volume  of  water  which  the  instrument  dis- 
places when  floating  in  this  liquid,  and  by  V  the  volume  of  any 


252 


CHEMICAL   PHYSICS. 


other  liquid  which  it  displaces,  it  is  evident  that  the  volumes  V 
and  V  of  the  two  liquids  have  the  same  weight,  namely,  that  of 
the  hydrometer.  But  it  follows  from  [56],  that  when  the  weights 
of  different  volumes  of  two  liquids  are  equal,  V  .  (Sp.Gr.)  = 
V  .  (  Sp.  Gr.y.  When  one  of  the  liquids  is  water,  (  Sp.  Gr.y  =  1, 
and  we  obtain,  for  the  specific  gravity  of  the  other  liquid, 

(Sp.Gr.)  =  ~.  [89.] 

From  this  it  appears,  that,  when  we  know  the  volumes  of  equal 
weights  of  water  and  any  given  liquid,  we  can  find  the  specific 
gravity  of  the  liquid  by  dividing  the  volume  of  the  water  by  the 
volume  of  the  liquid. 

3.  Gay-Lus sac's  Volumeter.  —  This  is  the  best  instrument  of 
its  class.  In  its  simplest  form  (Fig.  248),  it  consists  of  a  glass 
tube  closed  at  both  ends,  which  is  graduated 
into  parts  of  equal  capacity.  The  size  of 
the  parts  is  unimportant,  it  being  only  neces- 
sary that  they  should  all  be  equal.  The  di- 
visions are  numbered  from  1  to  100,  or  to 
150,  as  the  case  may  require,  commencing  at 
the  lower  end  of  the  tube.  Before  the  tube 
is  finally  closed,  it  is  loaded  with  mercury,  so 
that,  when  floating  on  water,  it  will  sink  to 
the  100th  division  on  the  scale  ;  or,  in  other 
words,  so  that  it  will  displace  100  measures  of 
water.  If,  now,  we  float  it  on  sulphuric  acid, 
it  will  only  sink  to  the  54th  division.  Hence 
100  measures  of  water  and  54  measures  of 
sulphuric  acid  have  the  same  weight,  and  the 
specific  gravity  of  sulphuric  acid  is,  there- 
fore, J&0-  =  1.85.  If  we  float  the  hydrome- 
ter on  alcohol,  it  will  sink  to  the  125th  divis- 
ion. Hence  the  specific  gravity  of  alcohol 
is  |§f  =  0.80.  Since  a  definite  specific  grav- 
ity corresponds  to  each  of  the  divisions  of  the  scale,  it  is  usual 
to  calculate  these,  and  inscribe  them  on  the  scale  in  place  of 
the  simple  numbers  denoting  the  volume.  The  instrument, 
when  so  prepared,  is  generally  called  a  densimeter.  As  there 
are  no  liquids  which  have  a  less  specific  gravity  than  0.60,  and 
only  two  (mercury  and  bromine)  which  have  a  greater  specific 


70 


40 


10 


150 


100 


Fig.  248         Fig.  249 


THE  THREE  STATES   OP  MATTER.  253 

gravity  than  2,  it  is  evident  that  the  divisions  on  the  scale  need 
only  extend  from  50  to  166.  It  is  not  usual,  however,  to  have 
the  whole  scale  on  a  single  instrument,  and,  as  a  general  rule, 
the  scale  is  divided  over  three  separate  hydrometers.  The  first 
one,  for  liquids  lighter  than  water,  is  graduated  from  100  (cor- 
responding to  the  specific  gravity  1.00),  near  the  middle  of  the 
tube,  to  166  (corresponding  to  0.60),  at  the  top  of  the  tube  ;  the 
second,  for  saline  solutions,  is  graduated  from  100  (corresponding 
to  1.00),  at  the  top  of  the  tube,  to  75  (corresponding  to  1.33), 
near  the  middle  ;  finally,  the  third  instrument  is  graduated  from 
75  (corresponding  to  1.33),  at  the  top  of  the  tube,  to  50  (cor- 
responding to  2.00),  near  the  middle  of  the  tube.  In  graduating 
each  instrument,  it  is  so  loaded  that  it  shall  sink  in  water  to  the 
100th  division  of  the  centesimal  scale,  and  in  all  cases  the  spe- 
cific gravities  are  subsequently  calculated,  and  inscribed  on  the 
scale  against  each  division. 

It  is  more  usual  to  give  to  the  hydrometer  the  form  rep- 
resented in  Fig.  249.  This  shortens  the  instrument  very  great- 
ly, since  the  volume  of  the  long  tube  in  Fig.  248  is  herd  re- 
placed by  a  short  bulb.  The  principle  of  the  two  forms  of  the 
instrument  is  precisely  the  same,  but  it  is  more  difficult  to  grad- 
uate the  second  pattern.  The  easiest  method  is  the  following. 
If  the  instrument  is  to  be  used  for  liquids  heavier  than  water, 
we  first  load  it  with  mercury  until  it  sinks  to  a  point  A,  near 
the  top  of  the  tube,  which  we  mark  100.  We  next  float  it  in 
a  liquid  of  known  specific  gravity,  for  example,  1.333,  and  it  will 
sink  to  a  point  B.  Now,  by  [85],  1.333  =  *-ja,  and  x  =  75. 
This  division  is,  therefore,  the  75th,  and  we  divide  the  space 
between  the  two  into  25  equal  parts,  and  continue  the  divisions  of 
the  same  size  to  the  base  of  the  stem.  Each  of  these  divisions 
will  then  be  T£g-  of  the  whole  volume  of  the  apparatus  below  the 
100th  division  first  marked  at  A.  If  the  instrument  is  to  be 
used  for  liquids  lighter  than  water,  we  adjust  it  so  that  the 
100th  division  shall  be  at  the  base  of  the  stem,  and  then,  by 
floating  the  instrument  in  alcohol  of  known  specific  gravity, 
determine  a  higher  point,  and  then  divide  the  stem  as  before. 

4.  Baume's  Hydrometer.  —  This  hydrometer  belongs  to  the 
same  class  with  that  of  Gay-Lussac,  but  it  is  graduated  in  a  man- 
ner which  is  entirely  arbitrary,  and  does  not  indicate  the  specific 
gravity  of  the  liquid.     There  are  two  methods  used  in  graduat- 
22 


254  CHEMICAL   PHYSICS. 

ing  it,  according  as  it  is  to  be  used  for  liquids  heavier  or  lighter 
than  water.     In  the  first  case,  it  is  loaded  so  that  it  will  sink  in 
water  to  a  point  A,  near  the  top  of  the  stem,  which  we  mark  0°. 
A  second  point  is  now  obtained  by  floating  the  instrument  in  a 
solution  of  fifteen  parts  of  common  salt  in  eighty-five  parts  of 
water.     This  solution  having  a  greater  specific  gravity  than  pure 
water,  the  instrument  rises  until  the  level  of  the  liquid  stands  at 
a  point  By  which  we  mark  15°.     Lastly,  we  divide  the  distance 
between  A  and  B  into  fifteen  equal  parts,  and  continue  the  divis- 
ions to  the  bottom  of  the  stem  of  the  same 
size  as  one  of  these   parts.     It  is   essential 
that  the  diameter  of  the  stem  should  be  the 
same  throughout.     This  instrument  is  called 
Pese-Sels.      To    prepare   a   hydrometer   for 
liquids    lighter   than   water,   Baume   floated 
the  hydrometer  in  a  solution  of  ninety  parts 
of  water  and  ten  parts  of  common  salt,  and 
marked   the  point  to  which   it   sank  as  0°. 
He  next  floated  the  instrument  in  water,  and 
marked  this  point  10°.     The  interval  between 
these  points  he  divided  into  ten  equal  parts, 
and  continued  the  divisions  of  the  same  size 
to  the  top  of  the  tube.     This  instrument  is 
called  Pese- Liqueurs.     Although  the  graduation  of  Baume  is 
entirely  arbitrary,  yet  this  hydrometer  is  in  more  general  use 
than  any  other.     It  is  principally  used  for  determining  when 
a  solution  or  an  acid  has  reached  the  proper  degree  of  con- 
centration.   For  example,  it  has  been  found  by  experiment,  that 
in  a  well-manufactured  syrup  the  pese-sels  of  Baume  stands  at 
35°  when  the  liquid  is  cold,  and  also  that  in  the  strongest  sul- 
phuric acid  it  stands  at  66° ;  so  that  the  instrument  enables  the 
manufacturer  to  tell  when  his  syrup  or  acid  has  reached  the 
proper  strength.     The  instrument,  therefore,  serves  as  a  useful 
indicator  in  the  arts,  but  it  has  no  scientific  value.     Correspond- 
ing to  each  degree  of  the  Baume  scale  is  a  definite  specific  grav- 
ity,  which   can  be    found  by  referring  to  appropriate  tables, 
as  can  also  those  corresponding  to  the  degrees  of  the  scales  of  Car- 
tier  and  Beck,  which,  like  that  of  Baume,  are  purely  arbitrary. 

5.   Gay-Tjus sac's  Alcoometer.  —  This  is  a  kind  of  hydrometer, 
which  is  used  for  measuring  the  strength  of  alcoholic  liquids. 


THE   THREE   STATES    OF    MATTER. 


255 


The  form  of  the  instrument  is  precisely  the  same  as  that  of 
Baume  ;  but  the  graduation,  which  is  made  at  15°,  is  different. 
The  scale  on  the  stem  is  divided  into  one  hundred  degrees,  each 
of  which  represents  one  per  cent  of  pure  alcohol  in  volume. 
The  hydrometer  sinks  to  0°  in  pure  water,  and  to  100°  in  pure 
alcohol.  If  in  any  given  alcoholic  liquid  it  sinks  to  30°,  the 
liquid  contains  30  per  cent  by  volume  of  pure  alcohol.  The  in- 
strument is  graduated  by  floating  it  in  liquids  of  known  strength, 
and  marking  the  points  on  the  stem  to  which  it  sinks.  It  is  only 
accurate  at  the  temperature  of  15°.  If  the  temperature  is  dif- 
ferent from  this,  the  indications  of  the  instrument  must  be  cor- 
rected by  means  of  tables,  which  have  been  prepared  for  the 
purpose. 

There  are  a  great  variety  of  other  hydrometers,  which  are 
graduated  so  as  to  give  the  strength  of  milk,  beer,  vinegar,  and 
other  liquids.  They  are  all  similar  in  principle  to  the  alco- 
ometer,  and  do  not  require  description. 

6.  Rousseau? s  Hydrometer.  — All  the  hydrometers  which  have 
been  described  require  a  sufficient  amount  of  liquid  to  fill  a  glass 
of  some  size  ;  but  there  are  many  cases  in  which  it  is  desirable 
to  ascertain  promptly  the  specific  gravity  of  a  liquid,  when  only  a 
few  grammes  of  it  can  be  obtained.  The  form 
of  hydrometer  represented  in  Fig.  251  has 
been  contrived  by  Rousseau  for  this  purpose. 
The  general  form  of  the  instrument  is  similar 
to  the  others  which  have  been  described  ;  but 
it  differs  in  having  on  the  top  of  the  stem  a 
small  cup,  A,  which  holds  the  liquids  to  be 
experimented  upon.  On  the  side  of  this  cup 
is  a  mark  which  indicates  a  capacity  of  one 
cubic  centimetre. 

In  order  to  graduate  the  instrument,  it  is 
floated  in  pure  water  at  4°,  and  loaded  with 
mercury  until  it  sinks  to  a  point,  B,  marked 
at  the  base  of  the  stem,  which  is  the  zero  of 
the  scale.     The  cup  A  is  next  filled  up  to  the 
mark  with  distilled  water  at  4°,  or,  what  amounts  to  the  same 
thing,  a  weight  of  one  gramme  is  placed  in  the  cup.     The  instru- 
ment is  so  constructed  that  it  will  then  sink  to  a  point  near  the 
middle  of  the  stem,  which  is   marked   20°.     The   interval  be- 


Fig.  251. 


256 


CHEMICAL  PHYSICS. 


tween  these  divisions  is  now  divided  into  twenty  equal  parts,  and 
the  divisions  are  continued  to  the  top  of  the  stem.  Since  this 
has  exactly  the  same  size  throughout,  each  division  corresponds 
to  one  twentieth  of  a  gramme,  or  0.05  gram. 

According  to  this  graduation,  if  we  wish  to  obtain  the  density 
of  any  liquid,  —  bile,  for  example,  —  we  fill  the  cup  with  the 
liquid  to  the  point  marked  on  the  side.  The  instrument  will  now 
sink,  perhaps,  to  the  20.5  division  on  the  stem.  The  weight  of 
one  cubic  centimetre  of  bile  is,  then,  0.05  X  20.5  =  1.025  gram. 
Since  the  weight  of  the  same  volume  of  water  at  4°  is  one 
gramme,  the  specific  gravity  of  bile  is  1.025  -r- 1  =  1.025.  In 

general,  then,  the  specific 
gravity  of  a  liquid  is  found 
with  this  instrument  by 
multiplying  0.05  by  the 
number  of  the  division  to 
which  it  sinks  in  water, 
when  loaded  with  one  cubic 
centimetre  of  the  liquid. 

The  indications  of  all  hy- 
drometers are  very  much 
influenced  by  capillary  at- 
traction, and  the  more  so 
the  more  delicately  they  are 
constructed.  They  are  not, 
therefore,  instruments  of 
precision ;  but  they  are  use- 
ful, since  they  give  rapidly 
approximate  results. 

(148.)  Fourth  Method. 
—  A  fourth  method  of  find- 
ing the  specific  gravity  of  a 
liquid,  which  may  be  ad- 
vantageously used  under 
certain  circumstances,  is  il- 
lustrated by  Fig.  252.  It 
depends  on  the  principle  of 
the  equilibrium  of  liquids 
in  connected  vessels  (131). 
The  apparatus  consists  of 


THE   THREE    STATES   OP   MATTER.  257 

two  tubes  connected  above  with  each  other  and  with  the  chamber 
of  an  air-syringe.  The  lower  ends  of  these  tubes  dip,  the  one  into 
a  glass  of  water,  and  the  other  into  a  glass  containing  the  liquid 
whose  specific  gravity  is  required.  On  partially  exhausting  the 
air  from  the  top  of  the  tubes  by  means  of  the  syringe,  the  liquids 
will  rise  in  the  two  tubes.  If,  now,  we  close  the  stopcock  con- 
necting with  the  syringe,  the  liquids  will  stand  permanently  at  a 
certain  height  in  either  tube.  Moreover,  it  is  evident,  from  the 
construction  of  the  apparatus,  that  the  two  columns  of  liquid  are 
in  equilibrium  with  each  other.  Using,  then,  the  notation  of 
(131),  we  have,  from  [81], 

H:H'  =  l:(Sp.Gr.),    or    (%GV.)=-^';     [90.] 

that  is,  the  specific  gravity  of  the  liquid  is  found  by  dividing  the 
height  of  the  column  of  water  by  that  of  the  liquid.  The  heights 
of  the  columns  may  be  measured  either  by  means  of  a  scale  on 
the  tube,  or  by  a  cathetometer  (see  Fig.  196).  If  the  liquid  were 
alcohol,  for  example,  and  the  height  of  the  water  column  meas- 
ured 60  c.m.,  the  height  of  the  alcohol  column  would  be  found 
to  measure  75  c.m.  Hence,  the  specific  gravity  of  alcohol 
is  fi  =  0.80. 


PROBLEMS. 
Buoyancy  of  Liquids. 

106.  A  man,  exerting  all  his  force,  can  raise  a  weight  of  50  kilog. 
What  would  be  the  weight  of  a  stone  (Sp.  Gr.  =  2.5)  which  he  could 
just  raise  under  water  ? 

107.  How  much  force  in  kilogrammes  would  be  required  to  raise  under 
water  a  mass  of  asphaltum  (Sp.Gr.  =  1.10)  weighing  500  kilogrammes? 

108.  How   many   kilogrammes   will    100    kilogrammes    of    cast-iron 
(Sp.  Gr.  =  7.25)  Weigh  under  water  ? 

109.  How  much  will  the  same  amount  of  iron  weigh  under  alcohol 
(Sp.  Gr.  =  0.798)  ? 

110.  If  a  given  piece  of  gold  be  balanced  by  its  weight  of  brass  in  a 
vacuum,  what  addition  must  be  made  to  the  brass  so  that  they  may  be  in 
equilibrium  when  immersed  in  water  ?  Sp.  Gr.  of  Brass  8.55 ;  of  Gold  19.36. 

111.  How  much  force  in  kilogrammes  would  be  required  to  sustain 
under  mercury  at  0°  a  cubic  decimetre  of  platinum  ?     The  specific  grav- 
ity of  platinum  is  21.5  ;  that  of  mercury,  13.598. 

22* 


258  CHEMICAL  PHYSICS. 

Floating  Bodies. 

112.  How  much  bulk  must  a  hollow  vessel  of  copper  fill,  weighing  one 
kilogramme,  which  will  just  float  in  water  ? 

113.  How  much  bulk  must  a  hollow  vessel  of  iron  occupy,  weighing 
10  kilogrammes,  which  sinks  one  half  in  water  ? 

114.  A  boat  displaces  10m.3  of  water.     What  is  the  weight  of  the 
boat? 

115.  A  cube  of  wood,  weighing  100  kilogrammes,  sinks  three  quarters 
in  water.     What  is  the  specific  gravity  of  the  wood,  and  what  is  the  size 
of  the  cube  ? 

116.  What  portion  of  a  cube  of  solid  iron  (Sp.  Gr.  =  7.7)  will  sink 
in  mercury  (Sp.  Gr.  =  13.G)  ? 

117.  A  life-boat  contains  100  m".3  of  wood,  whose  specific  gravity  is 
equal  to  0.8,  and  50  mT3  of  air,  whose  specific  gravity  is  0.0012.     When 
filled  with  fresh  water,  what  weight  of  iron  ballast,  whose  specific  gravity 
is  7.G45,  must  be  thrown  into  it  before  it  will  begin  to  sink  ? 

118.  If  the  specific  gravities  of  a  man,  of  water,  and  of  cork  be  1.120, 
1.000,  and  .240  respectively,  find  what  weight  of  cork  must  be  connected 
to  a  man,  weighing  75  kilogrammes,  that  he  may  just  float  in  the  water. 

119.  Determine  the  weight  of  a  hydrometer,  which  sinks  as  deep  in 
rectified  spirits,  whose  specific  gravity  is  0.866,  as  it  sinks  in  water  when 
loaded  with  4  gram. 

120.  A  ship,  sailing  into  a  river,  sinks  2  c.  m.,  and,  after  discharging 
12,000  kilogrammes  of  her  cargo,  rises  1  c.  m. ;  determine  the  weight  of 
the  ship  and  cargo,  the   specific  gravity  of  sea-water  being  to  that  of 
fresh  as  1.026  is  to  1. 

121.  If  a  solid,  whose  specific  gravity  =  6,  float  in  a  liquid,  whose  spe- 
cific gravity  =15,  determine  the  proportion  of  the  parts  immersed. 

122.  If  a  globe  of  wood,  when  placed  in  a  vessel  of  water,  rise  5  c.  m. 
above  the  surface,  but,  when  placed  in  a  liquid  whose  specific  gravity  is 
0.80,  rise  only  3  c.  m.  above  the  surface  of  the  liquid,  determine  the  di- 
ameter of  the  globe. 

123.  Having  given  the  specific  gravities  of  iron  and  water,  determine 
what  proportion  the  thickness  of  a  hollow  iron  globe  must  bear  to  its 
diameter,  that  it  may  just  float  in  water. 

124.  A   parallelepiped   of  ice,  whose   three  dimensions  are  10.5  m., 
15.75  m.,  and  20.45  m.,  is  floating  in  sea-water  on  its  broadest  face  ;  the 
specific  gravity  of  sea-water  is  1.026,  and  that  of  ice  0.930.     Required  the 
height  of  the  parallelepiped  above  the  surface  of  the  water. 

125.  A  cone,  1.5  m.  high  and  1.2  m.  in  diameter  at  the  base,  is  floating 
on  its  base  in  a  liquid  in  a  vertical  position,  and  sinks  in  it  20  d.  m.     How 
much  of  the  liquid  is  displaced  by  the  cone  ?     If  the  cone  is  inverted,  and 
made  to  float  on  its  apex,  how  deep  will  it  then  sink  ? 


THE   THREE   STATES   OF   MATTER.  259 

126.  A  hollow  cylinder  of  iron  plate  is  2.5  m.  in  diameter  and  1.75  m. 
high.     The  plate  is  1  c.  m.  thick,  and  its  specific  gravity  7.79.     Will  it 
float  on  water,  and  if  so,  how  deep  will  it  sink  when  its  axis  is  vertical  ? 

127.  A  cube  of  lead  measures  4  c.  m.  on  each  side.     It  is  required  to 
sustain  it  under  water  by  suspending  it  to  a  cube  of  cork.     What  must 
be  the  size  of  a  cube  of  cork  which  just  sustains  it,  assuming  that  the 
specific  gravity  of  cork  equals  0.24,  and  that  of  lead  11.35  ? 

Elasticity  of  Liquids. 

128.  A  cubic  metre  of  water  is  submitted  to  a  pressure  of  15  atmos- 
pheres.    I  low  great  is  the  condensation  ?  and  what  is  the  specific  gravity 
of  the  condensed  liquid  ? 

129.  At  a  depth  in  the  ocean  of  a  little  over  5  kilometres,  the  pressure 
amounts  to  500  atmospheres.     What  is  the  specific  gravity  of  the  water 
at  that  depth,  assuming  that  the  specific  gravity  of  sea- water  is  1.026, 
and  the  compressibility  0.0000436  ? 

Hydrostatic  Press. 

130.  In  the  hydrostatic  press  are  given  the  diameters  of  the  two  cylin- 
ders d  and  c?',  and  the  force  applied  to  the  pump  F.     Determine   the 
pressure  produced. 

131.  In  the  hydrostatic  press,  suppose  the  diameters  to  be  4  c.  m.  and 
80  c.  m.  respectively,  the  length  of  the  pump-handle  to  be  1  m.,  and  the 
distance  of  the  pump  from  the  fulcrum  of  the  handle  10  c.  m.     Deter- 
mine in  what  proportion  the  pressure  exerted  is  increased. 

Pressure  exerted  by  Liquids  in  Consequence  of  their  Weight. 

It  is  assumed,  in  the  following  problems,  that  liquids  are  incompressible,  and  hence  that  their 
specific  gravity  is  not  increased,  however  great  may  be  the  pressure  to  which  they  are  exposed. 

132.  The  whole  pressure  on  the  bottom  of  a  tub  of  water,  the  radius 
of  which  is  30  c.  m.,  is  50  kilogrammes.     What  is  the   depth   of  the 
water  in  the  pail? 

133.  What  is  the  pressure  exerted  by  the  water  on  every  square  cen- 
timetre of  the  base  of  a  cylindrical  vessel,  in  which  the  liquid  stands  at 
the  height  of  10.336  m.  above  the  base  ?     If  the  water  in  the  vessel  were 
replaced  by  mercury,  how  high  must  the  liquid  stand,  so  that  the  pressure 
should  be  the  same  as  before  ? 

134.  The  horizontal  and  circular  bottom  of  a  flask,  15  c.  m.  in  diame- 
ter, is  filled  with  mercury  to  the  depth  of  20  c.  m.     How   great  is  the 
pressure  on  the  bottom  ? 

135.  What  height  must  a  column  of  water  have,  which  will  exert  a 
pressure  of  1,000  kilogrammes  on  every  square  decimetre  ? 

136.  A  cubical  vessel  is  filled  with  water,  and  into  its  side  a  bent  tube 


260  CHEMICAL   PHYSICS. 

is  inserted,  filled  with  water,  and  communicating  with  the  water  in  the 
vessel.  Determine  the  pressure  on  the  top  of  the  vessel,  the  vertical 
height  of  the  extremity  of  the  tube  above  the  vessel  being  (m)  tunes  the 
height  of  the  vessel. 

137.  A  sphere,  10  c.  m.  in  diameter,  is  sunk  to  the  depth  of  100  m.  in 
a  fresh-water  lake.     Determine  the  total  pressure  exerted  on  its  surface. 

138.  A  cylinder,  15  c.  m.  in  diameter  and  20  c.  m.  high,  is  sunk  so 
that  its  centre  is  at  the  depth  of  1  m.  below  the  surface  of  the  water.    De- 
termine the  total  pressure  exerted  on  its  surface. 

139.  A  hollow  cone,  10  c.  m.  in  diameter  at  the  base  and  5  c.  m.  high, 
is  filled  with  water.     Determine  the  pressure  on  the  base  and  on  the  con- 
vex surface.     Centre  of  gravity  of  convex  surface  is  in  the  axis  of  the 
cone  at  £  of  the  altitude  from  the  base. 

140.  A  cylindrical  vessel,  10  c.  ra.  in  diameter  and  10  c.  m.  high,  is  filled 
with  water.    Determine  the  pressure  on  the  base  and  on  the  convex  surface. 

141.  A  hollow  cone,  without  a  bottom,  stands  on  a  horizontal  plane, 
and  water  is  poured  in  at  the  vertex.     The  weight  of  the  cone  being 
given,  how  far  may  it  be  filled  so  as  not  to  run  out  below  ? 

142.  A  hemispherical  vessel,  10  c.  m.  in  diameter,  without  a  bottom, 
stands  on  a  horizontal  plane.     When  just  filled  with  water,  the  liquid 
begins  to  run  out  at  the  bottom.     Determine  the  weight  of  the  vessel. 

143.  A  straight  line  is  just   immersed  vertically  in  a  liquid.     Re- 
quired to  divide  it  into  three  portions,  which  shall  be  equally  pressed. 

144.  Compare  the  pressures  on  the  three  sides  of  an  equilateral  tri- 
angle, just  immersed  in  a  liquid  in  such  a  manner  that  one  side  may  be 
perpendicular  to  its  surface. 

Specific  Gravity. 

145.  Determine  the  specific  gravity  of  absolute  alcohol  from  the  fol- 
lowing data :  — 

Weight  of  bottle  empty,   .     , .  ^   .  .  ..  »   ;>  .       4.326  gram. 
"             "         filled  with  water  at  4°,         .         19.654      " 

"  "         filled  with  alcohol  at  0°, .  .     16.741      « 

146.  Determine  the  specific  gravity  of  sulphuric  acid  from  the  follow- 
ing data  :  — 

Weight  of  bottle  empty,   .     .,»..,,-,  .;...,.:•         .       4.326  gram. 
"  "         filled  with  water  at  4°,        ,         19.654      " 

"  "         filled  with  sulphuric  acid  at  0°,     28.219      « 

147.  Determine  the  specific  gravity  of  lead  shot  from  the  following 
data :  — 

Weight  of  bottle  filled  with  water  at  4°,        .          19.654  gram. 
"          shot,        .       >_.,  /„:•  ,.../       .         .     15.456      « 
«         bottle,  shot,  and  water,          .         .          33.766      " 


THE   THREE   STATES   OF   MATTER.  261 

148.  Determine  the  specific  gravity  of  gold  from  the  following  data :  — 
"Weight  of  gold  in  air,      ....          4.213  gram. 

Loss  of  weight  in  water,     ....     0.2205    " 

149.  Determine  the  specific  gravity  of  hammered  copper  from  the  fol- 
lowing data :  — 

Weight  of  copper  in  air,     ....     1.809  gram. 
"  "          under  water,        .         .         1.608      " 

150.  Determine  the  specific  gravity  of  saltpetre  from  the  following 
data :  — 

Weight  of  saltpetre  in  air,  .         .         .         .1.216  gram. 

"  «  under  alcohol,  .  .         0.734      « 

Specific  gravity  of  alcohol, .         .         .         .     0.792      « 

151.  Determine  the  specific  gravity  of  ash  wood  from  the  following 
data :  — 

Weight  of  wood  in  air,    .         .         .  25.350  gram. 

"      "     a  copper  sinker,         .         .  11.000      " 

"      "     wood  and  sinker  under  water,  5.100      * 

Specific  gravity  of  copper,         .         .         .       8.950      u 

152.  A  sphere  of  platinum  weighs  in  air  84  gram.,  and  in  mercury  31 
gram.     What  is  the  specific  gravity  of  platinum  ? 

153.  A  piece  of  metal  weighs  5.219  gram,  in  air,  4.132  gram,  in  water, 
and  4.009  gram,  in  a  given  liquid.     What  is  the  specific  gravity  of  the 
metal  and  of  the  liquid  ? 

154.  A  body,  A,  weighs  in  air  7.55  gram.,  in  water  5.17  gram.,  in  an- 
other liquid  5.35  gram.     What  is  the  specific  gravity  of  the  body  and  of 
the  liquid  ? 

155.  A  body  weighs  14  gram,  in  a  vacuum  and  9  gram,  in  water ;  an- 
other weighs  8  gram,  in  a  vacuum  and  7  gram,  in  water.     Compare  their 
specific  gravities. 

156.  A  glass  ball,  weighing  10  gram.,  loses  3.636  gram,  in  water,  and 
2.88  gram,  in  alcohol.     What  is  the  specific  gravity  of  alcohol  ? 

157.  A  glass  ball,  weighing  10  gram,  and  whose  Sp.Gr.  =  2.75,  weighs, 
under  rape-seed  oil,  6.658  gram.    What  is  the  specific  gravity  of  this  oil  ? 

158.  A  glass  ball,  as  above,  weighs  under  water  6.364  gram.,  and  under 
another  liquid  7.12  gram.     What  is  the  specific  gravity  of  this  liquid? 

159.  A  volumetre,  whose  stem  is  exactly  cylindrical,  sinks  in  a  liquid 
whose  Sp.  Gr.  =  1.1  to  a  point  5,  and  in  pure  water  at  4°  C.  to  a  point  a. 
The  distance  from  a  to  b  is  4  c.  m.     How  far  from  a  must  the  divisions 
be  placed  to  which  the  hydrometer  will  sink  in  liquids  whose  Sp.  Gr.  — 
1.01,  1.02,  1.03,  1.04,  1.05. 

160.  A  similar  volumeter  sinks  in  a  liquid  whose  *Sj».  Gr.  =*=  y  to  a 
point  5,  and  in  a  liquid  whose  Sp.  Gr.  =  y1  to  a  point  a,  higher  on  the 
stem.     What  is  the  specific  gravity  of  a  liquid  in  which  it  sinks  to  an  in- 
termediate point,  rf,  when  b  d  =  A,  and  a  b  =  L 


262  CHEMICAL   PHYSICS. 

161.  A  column  of  water  1.55  m.  high  is  in  equilibrium  with  a  column 
of  liquid  2.17  m.  high.     What  is  the  specific  gravity  of  the  liquid? 

Miscellaneous. 

162.  An  alloy  of  gold  and  silver  weighs  10  kilogrammes  in  air,  and 
9.375  kilogrammes   in  water.     What  are  the  proportions  of  gold  and 
silver?     The  specific  gravity  of  gold  =  19.2,  of  silver  =10.5. 

163.  An  alloy  of  copper  and  silver  weighs  37  kilogrammes  in  the  air, 
and  loses  3.666  kilogrammes  when  weighed  in  water.    What  are  the  pro- 
portions of  silver  and  copper  ? 

164.  The  specific  gravity  of  zinc  is  7,  and  that  of  copper  9,  nearly. 
What  amounts  of  zinc  and  copper  must  be  taken  to  form  an  alloy  weigh- 
ing 50  gram.,  and  having  a  specific  gravity  equal  to  8.2,  assuming  that 
the  volume  of  the  alloy  is  exactly  the  sum  of  the  volumes  of  the  two 
metals  ? 

165.  Required  the  specific  gravity  of  a  mixture  of  18  kilogrammes  of 
sulphuric  acid  and  8  kilogrammes  of  water,  assuming  that  the  specific 
gravity  of  the  acid  is  equal  to  1.84,  and  that  the  volume  of  the  mixture 
is  condensed  ^. 

166.  Into  a  cylindrical  vessel  with  a  horizontal  base  10  c.m.  in  diame- 
ter, there  are  poured  12  kilogrammes  of  mercury.    At  what  height  will  the 
liquid  rise  in  the  cylinder?     The  specific  gravity  of  mercury  is  13.596. 

167.  Plow  much  mercury  will  a  conical  vessel  hold  which  is  87  c.m. 
high  and  46  c*.  m.  in  diameter  at  the  base  ? 

168.  A  cylinder  of  oak  wood  is  30  c.m.  in  diameter  and  2.5  m.  long ; 
the  specific  gravity  of  the  wood  is  1.17.     What  is  the  volume  and  the 
weight  of  the  cylinder  ? 

169.  A  cylindrical  vessel  is  36.9  c.m.  high,  and  24.6  c.m.  in  diameter, 
interior  measure.     How  much  alcohol  of  specific  gravity  0.863  will  the 
cylinder  contain  ? 

170.  Leaves  of  gold  are  made  only  0.001  m.  m.  in  thickness  ;  the  spe- 
cific gravity  of  gold  equals  19.632.     How  much  surface  can  be  covered 
with  10  gram,  of  gold  ? 

171.  A  cast-iron  ball  weighs  12  kilogrammes  ;   the  specific  gravity  of 
cast-iron  is  7.35.     What  is  the  radius  of  the  ball  ? 

172.  What  is  the  diameter  of  a  platinum  wire  which  weighs  28  gram, 
for  each  metre  of  length  ?     The  specific  gravity  of  platinum  is  22.06. 

173.  A  silver  wire  125  m.  long  weighs  6  gram.;  the  specific  gravity  of 
silver  is  10.474.     What  is  the  diameter  of  the  wire  ? 

174.  In  a  capillary  tube  is  contained  a  column  of  mercury,  weighing 
0.500  gram.,  which  measures  13.700  c.  m.  at  0°  C.     What  is  the  diameter 
of  the  tube  ? 

175.  A  wire  0.785  m.  long,  and  weighing  0.364  gram.,  loses  0.017  gram, 
when  weighed  under  water.     What  is  the  diameter  of  the  wire  ? 


THE   THREE   STATES    OF   MATTER. 


263 


III.  CHARACTERISTIC  PROPERTIES  OP  GASES. 

(149.)  Mechanical  Condition  of  Gases.  —  The  peculiar  prop- 
erties of  a  gas  seem  to  depend  on  the  fact,  that  the  repulsive 
forces  existing  between  its  particles  are  greater  than  the  attrac- 
tive forces  (78).  Consequently,  the  particles  of  a  gas  tend  to 
recede  from  each  other,  and  were  it  not  for  extraneous  causes  the 
gas  would  expand  —  so  far  as  is  known  —  indefinitely  into  space. 
This  natural  tendency  of  gases  is  restrained  on  the  surface  of  our 
globe  by  the  pressure  which  the  atmosphere  exerts  in  consequence 
of  its  weight ;  but  when  this  pres- 
sure is  removed,  the  expansive  ten- 
dency becomes  at  once  manifest. 
The  air  which  is  contained  in  the 
India-rubber  bag  (Fig.  253),  for 
example,  is  prevented  from  expand- 
ing by  the  pressure  of  the  atmos- 
phere on  its  exterior  surface.  If, 
however,  we  place  the  bag  under 
the  receiver  of  an  air-pump,  and 
remove  the  pressure  by  exhausting 
the  air,  the  bag  will  at  once  ex- 
pand ;  and  this  expansion  will  con- 
tinue until  the  expansive  tendency 
of  the  air  is  balanced  by  the  elas- 
ticity of  the  bag. 

The  force  with  which  a  gas  tends  to  expand  is  called  its  ten- 
sion ;  and  it  is  evident  that,  when  in  a  state  of  rest,  the  tension 
of  a  gas  must  be  exactly  equal  to  the  pressure  to  which  it  is  ex- 
posed ;  for  were  this  not  the  case,  the  force  which  was  in  excess 
would  cause  a  motion  in  the  particles,  which  is  inconsistent  with 
the  supposition.  It  appears,  therefore,  that  in  a  gas,  as  in  a 
liquid,  the  particles  are  in  a  condition  of  equilibrium ;  the  only 
difference  being,  that  in  a  liquid  the  equilibrium  exists  between 
the  attractive  and  repulsive  forces  in  the  liquid  itself,  but  in  the 
gas,  between  the  excess  of  repulsive  forces  in  the  body  and  an  ex- 
ternal pressure.  In  consequence  of  this  condition  of  equilibrium, 
the  particles  of  gases  are  endowed  with  perfect  freedom  of  motion, 
and  gases  are  therefore  fluids  (117).  Moreover,  since  they  are 
both  elastic  (77)  and  ponderable  (7),  it  follows  that  all  those 


Fig.  253. 


264  CHEMICAL   PHYSICS. 

properties  which  are  the  necessary  consequence  of  these  mechan- 
ical conditions  must  belong  to  gases  as  well  as  to  liquids.  These, 
as  before  (119),  naturally  divide  themselves  into  two  classes : 
first,  those  which  are  independent  of  the  action  of  gravity  ;  and, 
secondly,  those  which  depend  upon  it.  As  these  properties  have 
been  so  fully  discussed  in  the  case  of  liquids,  it  will  only  be 
necessary  to  extend  the  principles  already  established  to  the  case 
of  gases. 

Properties  Common  to  Gases  and  Liquids. 

(150.)  Pressure  which  is  independent  of  the  Action  of  Grav- 
ity. —  Let  us  now  suppose  that  the  vessel  (Fig.  254)  already 
described  (120)  is  filled  with  air,  instead  of  water.     As  this  air 
is  in  a  permanent  state  of  tension,  it  will, 
in  consequence  of  its  elasticity,  exert  pres- 
sure in  all  directions ;  and  it  is  evident, 
from  the  same  course  of  reasoning  used 
in  the  case  of  water  (120),  that  the  pres- 
sures it  exerts  against  the  pistons  «,  &,  c,  d 
will  be  proportional  to  their  areas.      In 
like  manner,  the  same  will  be  true  of  any 
portion  of  the  interior  surface  of  the  ves- 
sel, and  also  of  any  ideal  section  in  the  interior  of  the  vessel.     If 
two  sections  are  equal,  they  will  receive  equal  pressures  ;  if  un- 
equal, the  pressures  will  be  proportional  to  their  areas. 

If  the  air  in  the  interior  of  the  vessel  is  in  the  same  condition 
as  the  external  atmosphere,  it  is  evident,  from  what  has  been 
said,  that  the  pressure  of  the  air  on  the  interior  surface  of  the 
vessel  will  be  exactly  balanced  by  the  pressure  of  the  atmosphere 
on  the  outside.  The  piston,  therefore,  being  pressed  equally  on 
their  inner  and  outer  surfaces,  will  have  no  tendency  to  move. 
This  being  the  condition  of  the  air  in  the  vessel,  let  us  suppose 
that  we  condense  the  air  still  further,  by  pressing  in  one  of  the 
pistons ;  it  is  evident  that  we  shall  thus  develop  a  greater  elas- 
ticity in  the  particles,  and  each  particle  will  in  consequence  exert 
a  greater  pressure.  The  increased  pressures  now  exerted  against 
the  inner  surfaces  of  the  pistons  will  be  proportional  to  the  num- 
ber of  gaseous  particles  in  contact  with  them,  or,  in  other  words, 
proportional  to  their  areas.  The  pressures  on  the  inner  sur- 
faces being  also  greater  than  those  on  the  outer  surfaces,  the 


THE   THREE   STATES   OF   MATTER.  265 

pistons  will  tend  to  niove  out  with  forces  varying  in  the  same 
proportion. 

From  these  considerations,  it  appears  that  gases,  like  liquids, 
transmit  pressure  equally  in  all  directions ;  the  only  difference 
being  this,  that  in  our  experiments  on  gases  we  start  with  a  cer- 
tain initial  pressure  due  to  their  permanent  elasticity.  Gases, 
like  liquids,  will  transmit  pressure  through  long  tubes  and 
through  any  passages,  however  circuitous,  provided  only  that 
there  is  a  line  of  gaseous  particles.  A  good  example  of  this  is 
furnished  by  the  gas-pipes  of  large  cities.  Any  pressure  applied 
at  the  gasometer  is  transmitted  almost  instantaneously  through 
hundreds  of  miles  of  pipe  distributed  in  a  most  circuitous  man- 
ner over  several  square  miles  of  area.  The  close  resemblance 
which  gases  bear  to  liquids  is  also  shown  by  the  fact  that  they 
transmit  pressure  from  one  to  the  other  indifferently.  We  shall 
have  occasion  to  notice  several  examples  of  this  farther  on. 

Since  the  proof  used  in  (121)  applies  to  gases  as  well  as  to 
liquids,  it  follows  that  the  line  indicating"  the  direction  of  the 
pressure  exerted  by  any  gaseous  particle  against  the  section  with 
which  it  is  in  contact,  is  always  a  perpendicular  to  this  section 
at  the  point  of  contact. 

(151.)  Pressure  depending  on  the  Action  of  Gravity.  —  The 
facts  in  regard  to  the  pressure  exerted  by  liquids  in  consequence 
of  their  weight  are,  as  we  found  in  sections  (123)  to  (129),  all 
necessary  consequences  of  the  one  fundamental  property,  that 
they  transmit  pressure  equally  in  all  directions  ;  and  it  therefore 
follows,  that  each  of  these  facts  must  be  true  of  gases.  Let  us 
commence  with  an  ideal  case.  Suppose  a  closed  cylindrical  ves- 
sel, several  kilometres  high,  filled  with  air  of  the  same  density 
through  its  whole  extent,  and  rising  vertically  from  the  surface 
of  the  globe.  It  would  be  true  of  such  a  vessel,  that  the  pres- 
sure exerted  by  the.  air  on  the  base  of  the  cylinder,  or  on  any  por- 
tion of  its  side,  or,  in  fine,  on  any  section  whatsoever,  ivould  be 
equal  to  the  weight  of  a  column  of  air,  the  area  of  whose  base  is 
equal  to  the  area  of  the  section,  and  whose  height  is  equal  to  the 
vertical  distance  of  the  centre  of  gravity  of  the  section  from  the 
top  of  the  cylinder.  Moreover,  the  pressure  on  any  given  sec- 
tion would  be  entirely  independent  of  the  form  or  size  of  the 
vessel,  provided  only  that  the  height  remained  the  same. 

This  last  circumstance  is  one  of  great  importance,  because  it 
23 


266  CHEMICAL  PHYSICS. 

enables  us  to  extend  our  conclusions  at  once  to  the  case  of  the 
atmosphere.  The  atmosphere  is  a  mass  of  air  retained  upon  the 
surface  of  the  globe  by  the  force  of  gravitation,  and  rising  to  a 
height  which  is  estimated  at  the  lowest  at  forty-seven  kilometres. 
It  is  supposed  to  have,  like  the  ocean,  a  definite  surface,  which, 
when  at  rest,  is  perpendicular  at  each  point  to  the  direction  of 
gravity.  It  partakes  of  the  rotation  of  the  globe  on  its  axis,  and 
would  remain  at  rest  relatively  to  terrestrial  objects  were  it  not 
for  local  causes,  which  produce  winds  and  disturb  at  each  mo- 
ment its  equilibrium.  Neglecting  these  disturbances,  we  may 
regard  the  atmosphere  as  a  gaseous  ocean  in  equilibrium  covering 
the  earth  to  a  certain  level,  and  exerting  the  same  effects  of  pres- 
sure as  if  it  were  a  liquid  having  a  very  small  density.  It  fol- 
lows, therefore,  that  each  particle  of  the  air  exerts  a  pressure 
equal  to  the  weight  of  a  vertical  line  of  superincumbent  particles 
rising  to  the  surface  of  the  atmosphere.  This  pressure  will  be 
constant  on  surfaces  at  the  same  level ;  it  will  increase  as  we  de- 
scend in  the  atmosphere,  and  diminish  as  we  rise  in  it.  At  any 
one  position,  it  will  be  equal  on  surfaces  of  the  same  area,  what- 
ever may  be  their  direction  ;  and  on  surfaces  of  unequal  area  it 
will  be  in  proportion  to  the  extent  of  the  areas.  It  will  be  the 
same  in  the  interior  of  any  vessel  or  room  as  in  the  outer  air, 
provided  only  there  is  a  connection  with  the  exterior  atmosphere 
by  some  aperture,  however  small.  Finally,  the  air  will  buoy  up 
all  bodies  immersed  in  it  with  a  force  which  will  be  equal  to  the 
weight  of  the  volume  of  air  displaced.  As  the  validity  of  these 
conclusions  has  already  been  established  in  regard  to  liquids,  it 
will  only  be  necessary,  in  the  case  of  gases,  to  illustrate  the  gen- 
eral facts  by  a  few  experiments. 

(152.)  Pressure  of  the  Atmosphere.  —  The  pressure  exerted 
by  the  atmosphere  on  all  bodies  near  the  surface  of  the  globe  is 
exceedingly  great,  amounting,  as  we  shall  soon  prove,  to  over  one 
kilogramme  on  every  square  centimetre  of  surface,  and  to  about 
16,000  kilogrammes  on  the  surface  of  the  body  of  a  man  of  or- 
dinary stature.  But  since  this  pressure  is  exerted  equally  in  all 
directions,  and  since  the  cavities  of  the  body  are  filled  either  by 
air  or  other  gases,  which  exert  a  pressure  on  the  one  surface  of 
its  delicate  membranes  exactly  equal  to  that  exerted  on  the  other, 
this  great  pressure  is  not  perceptible,  and  indeed  was  not  known 
to  exist  until  it  was  discovered  by  Torricelli  in  1643.  If,  how- 


THE   THREE   STATES   OF   MATTER. 


267 


Fig.  256. 


ever,  by  any  means,  we  can  remove  the  pressure  from  one  side 
only  of  a  membrane,  then  the  pressure  on  the  other  side  will  be- 
come evident. 

We  can  readily  remove  the  pressure  from  the  interior  surface 
of  a  vessel,  by  removing  the  air  by  means 
of  an  air-pump  (175),  and  thus  remov- 
ing the  fluid  medium  through  which 
the  pressure  is  transmitted.  For  exam- 
ple, if  we  remove  the  air  from  the  cylin- 
drical glass  vessel  which  is  represent- 
ed in  Fig.  255,  resting  on  the  plate  of 
an  air-pump,  we  shall  also  remove  the 
pressure  from  the  lower  surface  of  the 
thin  animal  membrane  which  covers 
and  closes  the  cylinder  from  above. 
Then  the  great  pressure  on  the  upper 
surface,  being  no  longer  balanced,  will 
exert  its  full  effect,  first,  by  depressing 
the  membrane,  and  afterwards  by  bursting  it,  if  it  be  not  too 
strong. 

That  the  pressure  of  the  atmosphere  is  exerted  upwards  as 
well  as  downwards,  may  be  further  illustrated  by  means  of  the 
apparatus   represented   in   Fig.  256. 
It  consists  of  a  glass  vessel  supported 
on   a  tripod   stand,  having   a   large 
opening  below,  and  a  small  tubulature 
above.     The  lower  opening  is  closed 
by  a  bag  of  India-rubber  cloth,  as 
represented  in  the  figure,  and  the  tu- 
bulature is   connected  with   an   air- 
pump  by  means   of  a  flexible  hose. 
On   exhausting   the   air,  the   bag  is 
pressed  up  into  the  glass  vessel  with 
sufficient  force   to    raise    the    heavy 
weight  which   is    attached   to.  it  by 
means  of  a  leather  strap.     By  modi- 
fying the  apparatus,  it  is   easy  to  show  that  the  pressure  is 
exerted,  not  only  upwards  and  downwards,  but  also  in  all  direc- 
tions.    These  various  forms  of  apparatus,  however,  only  demon- 
strate the  existence  of  pressure.      They  do   not   enable  us  to 
measure  it. 


Fig.  256. 


268 


CHEMICAL   PHYSICS. 


Fig.  257. 


(153.)    Buoyancy  of  the  Air.  —  The   general  fact,  that  air, 
like  liquids,  buoys  up  all  bodies  immersed  in  it,  may  be  illus- 
trated by  means  of  the  apparatus 
represented  in  Fig.  257.     It  con- 
sists of  a  closed  globe  suspended 
to  one  arm  of  a  delicate  balance, 
equipoised  by  a  weight  suspend- 
ed to  the  other.     The  two  are  in 
equilibrium  in  the  air,  but  only 
because  the  globe,  being  larger 
than  the  weight,  is   buoyed  up 
by  a  greater  force.     If,  now,  the 
apparatus   is   placed    upon    the 
plate  of  an  air-pump  and  covered 
with  a  glass  bell,  we  shall  find, 
on   removing   the   air,  that  the 
globe   will    preponderate,   as   is 
shown  in  the  figure.     By  remov- 
ing the  air,  we  increase  the  ap- 
parent weight  both  of  the  globe  and  of  the  counterpoise  by  just 
the  weight  of  the  air  displaced  by  each  ;  but  as  the  globe  is  much 
the  largest,  we  increase  its  weight  more  than  that  of  the  smaller 
brass  counterpoise,  and  hence  the  result.     If  we  allow  the  air 
to  re-enter  the  bell,  it  will  buoy  up  the  globe,  as  before,  so  much 
more  than  the  counterpoise,  as  to  restore  the  equilibrium. 

(154.)  Weight  of  a  Body  in  Air.  —  An  important  consequence 
of  the  principle  just  illustrated  is  evident.  The  balance  does  not 
give  us  the  true  relative  weight,  TF,  of  a  body,  but  a  slightly  dif- 
ferent weight,  depending  on  the  weight .  of  air  displaced  by  the 
body  compared  with  the  weight  of  air  displaced  by  the  brass  or 
platinum  weights  used  in  weighing.  As  the  volume  of  these 
weights  is  generally  less  than  that  of  the  body,  the  weight  indi- 
cated by  the  balance  is  almost  always  too  small ;  but  when  the 
volume  of  the  weights  is  greater  than  that  of  the  body,  the  weight 
indicated  by  the  balance  is  too  large.  When  the  two  volumes 
are  equal,  the  balance  will  indicate  the  same  weight  in  air  as  in 
a  vacuum.  It  is  easy  to  ascertain  the  correction  which  it  is 
necessary  to  add  to  or  subtract  from  the  weight  of  a  body  in  air, 
in  order  to  obtain  its  true  weight. 

It  must  be  remembered  that  the  brass  and  platinum  weights 


THE   THBEE   STATES   OF   MATTER.  269 

which  are  used  in  delicate  determinations  of  weight  are  only 
standard  when  in  a  vacuum  (64).  Let  us,  then,  represent  the 
various  values  as  follows  :  — 

W  —  weight  of  the  body  in  air  as  estimated  by  standard  weights,  and 
also  the  weight  of  the  standard  weights  themselves  in  a 
vacuum. 

V  =  volume  of  the  standard  weights  in  cubic  centimetres. 

V    =  volume  of  the  body  in  cubic  centimetres. 

w    =  weight  of  one  cubic  centimetre  of  air  at  the  time  of  the  weighing. 

W   =•  weight  of  the  body  in  a  vacuum,  —  which  we  wish  to  find. 

We  can  now  easily  deduce  the  following  values  :  — 

V  w  —  buoyancy  of  air  on  the  weights. 

V  w    =  buoyancy  of  air  on  the  body. 

W  —  V  w  =  actual  weight  of  standard  weights  in  air. 

W  —  V  w   =  actual  weight  of  body  in  air. 

Since  these  weights  just  balanced  each  other,  we  have 

W—  Vw  =  W  —  V  w,    or     W  =  W  +  w  (  V—  V).      [91.] 

The  correction  w  (V —  F'),  which  must  be  made  to  the  weight 
determined  by  a  balance  in  air  in  order  to  obtain  the  weight  in  a 
vacuum,  is  evidently  additive  when  the  volume  of  the  body  is 
greater  than  that  of  the  weights,  and  subtractive  when  these  con- 
ditions are  reversed.  When  the  volumes  are  equal,  the  correc- 
tion becomes  0. 

In  all  ordinary  cases  of  weighing,  the  correction  is  so  small 
that  it  may  be  neglected  without  sensible  error  ;  but  it  becomes 
of  the  greatest  importance  in  determining  the  weight  of  a  gas. 
In  such  cases,  we  have  to  determine  the  weight  of  a  large  glass 
globe  when  completely  vacuous  and  when  filled  with  gas  ;  and  it 
not  unfrequently  happens  that  the  buoyancy  of  the  air  is  greater 
than  the  weight  of  the  gas  itself,  and  it  is  always  a  considerable 
part  of  it.  If  the  buoyancy  of  the  air  is  the  same  when  the 
globe  is  weighed  in  its  vacuous  condition  and  when  filled  with 
gas,  it  would  not  affect  the  weight  of  the  gas,  which  would  be 
obtained  by  subtracting  the  first  weight  from  the  last.  But, 
unfortunately,  the  buoyancy  is  constantly  changing;  and  it  is 
therefore  necessary  to  determine  the  amount  carefully  at  each 
weighing,  and  reduce  the  weights  of  the  globe  in  the  two  condi- 
tions to  what  they  would  be  if  the  experiments  had  been  made 
in  a  vacuum. 

23* 


270 


CHEMICAL   PHYSICS. 


When  the  temperature  is  0°  C.  and  the  barometer  stands  at 
76  c.  m.,  and  when  the  air  contains  neither  vapor  of  water  nor 
carbonic  acid,  w  is  equal  to  0.001293  gram.  Were  the  atmos- 
phere always  in  this  condition,  nothing  would  be  easier  than  to 
calculate  the  actual  weight  of  a  body  from  the  weight  found  by 
weighing  in  this  normal  atmosphere.  But  this  is  far  from  being 
the  case  ;  for  the  temperature,  the  pressure,  and  the  composition 
of  the  atmosphere  are  changing  at  each  moment,  and  the  value 
of  w  varies  with  all  these  atmospheric  changes.  We  shall  here- 
after show  in  what  way  the  value  of  w  may  be  ascertained,  at  any 
given  time,  when  the  condition  of  the  atmosphere  is  known. 

It  is  frequently  possible  to  conduct  the  process  of  weighing  in 
such  a  way  that  the  correction  for  the  buoyancy  of  the  atmos- 
phere, always  some- 
what uncertain,  may 
be  avoided.  For  ex- 
ample, in  weighing 
a  gas,  instead  of 
equipoising  the  glass 
globe  when  empty, 
by  means  of  ordina- 
ry weights,  we  may 
equipoise  it  by  means 
of  a  second  globe, 
hermetically  closed, 
and  having  the  same 
volume  as  the  first, 
in  the  manner  repre- 
sented in  Fig.  258. 
It  is  evident  that  in 
this  case,  whatever 
may  be  the  buoyancy 
of  the  atmosphere,  it 

will  equally  affect  both  globes,  and  we  shallonly  have  to  consider 
the  buoyancy  of  the  air  on  the  small  weights  necessary  to  restore 
the  equilibrium  after  the  globe  is  filled  with  the  gas  to  be  weighed ; 
but  this  is  so  small  that  it  may  always  be  neglected. 

(155.)  Balloons.  —  If  the  weight  of  a  body  is  less  than  that  of 
the  gas  which  it  displaces,  it  is  evident  that  the  body  will  rise  in  the 
gas  ;  and  hence  the  phenomena  of  floating  bodies,  which  we  have 


Fig.  258. 


THE   THREE   STATES   OF   MATTER.  271" 

already  studied  in  the  case  of  liquids  (140),  must  be  repeated  in 
the  case  of  gases.  It  is  not  difficult  to  construct  a  body  which 
shall  be,  taken  as  a  whole,  specifically  lighter  than  air,  and  which 
will  therefore  rise  in  the  atmosphere  as  wood  rises  in  water.  Hy- 
drogen gas  is  14J  times  lighter  than  air,  and  by  enclosing  a  large 
volume  of  this  gas  in  a  light  bag  made  of  oiled  silk,  called  a 
balloon,  we  shall  have  a  body  which  will  displace  a  weight  of  air 
much  greater  than  its  own  weight.  For  example,  let  us  suppose 
that  the  balloon,  when  fully  inflated,  forms  a  sphere  two  me- 
tres in  diameter.  It  is  easy  to  calculate  that  it  will  contain 
4.1887902  m.3  of  hydrogen,  which  will  weigh  374.436  gram. 
Neglecting  the  volume  occupied  by  the  material  of  the  balloon, 
it  will  displace  an  equal  volume  of  air,  weighing  5,418.75  gram. 
The  difference  between  these  weights,  or  5,044.31  gram.,  will 
represent  the  excess  of  the  buoyancy  of  the  air  over  the  weight 
of  the  hydrogen  ;  and  hence,  if  the  balloon  and  its  attachments 
weigh  less  than  this,  it  will,  when  inflated  with  hydrogen,  rise  in 
the  atmosphere.  The  difference  between  the  weight  of  the  bal- 
loon inflated  with  hydrogen  and  that  of  the  air  displaced  by  it  is 
termed  the  ascensional  force  of  the  balloon.  If  the  balloon  is 
ten  metres  in  diameter,  and  weighs  100  kilogrammes,  it  would 
have  an  ascensional  force  of  530.5  kilogrammes,  and  therefore 
sufficient  to  raise  a  car  with  several  passengers  into  the  atmos- 
phere. 

In  practice,  a  balloon  is  never  at  first  more  than  two  thirds  filled 
with  hydrogen  ;  because,  as  it  rises  in  the  atmosphere,  the  gas 
rapidly  expands,  and  it  is  necessary  to  allow  for  this  expansion. 
Moreover,  the  hydrogen  used  is  mixed,  to  a  greater  or  less  extent, 
with  air  and  vapor,  which  greatly  increase  its  weight.  These  causes 
diminish  the  ascensional  force  to  such  an  extent,  that  in  practice 
the  ascensional  force  of  a  balloon  ten  metres  in  diameter  would 
not  be  more  than  one  half  of  what  it  is  estimated  above. 

Since  the  introduction  of  coal-gas  as  an  illuminating  material, 
this  is  almost  exclusively  used  for  inflating  large  balloons.  The 
specific  gravity  of  this  gas  is  on  an  average  about  0.5,  and  it  is 
only,  therefore,  about  twice  as  light  as  air.  Hence,  in  order  to 
obtain  the  same  ascensional  force  with  coal-gas  as  with  hydrogen, 
it  is  necessary  to  use  very  much  larger  balloons.  When  the  spe- 
cific gravity  of  a  gas  is  given,  it  is  easy  to  calculate  the  ascensional 
force  which  in  any  given  case  may  be  obtained  with  it. 


212  CHEMICAL   PHYSICS. 

Let  us  represent  by  d  and  d'  the  specific  gravities  of  air  and 
the  gas  to  be  used,  referred  to  water  [58]  ;  by  W,  the  weight  of  the 
material  of  the  balloon  and  its  attachments;  and  by  F,  its  volume 
when  inflated.  Then,  by  [56],  we  have  for  the  weight  of  the 
gas  in  grammes  Yd',  and  for  the  weight  of  the  air  it  displaces  Vd. 
Neglecting,  for  the  moment,  the  weight  of  the  balloon  itself,  we 
should  have  for  the  ascensional  force  F  (d  —  d1) .  Subtracting 
the  weight  of  the  balloon  and  its  attachments,  we  have,  for  the 
total  ascensional  force  -F, 

F=  F(d  —  d!}—W.  [92.] 

If  the  balloon  is  a  sphere  of  which  R  is  the  radius,  then  we 
should  have  for  the  value  of  F,  when  the  balloon  was  fully  in- 
flated, £  it  R3,  and  for  the  value  of  .F, 

F=  f  7t  R*  (d  —  d1)  —  TF.  [93.] 

When  the  gas  used  is  pure  hydrogen,  d  =  0.00129363,  and  d'  — 
0.00008939.  Substituting  these  values,  and  also  for  n  its  well- 
known  value,  the  expression  becomes 

F  =  0.00504431  R3  —  TF,  [94.] 

in  which  R  stands  for  a  certain  number  of  centimetres,  and  W 
for  a  certain  number  of  grammes. 

As  we  live  at  the  bottom  of  the  ocean  of  air  which  surrounds 
the  globe,  we  cannot,  from  the  nature  of  the  case,  imitate  with  it 
the  condition  of  a  vessel  floating  on  the  surface  of  the  water ; 
but  with  other  gases  this  condition  of  things  may  be,  at  least  in  a 
small  way,  very  nearly  approached. 

The  large  fermenting-vats  of  breweries  and  distilleries  are  al- 
most constantly  filled  with  carbonic  acid  gas,  which,  being  heav- 
ier than  the  air,  remains  in  the  tank,  and  has  a  surface  like  that 
of  water,  although  it  is  not  quite  so  definite.  By  exploding  a 
little  gunpowder  in  the  gas,  and  thus  filling  it  with  smoke,  the 
surface  becomes  distinctly  visible.  A  very  illustrative  experiment 
can  be  made  at  such  vats,  by  allowing  soap-bubbles,  blown  with  a 
common  tobacco-pipe,  to  fall  on  the  gas  thus  clouded.  They  will 
for  a  few  moments  float  on  the  surface,  and  illustrate  in  a  most 
striking  manner  the  analogy  between  gases  and  liquids. 


THE   THREE   STATES    OP   MATTER.  273 

Differences  between  Liquids  and  Gases. 

(156.)  We  shall  fail  to  give  an  accurate  idea  of  the  nature 
of  a  gas,  if,  after  having  dwelt  upon  the  analogies  between  liquids 
and  gases,  we  do  not  point  out  those  qualities  which  distinguish 
these  two  conditions  of  matter. 

1.  Difference  of  Specific  Gravity.  —  The  most  obvious  differ- 
ence between  gases  arid  liquids  is  to  be  found  in  their  relative- 
weight.     A  litre  of  water  weighs  1,000  grammes,  and  the  weight 
of  the  same  volume  of  other  liquids  varies  from  600  to  3,000 
grammes,  leaving  out  of  account  mercury  and  other  metals,  when 
in  a  melted  state,  which  are  much  heavier.    Between  these  limits 
we  find  almost  every  possible  gradation.     One  litre  of  air  weighs 
1.294  gram.,  and  the  weight  of  one  litre  of  other  gases  varies 
between  0.089  gram,  and  20  gram.     There  is,  therefore,  a  wide 
gap  between  the  lightest  liquid  and  the  heaviest  gas,  but  yet 
this  difference  is  one  entirely  of  degree  ;  and  although  this  gap 
is  not  filled  by  any  known  substance  in  its  normal  condition  on 
the  globe,  yet  Natterer,  in  his  experiments  on  the  condensation  of 
gases,*  must  have  had  atmospheric  gas  in  every  degree  of  density 
between  its  ordinary  density  and  that  of  water. 

2.  Compressibility.  —  Gases  are  also  distinguished  from  liquids 
by  being  far  more  compressible.     When  by  means  of  a  piston  we 
attempt  to  condense  a  liquid,  we  find  that  we  can  only  reduce  its 
volume  very  slightly.  *  But  this  almost  insensible  diminution  of 
volume  develops  a  very  great  elasticity  ;  for  it  is  only  necessary 
to  reduce  the  volume  one  forty-five-millionth  to  produce  a  resist- 
ance equal  to  the  pressure  of  our  atmosphere.    It  is  different  with 
gases.    When,  for  example,  we  press  down  a  piston  into  a  cylinder 
containing  air  (Fig.  51),  it  is  necessary  to  reduce  the  volume  to 
one  half  in  order  to  double  the  resistance,  and  to  one  third  in 
order  to  treble  it.     As  the  pressure  is  increased,  the  volume  of  a 
gas  is  diminished  almost  in  the  same  proportion ;  as  the  pressure 
is  diminished,  on  the   other  hand,  the  volume  of  the  gas  is 
proportionally  increased.     For  this  reason,  gases  are  frequently 
called  compressible,  and  liquids  incompressible  fluids ;  but  here 
again  the  difference  is  one  of  degree  rather  than  of  kind. 

This  difference  of  compressibility  gives  rise  to  an  important  dif- 

*  Poggendorff,  Annalen,  XCIV.  436. 


274  CHEMICAL  PHYSICS. 

ference  of  condition  between  the  atmosphere,  regarded  as  an 
ocean  of  gas,  and  the  liquid  oceans  of  our  globe.  As  we  de- 
scend in  the  ocean,  although  the  pressure  increases  with  great 
rapidity,  yet  the  density  of  the  water  is  not  materially  increased. 
It  is  very  different  with  the  atmosphere.  As  we  rise  in  this  ocean 
of  gas,  the  air  becomes  less  dense  in  proportion  as  the  pressure  is 
diminished,  and  when  at  a  height  of  about  5,520  m.  the  pressure  is 
reduced  one  half,  the  density  is  also  reduced  one  half.  On  the 
other  hand,  when  we  descend  into  mines,  and  the  pressure  from 
above  is  increased,  the  density  of  the  air  increases  in  the  same 
proportion.  The  atmosphere  does  not,  therefore,  like  the  sea, 
consist  of  a  fluid  of  nearly  uniform  density  throughout,  but  its 
density  very  rapidly  diminishes  as  we  rise  above  the  surface  of 
the  globe.  It  would  not,  then,  be  possible  to  have  a  cylin- 
drical vessel  filled  with  air  of  uniform  density  throughout  its 
whole  height,  as  we  supposed  in  (151).  Such  a  condition  of 
things  is  wholly  ideal,  and  was  introduced  merely  for  the  sake 
of  illustration.  Were  the  atmosphere,  like  the  sea,  of  nearly 
uniform  density,  its  height  would  be  only  about  eight  kilome- 
tres, instead  of  forty-seven,  as  already  stated.  The  pressure 
exerted  by  such  an  ideal  fluid  would  be  precisely  the  same  as 
that  exerted  by  the  atmosphere  ;  so  that,  while  merely  studying 
the  pressure  on  the  surface  of  the  earth,  we  may  conceive  of  the 
pressure  as  exerted  by  a  fluid  of  uniform  density,  without  com- 
mitting any  material  error  ;  but  it  must  be  remembered  that  the 
real  state  of  the  case  is  very  different.  We  shall  return  to  this 
subject  in  a  future  section. 

3.  Permanent  Elasticity.  —  We  have  already  dwelt  at  some 
length  on  this  property  of  gases,  which  distinguishes  them  pre- 
eminently from  liquids  (149)  ;  but  even  here  the  difference  is 
not  so  strongly  marked  as  it  would  at  first  sight  seem.  A 
simple  experiment  will  illustrate  this  point,  and  at  the  same 
time  make  the  distinction  between  the  two  fluid  conditions  of 
matter  clearer. 

Let  us  take,  then,  a  volume,  F,  of  water,  contained  in  a  vessel 
of  much  greater  capacity,  and  let  us  suppose  that  its  temperature 
is  100°,  and  that  it  is  exposed  to  a  given  pressure,  for  example 
of  ten  atmospheres.  If,  now,  we  diminish  the  pressure  succes- 
sively by  one  atmosphere  each  time,  the  volume  F  will  increase  by 
a  very  small  amount,  represented  by  F^i,  at  each  operation.  As 


THE   THREE   STATES   OF   MATTER.  275 

soon,  however,  as  the  pressure  is  reduced  to  one  atmosphere,  this 
law  of  expansion  ceases  abruptly,  and  the  water,  without  any 
intermediate  transition,  takes  a  volume  1,200  times  greater  than 
before,  changing  into  a  gas  having  all  the  properties  of  air,  and 
preserving  these  properties  at  any  pressure  less  than  one  at- 
mosphere. 

We  may  now  reverse  this  experiment.  Let  us,  then,  increase 
the  pressure  upon  this  gas  formed  by  water ;  we  shall  find  that, 
when  the  pressure  is  doubled,  the  volume  of  the  gas  will  be  re- 
duced one  half,  but  as  soon  as  the  pressure  exceeds  one  atmos- 
phere it  will  suddenly  take  a  volume  1,200  times  smaller  than  be- 
fore, and  a  density  1,200  times  greater,  collecting  in  the  lower  part 
of  the  vessel  in  a  liquid  form.  After  this,  it  can  be  compressed 
but  very  slightly  by  increasing  pressures.  We  have  taken,  as  an 
example,  water  at  100°,  because  the  change  of  state  which  it 
undergoes  at  this  temperature  is  a  familiar  fact  to  every  one. 
We  might  have  cited  sulphurous  acid  gas,  which  liquefies  at 
— 10°,  or  carbonic  acid  gas,  which  liquefies  at  — 78° ;  but  what- 
ever might  be  the  body  examined,  the  result  would  be  the  same. 

What  has  now  been  stated  in  regard  to  gases  may  be  summed 
up  in  a  few  words.  They  are  bodies  constituted,  like  liquids,  of 
molecules  which  repel  each  other,  bodies  which  transmit  pressure 
equally  in  all  directions,  which  arrange  themselves  under  the  influ- 
ence of  gravity  in  strata  whose  density  and  elasticity  increase  as  we 
descend,  which  buoy  up  all  bodies  immersed  in  them  with  a  force 
equal  to  the  weight  of  the  fluid  displaced,  and  in  which  the  laws 
of  the  equilibrium  of  floating  bodies  are  reproduced.  These  ,are 
the  analogies.  On  the  other  hand,  they  are  bodies  having  a  very 
small  density,  obeying  a  special  law  of  compressibility,  and  which, 
when  submitted  to  a  sufficient  pressure,  change  into  liquids.* 
Such,  then,  are  the  characteristic  properties  of  gases  ;  but  before 
studying  these  more  in  detail,  we  must  consider  the  mode  by 
which  the  pressure  of  a  gas  may  be  accurately  measured. 

THE   BAROMETER. 

(157.)  Experiment  of  Torricelli.  —  Before  the  middle  of  the 
seventeenth  century,  the  phenomena  which  we  now  refer  to 
the  pressure  of  the  air  were  explained  by  a  principle  invented 

*  We  shall  hereafter  learn  that  there  are  some  gases  which  have  not  been  liquefied. 


276  CHEMICAL   PHYSICS. 

by  the  Aristoteleans,  namely,  that  "  Nature  abhors  a  vacuum." 
These  ancient  philosophers  noticed  that  space  was  always  filled 
with  some  material  substance,  and  that,  the  moment  a  solid  body 
was  removed,  air  or  water  always  rushed  in  to  fill  the  space  thus 
deserted.  Hence  they  concluded  that  it  was  a  universal  law  of 
nature  that  space  could  not  exist  unoccupied  by  matter,  and  the 
phrase  just  quoted  was  merely  their  figurative  expression  of  this 
idea.  When,  for  example,  the  piston  of  a  common  pump  was 
drawn  up,  the  rise  of  the  water  was  explained  by  declaring  that, 
as  from  the  nature  of  things  a  vacuum  could  not  exist,  the  water 
necessarily  filled  the  space  deserted  by  the  piston. 

This  physical  dogma  served  the  purposes  of  natural  philosophy 
for  two  thousand  years,  and  it  was  not  until  the  seventeenth  cen- 
tury that  men  discovered  any  limit  to  Nature's  horror  of  a  vacuum. 
Even  as  late  as  1644,  Mersenne  speaks  of  a  siphon  which  shall 
go  over  a  mountain,  being  then  ignorant  that  the  effect  of  such  an 
instrument  was  limited  to  a  height  of  ten  metres.  This  limit 
appears  to  have  been  first  discovered  by  Galileo.  Some  Floren- 
tine engineers,  being  employed  to  sink  a  pump  to  an  unusual 
depth,  found  that  they  could  not  raise  water  higher  than  ten  me- 
tres in  the  barrel.  Galileo  was  consulted,  and  he  is  said  to  have 
replied,  that  Nature  did  not  abhor  a  vacuum  above  ten  metres. 
However  this  may  be,  it  appears  that  Galileo  did  not  understand 
the  cause  of  the  phenomenon,  although  he  had  previously  taught 
that  air  has  weight ;  and  it  was  left  for  his  pupil,  Torricelli,  to 
discover  the  true  explanation.  Torricelli  reasoned  that  the  force, 
whatever  it  is,  which  sustains  a  column  of  water  ten  metres  high 
in  a  cylindrical  tube,  must  be  equivalent  to  the  weight  of  the  mass 
of  water  sustained ;  and  consequently,  if  another  liquid  were 
used,  heavier  than  water,  the  same  force  could  only  sustain  a 
column  of  proportionally  less  height.  The  weight  of  mercury 
being  13J  times  greater  than  that  of  water,  Torricelli  argued  that, 
if  the  force  imputed  to  the  abhorrence  of  a  vacuum  could  siistain 
a  column  of  water  10  metres  high,  it  could  only  sustain  a  column 
of  mercury  13  J  times  lower,  or  about  76  c.  m.  high.  This  led  to 
the  following  experiment,  which  has  since  become  so  celebrated 
in  the  history  of  science. 

Torricelli  took  a  long  glass  tube,  open  -at  one  end,  such  as  d  c, 
Fig.  259,  and,  having  filled  it  with  mercury,  closed  the  open  end 
with  his  thumb,  and,  inverting  the  tube,  plunged  this  end  into 


THE  THREE   STATES   OP   MATTER. 


277' 


a  basin  of  mercury.     On  removing  his  thumb,  the  mercury,  in- 
stead of  remaining  in  the  tube,  fell,  as  he  expected,  and  after 
a  few  oscillations  came   to  rest  at  a  height  of  about  76  c.  m. 
above  the  level  of  the  mercury 
in   the  basin.     The   correctness 
of  his  induction  having  been  thus 
completely    verified,     Torricelli 
soon  discovered  the  real  nature 
of  the  force  which  sustained  both 
the  water  in  the  pump  and  the 
mercury  in  his  tube. 

This  experiment  excited  a 
great  sensation  among  the  sci- 
entific men  of  Europe ;  but,  as 
might  have  been  expected,  the 
explanation  given  of  it  by  Torri- 
celli was  very  generally  rejected. 
It  was  opposed  to  a  long-estab- 
lished dogma,  and  Nature's  hor- 
ror of  a  vacuum  could  not  be 
so  easily  overcome.  The  cele- 
brated Blaise  Pascal,  however, 
had  the  sagacity  to  perceive  the 
force  of  Torricelli's  reasoning, 
and  devised  an  experimentum 
crucis  which  put  an  end  to  all 
controversy  on  the  subject.  "  If,"  said  Pascal,  "  it  be  really  the 
weight  of  the  atmosphere,  under  which  we  live,  that  supports  the 
column  of  mercury  in  Torricelli's  tube,  we  shall  find,  by  trans- 
porting this  tube  upwards  in  the  atmosphere,  that  in  proportion 
as  it  leaves  below  it  more  and  more  of  the  air,  and  has  conse- 
quently less  and  less  above  it,  there  will  be  a  less  column  sus- 
tained in  the  tube,  inasmuch  as  the  weight  of  the  air  above  the 
tube,  which  is  declared  by  Torricelli  to  be  the  force  which  sus- 
tains it,  will  be  diminished  by  the  increased  elevation  of  the 
tube."  *  Accordingly,  Pascal  carried  the  tube  to  the  top  of  a 
church-steeple  in  Paris,  and  observed  that  the  height  of  the 
mercury  in  the  tube  fell  slightly  ;  but,  not  satisfied  with  this 


Fig.  259- 


*  Lardner's  Hand-Book  of  Natural  Philosophy. 

24 


278  CHEMICAL   PHYSICS. 

result,  he  wrote  to  his  brother-in-law,  who  lived  near  the  high 
mountain  of  Puy  de  Dfane,  in  Auvergne,  to  make  the  experiment 
there,  where  the  result  would  be  more  decisive.  "  You  see,"  he 
writes,  "  that  if  it  happens  that  the  height  of  the  mercury  at  the 
top  of  the  hill  be  less  than  at  the  bottom,  (which  I  have  many 
reasons  to  believe,  though  all  those  who  have  thought  about  it 
are  of  a  different  opinion,)  it  will  follow  that  the  weight  and 
pressure  of  the  air  are  the  sole  cause  of  this  suspension,  and  not 
the  horror  of  a  vacuum :  since  it  is  very  certain  that  there  is 
more  air  to  weigh  on  it  at  the  bottom  than  at  the  top ;  while  we 
cannot  say  that  Nature  abhors  a  vacuum  at  the  foot  of  a  moun- 
tain more  than  on  its  summit."  M.  Perrier,  Pascal's  cor- 
respondent, made  the  observation  as  he  desired,  and  found  a 
difference  of  nearly  eight  centimetres  of  mercury,  "  which,"  he 
replies,  "  ravished  us  with  admiration  and  astonishment."  * 

Pascal  still  further  varied  and  extended  the  original  experi- 
ment of  Torricelli,  and  deduced  the  theory  of  the  equilibrium  of 
liquids  and  gases,  which  he  left  almost  perfect. 

(158.)  Theory  of  the  Barometer.  —  It  is  hardly  necessary 
to  state  that  the  tube  of  Torricelli  is  the  instrument  which  is 
now  so  well  known  as  the  Barometer.  This  name,  indeed,  is  de- 
rived from  two  Greek  words,  fiapv?  and  nt-Tpov,  which  indicate 
its  use  as  a  measure  of  the  pressure  of  the  air.  The  theory  of 
the  barometer  can  be  readily  deduced  from  the  principles  of  the 
equilibrium  of  fluids,  already  established.  The  mercury  is  sus- 
tained in  the  tube  by  the  pressure  of  the  air  on  the  surface  of 
the  mercury  in  the  basin.  Let  us  consider  how  much  of  this 
pressure  is  effective  in  producing  the  result. 

Consider,  then,  a  section  made  across  the  tube  at  the  level  of 
the  mercury  in  the  basin.  All  the  liquid  below  this  level  is  evi- 
dently in  equilibrium  (130  and  131).  Represent  the  area  of 
the  surface  of  the  mercury  in  the  basin  by  S',  and  that  of  the 
section  of  the  tube  by  S.  The  pressure,  4F',  exerted  by  the  air  on 
£',  is  transmitted  through  the  liquid  mercury  to  S.  The  pressure 
thus  exerted  on  the  under  face  of  the  section  will  be,  by  [77],  as 
many  times  less  than  f  as  S  is  less  than  £',  or  £  :  £'  =  S  :  /S', 

and  f  =  f  —  .    For  example,  if  S'  =  100  c^2  and  S  =  1  cTml2, 

*  Whewell's  History  of  the  Inductive  Sciences,  Vol.  II.  pp.  67,  68. 


THE   THREE   STATES   OP   MATTER.  279 


then  £  =  f  yj-g-.  The  pressure,  therefore,  which  is  exerted 
by  the  air  on  the  lower  face  of  this  section  is  the  same  as 
that  it  would  exert  if  applied  directly  to  the  section  itself. 
As  this  pressure  just  sustains  a  column  of  mercury  whose 
height  we  may  represent  by  H,  it  is  evidently  just  equal 
to  the  pressure  exerted  by  this  column  on  the  upper  side 
of  the  same  section.  But  by  [78]  this  pressure  is  equal  to 
H.  S.  (Sp.Gr.).  Substituting,  then,  for  Sp.  Gr.,  the  value  for 
mercury  at  0°,  or  13.596,  we  have  for  the  pressure  of  the  air  on  a 
given  surface,  $,  the  value, 

f  =  13.596  .  S  .  H,  [95.] 

in  which  H  denotes  the  height  of  the  mercury  in  the  barometer 
at  0°.  For  any  other  height  we  should  have  £'  =  13.596  .  S  .  H', 
and,  comparing  the  two  equations,  we  obtain 

£:£'  =  H:H';  [96.] 

that  is,  the  pressure  of  the  air  on  a  given  surface  is  proportional 
to  the  height  of  the  barometer  column.  We  may,  therefore,  use 
the  height  of  the  barometer  as  a  measure  of  the  pressure,  in  the 
same  way  that  we  use  an  arc  as  a  measure  of  an  angle,  or  weight 
as  a  measure  of  mass.  The  height  is  not  the  same  sort  of  quan- 
tity as  the  pressure,  but  it  is  sufficient  for  any  measure  that  it 
should  be  proportional  to  the  quantity  measured.  It  is  there- 
fore customary  to  speak  of  the  pressure  of  the  air  as  amounting 
to  so  many  centimetres  of  mercury  ;  meaning  thereby,  that  it 
will  support  a  column  of  mercury  of  that  height.  The  use  of 
the  barometer  is  not  confined  to  measuring  the  pressure  exerted 
by  the  atmosphere.  We  may  use  it  for  measuring  the  pressure 
exerted  by  any  gas  ;  and  here,  as  before,  we  speak  of  the  pres- 
sure as  amounting  to  so  many  centimetres  of  mercury.  When 
the  pressure  is  equivalent  to  seventy-six  centimetres  of  mercury, 
we  say  that  it  is  equal  to  one  atmosphere.  When  two,  three,  or 
four  times  as  great  as  this,  we  say  that  it  is  equal  to  two,  three, 
or  four  atmospheres. 

It  is  always  easy  to  reduce  pressure  expressed  in  centimetres 
of  mercury  to  weight.  For  this  purpose,  it  is  only  necessary  to 
substitute  in  [95]  the  values  of  H  and  S  in  the  given  case,  and 
the  result  will  be  the  amount  of  pressure  in  grammes.  For  ex- 
ample, in  the  air  the  height  of  the  barometer  column  is,  on  the 


280  CHEMICAL   PHYSICS, 

average,  76  c.  m.  Substituting  this  value,  and  also  for  S9 1  cTm.*, 
we  obtain 

£  =  1,033.296  gram. ;  [97.] 

which  is  the  pressure  exerted  by  the  atmosphere  on  every  square 
centimetre  of  surface.  The  height  of  the  barometer  column  varies 
on  the  surface  of  the  earth  from  about  72  c.  m.  to  78  c.  m.,  and 
hence  the  pressure  on  the  square  centimetre  varies  from  978.9 
grammes  to  1,060.5  grammes.  The  total  pressure  exerted  by  the 
atmosphere  on  large  objects  is  therefore  exceedingly  great ;  that 
on  a  man  of  ordinary  stature  amounts,  as  already  stated,  to  about 
16,000  kilogrammes. 

Having  studied  the  theory  of  the  barometer,  we  will  now  ex- 
amine a  few  of  the  most  useful  forms  of  the  instrument,  pre- 
mising that  the  essential  parts  are  a  tube  over  seventy-six 
centimetres  long,  a  basin  of  mercury,  and  a  graduated  scale 
for  determining  the  height  of  the  column. 

(159.)  RegnauWs  Barometer.  —  The  simplest  and  most  accu- 
rate form  of  the  barometer  is  the  one  represented  in  Fig.  260, 
which  was  invented  by  Regnault.  The  basin  of  mercury  is 
formed  by  an  iron  trough,  which  is  divided  by  a  partition  into 
two  parts ;  but  the  partition  does  not  rise  to  the  top  of  the  trough, 
and  is  covered  by  the  mercury  which  fills  the  basin.  The  basin 
is  supported  on  a  shelf,  attached  to  the  lower  part  of  a  wooden 
plank,  to  which  the  glass  tubes  are  securely  fastened  by  means 
of  clamps.  This  plank  is  itself  immovably  fastened  to  a  brick 
wall.  The  barometer  tube  at  the  left  of  the  figure  dips  into  the 
left-hand  compartment  of  the  trough.  The  tube  on  the  right  is 
called  a  manometer,  and  its  use  will  soon  be  explained.  The 
height  of  the  mercury  in  the  barometer  is  measured  by  means  of 
the  cathetometer,  represented  on  the  right-hand  side  of  the  fig- 
ure, which  is  placed  on  a  firm  support  in  front  of  the  instrument. 
In  order  to  obtain  the  measure  with  the  greatest  possible  accu- 
racy, a  vertical  screw,  M,  with  two  points  and  of  a  known  length, 
is  attached  to  the  basin,  as  represented  in  the  figure.  At  the  mo- 
ment of  observation,  we  lower  the  screw  by  turning  it  on  its  axis 
until  the  lower  point  just  touches  the  mercury.  This  contact  can 
be  obtained  with  the  most  perfect  precision,  for  until  it  takes  place 
the  observer  sees  at  the  same  time  the  point  and  its  image  reflect- 
ed by  the  mercury.  The  two  seem  to  approach  each  other  until 


THE   THREE   STATES    OF   MATTER. 


281 


contact  is  attained,  and  the  surface  of  the  mercury  is  seen  de- 
pressed the  moment  this  point  is  passed.     The  contact  obtained, 


Fig.  260. 

we  measure  the  distance,  with  the  cathetometer,  between  the 
upper  surface  of  the  mercury  in  the  tube  and  the  upper  point  of 
the  screw,  and  we  have  only  to  add  to  this  length  the  known 
length  of  the  screw.  Of  all  barometers  this  one  is  the  simplest, 
and  of  all  methods  of  measuring  the  height  of  the  column  the 
one  just  described  is  the  best.  We  thus  measure  directly  the 
vertical  height,  and  it  is  no  matter  whether  the  instrument  is  in- 
24* 


282 


CHEMICAL   PHYSICS. 


clined  or  not.  We  thus  avoid  instrumental  errors  ;  and,  more- 
over, with  a  good  cathetometer,  the  difference  of  level  can  be 
determined  within  the  fiftieth  part  of  a  millimetre. 

(160.)  Barometer  of  Fortin.  —  It  is  not  always  possible  to 
fix  a  barometer  permanently  to  a  wall  in  the  way  just  described. 

For  example,  in  using  the  instrument 
for  measuring  the  heights  of  moun- 
tains, it  is  necessary  that  it  should  be 
portable  ;  and  without  diminishing 
materially  the  accuracy,  it  is  impor- 
tant to  simplify  the  method  of  meas- 
uring the  height  of  the  mercury 
column.  The  barometer  of  Fortin 
(Fig.  261)  satisfies  completely  all 
these  requirements.  The  glass  tube 
is  enclosed,  for  protection,  in  a  brass 
case,  towards  the  upper  part  of  which 
two  longitudinal  o- 
penings  are  provided 
opposite  to  each  oth- 
er for  observing  the 
height  of  the  mercu- 
ry column,  by  means 
of  a  scale  graduated 
on  the  case,  as  rep- 
resented in  Fig.  262. 
A  vernier,  B  C,  moves 
up  and  down  in  the 
opening,  and  its  po- 
sition can  be  care- 
fully regulated  by 
means  of  the  rack 
and  pinion  work  represented  in  the  figure.  To  the  lower  end  of 
the  case  is  fastened,  by  a  screw,  the  reservoir  of  mercury,  in 
which  the  glass  tube  dips,  as  represented  in  Fig.  263.  This 
reservoir  is  formed  principally  by  a  cylinder  of  glass  cemented  at 
both  ends  to  wooden  caps  surmounted  by  brass  mountings,  which 
last  are  kept  in  place  by  three  long  screws  (Fig.  261).  The 
bottom  of  the  reservoir  is  formed  by  a  leathern  bag,  m  n  (Fig. 
263),  which  can  be  raised  or  lowered  by  the  screw  C.  To  the 


Fig.  261. 


Fig.  262. 


Fig.  2G3. 


THE   THREE   STATES   OF   MATTER. 


283 


cover  of  the  cylinder  is  fastened  an  ivory  pin,  a,  whose  point 
corresponds  exactly  to  the  zero  of  the  scale  graduated  on  the 
case.     The  reservoir  is  closed  above,  also,  hy  a  leathern  cover, 
firmly  tied  both   to   the  glass   tube  and  the 
wooden  cap,  which,  while  it  prevents  the  mer- 
cury from   escaping   when  the   barometer  is 
reversed,  nevertheless  gives  free   passage   to 
the  air.     All  the  parts  of  the  reservoir  are 
represented  in  Fig.  264,  in  perspective,  un- 
screwed and  inverted. 

In  using  this  barometer,  it  is  first  suspended 
by  the  ring  (7,  so  that  the  instrument  may 
swing  freely,  when,  like  a  plumb-line,  it  will 
come  to  rest  with  the  scale  perfectly  vertical. 
Next,  the  level  of  the  mercury  in  the  reservoir  is 
brought  to  correspond  with  the  point  of  the 
ivory  pin,  by  turning  the  screw  C  (Fig.  263)  in 
one  direction  or  the  other.  This  coincidence 
can  be  attained  with  great  accuracy  in  the  way 
already  described  in  the  last  section.  Since 
the  level  of  the  mercury  in  the  basin  now  co- 
incides with  the  zero  of  the  scale  graduated  on 
the  brass  case,  it  only  remains  to  read  off  the 
height  of  the  column  of  the  mercury  in  the  tube 
by  means  of  the  scale  at  its  side.  For  this  pur- 
pose, the  vernier  is  raised  or  lowered  by  means 
of  the  thumb-screw  until  its  lower  edge  is  just 
tangent  to  the  convex  surface  of  the  mercury 
in  the  tube  (Fig.  262).  This  adjustment  can 
also  be  obtained  with  great  accuracy  by  sus- 
pending the  barometer  in  front  of  a  light  wall, 
sighting  across  the  front  and  back  edge  of  the 
brass  tube  carrying  the  vernier,  which  moves 
within  the  brass  case  of  the  instrument.  It 
only  remains,  then,  to  read  on  the  scale  the  position  of  the  ver- 
nier, to  obtain  the  height  of  the  barometer  within  a  tenth  of  a 
millimetre. 

A  great  advantage  of  this  form  of  barometer  is  the  facility  and 
safety  with  which  it  may  be  transported.  By  raising  the  screw  C 
sufficiently,  the  whole  interior  of  the  tube  and  reservoir  may  be 


Fig.  264. 


284 


CHEMICAL   PHYSICS. 


filled  with  mercury,  and  then  the  instrument  may  be  reversed 
and  transported  from  place  to  place  without  danger  ;  and  even  if 
the  tube  is  accidentally  broken,  it  is  always  possible,  with  a  little 
skill,  to  replace  it. 

A  thermometer  is  always  attached  to  the  barometer,  since 
the  height  of  the  mercury  column  varies  slightly  with  the  tem- 
perature ;  for  heat,  by  expanding  the  mercury,  changes  slight 
ly  its  specific  gravity,  and  on  this  the  height  of  the  column 
depends.  The  standard  temperature  which  has  been  adopted 
is  0°  C.,  and  all  barometrical  observations  are  corrected  so  as  to 
reduce  them  to  the  standard  temperature.  A  table  for  applying 
this  correction  will  be  found  in  most  works  of  meteorology,*  and 
the  method  of  calculating  it  will 
be  explained  in  the  chapter 
on  Heat.  A  second  correction 
is  also  required  for  capillarity, 
the  nature  of  which  will  be 
explained  in  a  future  section. 
This  correction,  however,  is  a 
constant  quantity  for  the  same 
instrument,  and  is  generally 
allowed  for  by  the  instrument- 
maker  f  in  adjiisting  the  scale 
of  the  instrument. 

(161.)  Common  Barometer. 
—  Having  described  at  length 
the  two  most  useful  and  accu- 
rate forms  of  the  barometer,  it 
will  not  be  necessary  to  do 
more  than  allude  to  the  nu- 
merous modifications  of  the 
instrument  which  have  been 
devised  by  Gay-Lussac  and 
other  physicists,  for  the  pur- 
pose of  obviating  the  correc- 
tion for  capillarity.  They  will  Fig'265'  Fig266' 
be  found  described  at  length  in  the  large  works  on  physics. 
A  very  common  form  of  barometer,  which  is  much  used  as  a 


*  See  Guyot's  Meteorological  Tables,  published  by  the  Smithsonian  Institution, 
t  Good  barometers,  like  the  one  described,  are  made  by  Green,  of  New  York. 


THE   THREE   STATES   OF   MATTER. 


285 


weather-indicator,  is  represented  in  Fig.  265.  The  glass  tube 
has  the  form  of  a  siphon,  as  represented  in  Fig.  266.  When  the 
mercury  falls  in  the  barometer,  it  must  of  course  rise  to  a  pro- 
portional height  in  the  short  arm  of  the  siphon,  and  it  raises  a 
float  resting  upon  it.  This  float  is  fastened  to  a  cord  which 
passes  round  a  wheel,  O,  and  is  attached  to  a  weight,  P,  on  the 
other  side.  The  motion  of  the  float  thus  communicates  motion 
to  the  wheel,  and  this,  in  its  turn,  moves  the  index  over  the  dial- 
plate  of  the  instrument.  Such  barometers  admit  of  no  precis- 
ion, and  are  of  little  value  except  as  ornaments. 

A  variety  of  barometer  depending  on  the  laws  of  elasticity 
has  already  been  described  (104),  and  is  represented  in  Fig.  267. 
Another  form  of  barometer,  dif- 
ferently constructed,  but  depend- 
ing on  the  same  principle,  is  the 
aneroid*  barometer,  invented  by 
M.  Yidi.  Both  of  these  barome- 
ters, on  account  of  their  small 
volume  and  the  absence  of  any 
fragile  material  in  their  construc- 
tion, are  very  portable.  They  are 
very  sensible,  and  more  ^regular 
in  their  indication  than  the  com- 
mon mercury  barometers,  especial- 
ly when  the  differences  of  pressure 
are  not  great ;  but  they  cannot  be 
relied  upon  where  high  scientific 
accuracy  is  required.  They  can,  however,  be  highly  recom- 
mended as  common  house  or  ship  barometers.  Since  the  elas- 
ticity of  the  metal  of  these  barometers  is  liable  to  change  with 
long  use,  it  is  important  to  adjust  the  instruments  from  time  to 
time,  by  comparing  them  with  a  standard  mercury  barometer. 
In  case  of  disagreement,  they  can  easily  be  made  to  accord,  by 
turning  a  screw  provided  for  the  purpose. 

(162.)  Uses  of  the  Barometer.  —  The  barometer  is,  without 
question,. one  of  the  most  useful  instruments  in  the  hands  of  the 
chemist.  The  volumes  of  the  gases  on  which  he  experiments 
are  liable  to  considerable  variations,  depending  on  changes  in  the 


Fig.  267. 


*  From  a  and  vepos,  without  moisture,  since  the  instrument  is  constructed  without 
any  liquid. 


286  CHEMICAL   PHYSICS. 

pressure  of  the  atmosphere  ;  the  boiling  points  of  liquids  are  also 
materially  influenced  by  them  ;  and  it  is  therefore  essential  to 
observe  the  height  of  the  barometer  at  each  experiment,  and  to 
correct  the  results  by  reducing  them  to  that  which  would  have 
been  obtained  had  the  barometer  stood  at  76  c.  m.  at  the  time  of 
observation.  These  uses  of  the  barometer  will  all  be  explained 
in  future  sections  of  this  volume,  and  it  is  not  therefore  neces- 
sary to  dwell  upon  them  here.  As  a  meteorological  instrument, 
the  barometer  is  the  most  important  means  of  investigating  the 
Jaws  of  the  changes  which  are  constantly  taking  place  in  the  at- 
mosphere, —  a  problem  which  is  of  the  greatest  interest  to  man- 
kind. This  atmosphere,  as  has  been  already  stated,  may  be 
regarded  as  a  great  liquid  sea,  and  its  waves  are  constantly  roll- 
ing over  our  heads.  When  the  crest  of  one  of  its  immense  tidal 
waves  is  over  the  barometer,  the  instrument  rises,  and  when  the 
depression  follows,  the  barometer  falls ;  and  thus,  by  watching 
the  height  of  the  mercury  column,  we  are  able  to  follow  changes 
in  the  atmosphere  which  would  otherwise  escape  notice.  For 
many  years  the  height  of  the  barometer  has  been  registered  at 
stated  hours,  night  and  day,  at  a  large  number  of  meteorological 
stations  all  over  the  world  ;  and  although  but  few  general  results 
have  been  obtained,  yet  sufficient  has  been  learned  to  warrant  us 
in  expecting  much  in  the  future. 

The  mean  height  of  the  barometer  during  a  year  at  any  one 
place  is  constant ;  but  it  varies  at  different  latitudes,  gradually 
increasing  from  the  equator  to  the  thirty-sixth  parallel,  and  thence 
diminishing  to  the  pole.  During  the  same  day,  the  barometer 
undergoes  very  regular  oscillations,  which  are  greatest  at  the 
equator.  According  to  Humboldt,  at  the  equator  there  are  two 
maxima,  at  ten  o'clock,  morning  and  evening,  and  two  minima, 
at  four  o'clock,  morning  and  evening ;  the  amplitude  of  the  os- 
cillation during  the  day  amounting  to  2.55  m.m.,  but  that  during 
the  night,  from  four  o'clock  in  the  evening  to  four  o'clock  in  the 
morning,  being  only  0.84  m.  m.  The  same  oscillations  are  no- 
ticed all  over  the  torrid  zone ;  but  in  the  temperate  zone  they 
have  a  less  amplitude,  and  are  more  masked  by  accidental 
changes.  But  nevertheless,  by  comparing  the  means  of  a  large 
number  of  observations  continued  during  a  long  interval,  they 
can  be  detected,  and  nearly  at  the  same  hours.  It  has  been 
further  discovered  that  their  amplitude  is  variable,  being  greater 
in  summer  than  in  winter. 


THE   THREE   STATES   OP   MATTER.  287 

Besides  these  regular  oscillations,  the  barometer  in  temperate 
climates  is  liable  to  apparently  irregular  changes,  produced  by 
storms  in  the  atmosphere.  As  a  general  rule,  it  may  be  stated 
that  during  fair  weather  the  barometer  is  high,  while  it  is  gen- 
erally very  much  depressed  during  a  rain-storm.  So,  also,  a 
sudden  fall  of  the  barometer  usually  indicates  the  approach  of  a 
storm ;  and,  on  the  other  hand,  the  clearing  up  of  a  storm  is 
frequently  preceded  by  a  rise  in  the  mercury  column.  Hence 
one  of  the  most  valuable  uses  of  the  instrument,  in  forewarning 
the  navigator  of  the  approach  of  a  storm.  Those  who  have 
studied  the  indications  of  the  barometer  know  that  they  are  fre- 
quently at  fault,  and  that  they  are  only  probably  correct.  It  is 
hardly  necessary  to  add,  that  the  words  "  Fair,"  "  Rainy,"  etc., 
which  are  frequently  placed  against  certain  points  of  the  scale 
of  common  barometers,  have  no  further  foundation  in  fact  than 
what  has  just  been  stated,  and  are  therefore  simply  useless. 
Sufficient  has  now  been  said  to  show  the  importance  of  baromet- 
ric observations  in  meteorology,  and  we  must  refer  to  the  works 
on  this  science  for  the  details  of  the  subject. 

Mariettas  Law. 

(163.)  Statement  of  Mariotte's  Law. — We  have  already  stated 
that  gases  obey  a  special  law  of  compressibility.  This  law  was 
discovered  independently  by  the  Abbe*  Mariotte  in  France,  and 
by  the  famous  English  philosopher  Boyle,  during  the  last  half 
of  the  seventeenth  century.  It  may  be  thus  stated:  The  vol- 
ume of  a  given  weight  of  gas  is  inversely  as  the  pressure  to 
which  it  is  exposed  ;  that  is,  the  greater  the  pressure,  the  smaller 
is  the  volume,  and  the  less  the  pressure,  the  larger  is  the  volume. 
This  may  be  illustrated  by  an  India-rubber  bag  holding  one  litre 
of  air  or  any  other  gas.  This  is  exposed  to  a  pressure,  under  the 
ordinary  conditions  of  the  atmosphere,  of  a  little  over  one  kilo- 
gramme on  every  square  centimetre  of  surface.  If  this  pressure 
is  doubled,  the  volume  of  the  bag  will  be  reduced  to  one  half;  if 
trebled,  to  one  third,  etc.  On  the  other  hand,  if  the  pressure  is 
reduced  to  one  half,  the  volume  will  be  doubled  ;  if  to  one  third, 
the  volume  will  be  trebled,*  etc.  The  principle  is  expressed  in 
mathematical  language  by  the  proportion, 

V  :  V  =  H1  :  H,  [98.] 

*  We  suppose  the  bag  to  have  no  elasticity. 


288  CHEMICAL  PHYSICS. 

in  which  H  and  H'  are  the  heights  of  the  barometer  which  meas- 
ure the  pressure  to  which  the  gas  is  exposed  under  the  two 
conditions  of  volume  F  and  V. 

It  follows  from  [52],  that  the  density  of  a  given  weight  of 
gas  is  inversely  as  the  volume,  or  F :  V  =  D'  :  D ;  and  by 
comparing  this  proportion  with  the  last,  we  obtain 

D  :  D'  =  H  :  H' ;  [99.] 

or  the  density  of  a  gas  is  proportional  to  the  pressure  to  which 
it  is  exposed.  Moreover,  since  the  weight  of  a  given  volume  of 
gas  is  proportional  to  the  amount  of  matter  which  it  contains  (its 
density),  and  its  density,  as  just  proved,  proportional  to  the  pres- 
sure, it  follows  that  the  weight  of  a  given  volume  of  gas  is  directly 
as  the  pressure  to  which  it  is  exposed;  or 

TF  :  W  =  H  :  H'.  [100.] 

These  three  proportions  are  very  important,  and  will  be  con- 
stantly referred  to  in  the  following  pages.  The  student  must  be 
careful  to  notice,  that  in  [98]  the  weight  of  gas  is  supposed  to 
be  constant  and  the  volume  to  vary,  and  in  [100]  the  volume  is 
supposed  to  be  constant  and  the  weight  to  vary.  It  is  unneces- 
sary to  add,  that,  as  the  volumes  of  gases  vary  also  with  the 
temperature,  the  law  of  Mariotte  is  true  only  so  long  as  the 
temperature  remains  constant. 

The  variations  in  the  pressure  of  the  atmosphere,  amounting 
at  times  to  one  tenth  of  the  whole,  necessarily  cause  equally  great 
changes  in  the  volume  of  gases  which  are  the  objects  of  chemical 
experiment.  Hence,  in  order  to  compare  together  different  vol- 
umes of  gas,  it  is  essential  that  they  should  have  been  measured 
when  exposed  to  the  same  pressure.  A  standard  pressure  has 
therefore  been  agreed  upon,  that  measured  by  seventy-six  cen- 
timetres, to  which  the  volumes  of  gases  measured  under  any 
other  pressure  must  always  be  reduced. 

(164.)  Experimental  Illustration.  —  The  law  of  compressibil- 
ity of  gases  may  be  readily  illustrated  by  the  following  experi- 
ments, which  were  devised  by  Mariotte  himself. 

For  pressures  greater  than  the  atmosphere,  we  use  the  appara- 
tus represented  in  Fig.  268,  which  consists  of  a  glass  tube  bent 
in  the  form  of  a  siphon,  closed  at  the  end  jB,  and  fastened  to  a 
wooden  support.  At  the  side  of  each  arm  of  the  bent  tube  is 


THE   THREE   STATES   OF   MATTER. 


289 


placed  a  graduated  scale,  the  zero  point  of  the  two  scales  being  on 
the  same  horizontal  line.     The  scale  at  the  right  of  the  long  arm 
indicates  centimetres,  and  measures  the  heights  of  the  mercury 
columns,  while  that  at  the  left  of  the  short 
arm  measures  the  volume  of  confined  gas  in 
the  closed  end  of  the  tube.    In  commencing 
the  experiment,  mercury  is  poured  into  the 
tube  at  the  end  C,  and  by  inclining  the 
apparatus  is  brought,  with  a  little  manipu- 
lation, to  stand  at  the  zero  point  on  both 
scales.      The   volume   of    air   confined    in 
the  tube  A  B  is  now  evidently  exposed  to 
the  pressure  of  the  atmosphere,  which  is 
equivalent   to   about  76  c.  m.  of  mercury. 
If,  now,  we  pour  mercury  into  the  tube  C 
until  the  difference  of  level  of  the  mercury 
in  the  tubes  is  76  c.  m.,  the  confined  air 
will  be  exposed  to  a  pressure  of  two  atmos- 
pheres, and  its  volume  will  be  reduced  one 
half,  as  is  represented 
in  the  figure.     If  the 
tube  were  sufficiently 
long,  so  that  we  could 
make  the  difference  of 
the  two  columns  equal 
to  152  c.  m.,  the  vol- 
ume would  be  reduced 
to  one  third.  Were  the 
difference  made  equal 
to  three  or  four  times  76  c.  m.,  the  volume 
would  be  reduced  to  one  fourth  or  one  fifth. 
For  pressures  less  than  an  atmosphere, 
we  use  the  apparatus  represented  in  Fig. 
269,  consisting  of  a  barometer  tube  divided 
into  cubic  centimetres,  and  a  deep  mercury 
cistern,  to  the  side  of  which  is  fastened  a 
scale  divided  into   centimetres   for  meas- 
uring the  differences  of  level.     The  experi- 
ment is  commenced  by  filling  the  barom- 
eter tube  nearly  to  the  top  with  mercury, 
25 


Fig.  268. 


Fig.  269. 


290  CHEMICAL  PHYSICS. 

leaving  a  space  of  only  ten  cubic  centimetres  filled  with  air. 
The  tube,  being  closed  with  the  thumb  and  inverted,  is  sunk  in 
the  mercury  cistern  until  the  mercury  in  the  tube  and  the  cistern 
stands  at  the  same  level  and  at  the  tenth  division  on  the  tube. 
The  confined  air  in  the  tube,  measuring  in  volume  ten  cubic 
centimetres,  is  now  evidently  exposed  to  the  pressure  of  the  at- 
mosphere, which  we  will  suppose  equivalent  to  76  c.  m.  of  mer- 
cury. If,  now,  we  raise  the  tube  in  the  reservoir,  the  level  of  the 
mercury  in  the  tube  will  rise  above  that  in  the  cistern,  as  rep- 
resented in  the  figure.  The  confined  air  is  now  exposed  to  a  less 
pressure  than  76  c.  m.  by  exactly  the  difference  of  level ;  because, 
as  can  easily  be  seen,  the  pressure  of  the  atmosphere  is  in  part 
expended  in  supporting  the  column  of  mercury,  and  only  the  re- 
mainder of  its  pressure  is  exerted  on  the  confined  air.  When, 
therefore,  the  height  of  the  column  of  mercury  in  the  tube  above 
the  mercury  level  in  the  cistern  is  38  c.  m.,  the  pressure  on 
the  confined  air  is  76  —  38c.m.,  or  one  half  of  an  atmosphere, 
and  its  volume  will  be  found  to  have  doubled.  When  the  differ- 
ence of  level  is  equal  to  50.666+  c.  m.,  the  pressure  on  the  con- 
fined air  is  76  —  50.666+  =  25.3+  c.m.,  or  one  third  of  an 
atmosphere,  and  its  volume  will  be  found  to  have  trebled.  When 
the  difference  of  level  is  equal  to  57  c.  m.,  the  air  is  exposed  to 
the  pressure  of  only  one  fourth  of  an  atmosphere,  and  its  volume 
will  be  found  to  have  quadrupled. 

(165.)  History  of  Mariotte' s  Law.  —  The  law  of  the  com- 
pressibility of  gases,  as  established  by  Mariotte,*  was  for  a  long 
time  received  as  absolute  and  invariable;  for  although  Boyle f 
and  Musschenbroek  J  found  that  the  compressibility  diminished 
with  the  pressure,  on  the  other  hand  Sulzer  §  and  Robinson  || 
found  that  it  increased  with  the  pressure ;  and  these  obviously 
inaccurate  results  do  not  appear  to  have  diminished  the  general 
confidence  in  the  law.  In  1826,  Oersted  and  Swendsen  ^f  re- 
peated the  experiments  of  Mariotte,  extending  their  investigation 

*  CEuvres  de  Mariotte,  (La  Haye,  1740,)  Tom.  I.  p.  152. 

t  Boyle's  Defence  of  his  Doctrine  touching  the  Spring  and  Weight  of  the  Air. 
Works,  Vol.  I.  (folio.) 

|  Cours  de  Physique,  (Paris,  1759,)  Tom.  III.  p.  142. 

§  Me'moires  de  1' Academic  de  Berlin,  1753,  p.  116. 

||  System  of  Mechanical  Philosophy,  Vol.  III.  p.  637.  Also,  Encyclopaedia  Britan- 
nica,  Article  Pneumatics,  Vol.  XVI.  p.  700. 

1  Edinburgh  Journal  of  Science,  Vol.  IV.  p.  224. 


THE   THREE   STATES   OF   MATTER.  291 

to  pressures  of  eight  atmospheres,  and  apparently  confirmed  the 
accuracy  of  the  law  ;  for  although  the  numbers  they  obtained  in- 
dicate a  greater  compressibility  than  would  accord  with  the  law, 
yet  they  attributed  the  differences  to  errors  of  observation.  They 
afterwards  extended  their  investigation  to  greater  pressures  than 
eight  atmospheres ;  but  the  method  of  experimenting*  which  they 
employed  was  too  rude  to  establish  the  absolute  accuracy  of  the 
law,  although  it  was  sufficiently  exact  to  show  that  the  law  was 
approximative^  true  up  to  very  high  pressures. 

At  the  time  when  the  law  was  thus  universally  admitted  as 
absolutely  accurate,  M.  Despretz  f  investigated  the  subject  from  a 
new  point  of  view.  Without  questioning  the  law  in  regard  to 
air,  he  merely  sought  to  ascertain  whether  all  gases  obeyed  ex- 
actly the  same  law,  or  whether,  when  submitted  to  the  same 
pressure,  they  indicated  different  degrees  of  compressibility. 
His  experiments  were  conducted  in  the  following  way.  He  took 
a  number  of  cylindrical  tubes,  closed  at  the  top  and  of  the  same 
height,  and  filled  one  of  them  with  air,  but  the  rest  with  different 
gases.  These  were  then  arranged  side  by  side,  standing  in  a  res- 


Fig.  270.  Fig.  271. 

ervoir  of  mercury,  and  supported  against  a  graduated  scale,  as 
represented  in  Fig.  270.     The  apparatus  thus  arranged  was  in- 

*  They  condensed  the  air,  by  means  of  a  force-pump,  into  the  chamber  of  an  air-gun. 
Then  by  means  of  a  balance  they  determined  the  weight  of  air  introduced,  and,  knowing 
the  volume  of  the  chamber,  they  easily  calculated  its  density.  Lastly,  they  determined 
the  elastic  force  of  the  condensed  air  with  the  aid  of  a  safety-valve.  This  valve  was 
closed  by  a  weight  acting  on  the  arm  of  a  lever ;  and  in  the  experiments  the  weight 
was  moved  along  the  arm  until  the  elastic  force  of  the  confined  air  raised  the  valve. 

t  Bullet,  des  Sciences,  Sect.  I.  Tom.  VIII.  p.  325.  Also,  Annales  de  Chimie  et  de 
Physique,  2e  SeVie,  Tom.  XXXIV.  pp.  335,  448. 


292  CHEMICAL  PHYSICS. 

troduced  into  a  glass  cylinder  full  of  water,  similar  to  that  repre- 
sented in  Fig.  271.  This  cylinder  is  connected  with  a  small  force- 
pump,  by  which  water  may  be  forced  into  it,  and  a  pressure  thus 
exerted  on  the  surface  of  the  mercury  in  the  basin.  Before  com- 
mencing the  experiment,  the  level  of  the  mercury  is  made  the 
same  in  all  the  tubes  as  in  the  basin,  so  that  the  gases  they 
contain  are  submitted  to  the  pressure  of  the  atmosphere.  On 
increasing  the  pressure  by  forcing  water  into  the  cylinder,  it  is 
evident  that,  if  the  gases  all  obeyed  Mariotte's  law,  they  would 
all  suffer  the  same  amount  of  condensation  ;  for  example,  when 
the  pressure  had  reached  two  atmospheres,  the  volume  of  each 
gas  would  be  reduced  to  one  half,  and  so  on.  Moreover,  since 
the  tubes  are  perfectly  cylindrical,  an  equal  condensation  would 
be  indicated  by  an  equal  rise  of  the  mercury ;  and  therefore,  if 
the  law  were  general,  the  level  of  the  mercury  would  be  the 
same  in  all  the  tubes,  however  great  the  pressure.  It  is  evident, 
also,  that,  if  the  law  is  not  absolutely  general,  the  apparatus  was 
exceedingly  well  calculated  to  detect  the  discrepancy ;  since  a 
very  slight  difference  in  the  level  of  the  mercury  could  easily  be 
distinguished.  In  fact,  Despretz  found,  on  increasing  the  pressure 
progressively,  that  the  mercury  rose  in  each  tube,  but  rose  un- 
equally. Carbonic  acid  gas,  sulphide  of  hydrogen,  ammonia  gas, 
and  cyanogen,  were  compressed  under  the  same  circumstances 
more  than  air,  and  the  difference  increased  as  the  pressure  was 
augmented.  With  hydrogen,  on  the  other  hand,  a  contrary  effect 
was  observed.  This  gas  acted  like  air  until  the  pressure  rose 
to  fourteen  atmospheres  ;  but  under  greater  pressure  than  this 
it  was  compressed  less  than  air,  and  consequently  maintained  a 
greater  volume. 

These  experiments,  in  which  errors  are  almost  impossible,  — 
since  the  gases  are  placed  under  identically  the  same  conditions, 
—  proved  that  the  law  as  enounced  by  Mariotte  is  not  universal, 
and  that  each  gas  has  a  special  law  of  compressibility.*  More 
recently  these  results  have  been  confirmed  by  Pouillet,f  who 
constructed  an  apparatus  on  a  similar  principle,  by  which  he  was 
enabled  to  continue  the  experiment  up  to  very  great  pressures. 

*  Oersted,  loc.  cit.,  had  previously  noticed  that  sulphurous  acid  gas  was  condensed 
more  than  air,  when  submitted  to  the  same  pressure  in  an  apparatus  very  similar  to  that 
described  above  ;  but  he  attributed  the  phenomena  he  noticed  to  a  partial  condensation 
of  the  gas  to  a  liquid,  and  not  to  a  deviation  from  Mariotte's  law. 

t  Pouillet,  Elements  de  Physique,  5me  edition,  Tom.  I.  p.  339. 


THE   THREE   STATES   OF   MATTER.  293 

The  experiments  of  Despretz  had  proved  that  the  law  of  Mari- 
otte  was  not  general ;  but  it  was  still  supposed  to  hold  true  of  air, 
and  of  the  gases  of  which  air  consists.  This  opinion  was  soon 
after  apparently  confirmed  by  the  celebrated  investigation  of 
Arago  and  Dulong  on  the  elastic  force  of  steam  at  high  temper- 
atures, made  under  the  direction  of  the  French  Academy  of  Sci- 
ences, at  the  request  of  the  government. 

As  a  preliminary  to  the  main  object,  these  distinguished  physi- 
cists determined  the  amount  of  diminution  of  volume  of  at- 
mospheric air  under  increasing  pressure  up  to  twenty-seven 
atmospheres.  The  method  which  they  employed  was  precisely 
the  same  as  that  of  Mariotte.  The  volume  of  the  air  was  meas- 
ured in  a  vertical  glass  tube  one  hundred  and  seventy  centimetres 
long,  graduated  into  parts  of  equal  capacity,  and  forming  the  short 
arm  of  an  inverted  siphon.  The  pressure  was  exerted  by  means 
of  a  column  of  mercury  in  a  glass  tube  twenty-six  metres  high, 
forming  the  longer  arm  of  the  siphon  ;  and  it  was  determined  by 
measuring  the  difference  of  level  of  the  mercury  in  the  two  tubes. 

Although  this  apparatus  was  precisely  similar  in  principle  to 
that  of  Mariotte,  it  was  a  vast  improvement  upon  it,  and  would 
stand  in  the  same  relation  to  Mariotte's  simple  tube  that  a  mod- 
ern chronometer  does  to  a  common  watch.  If  we  had  space,  it 
would  be  interesting  to  describe  the  apparatus  in  detail,  in  order 
to  illustrate  the  advance  which  was  made  in  experimental  science 
during  the  century  and  a  half  which  had  elapsed  since  the  death 
of  Mariotte  in  1684 ;  but  we  must  refer  the  student  to  the  origi- 
nal memoir,*  which  was  presented  to  the  French  Academy  of 
Sciences  on  the  30th  of  November,  1829. 

Arago  and  Dulong  made  three  different  series  of  observa- 
tions. In  each  they  commenced  with  the  gas  in  the  measuring- 
tube  under  the  pressure  of  an  atmosphere,  and  condensed  it 
progressively  by  increasing  the  column  of  mercury  in  the  long 
tube  until  it  attained  the  height  of  several  metres ;  and  after 
each  increase  of  pressure  they  measured  the  volume  of  the  gas 
and  the  difference  of  level  of  the  mercury  in  the  two  tubes. 
In  one  of  these  series  of  experiments,  the  temperature  of  the  gas 
was  kept  constant  (at  13°)  during  the  whole  time,  and  the  pres- 


*  Memoires  de  1' Academic  des  Sciences,  Tom.  X.  ;  and  Annales  de  Chimie  et  de 
Physique,  2<  Serie,  Tom.  XLIII.  p.  74. 

25* 


294 


CHEMICAL   PHYSICS. 


sure  increased  to  twenty-seven  atmospheres.  It  was  the  best 
of  the  three,  and  we  have  copied  the  results  in  the  following 
table  :  — 


Pressure  in 
Atmospheres. 
(Approxi- 
mate.) 

Pressure  in 
Centimetres  of 
Mercury. 

Volume 
Observed. 

Volume 
Calculated. 

Difference. 

Proportion  to 
Observed 
Volume. 

1.00 

76.000 

501.300 

4.75 

361.243 

105.247 

105.470 

+0.223 

0.0021 

4.94 

375.718 

101.216 

101.412 

+0.196 

0.0019 

5.00 

381.228 

99.692 

99.946 

+0.254 

0.0025 

6.00 

462.518 

82.286 

82.380 

+0.094 

0.0011 

6.58 

500.078 

76.095 

76.193 

+0.098 

0.0013 

7.60 

573.738 

66.216 

66.417 

+0.201 

0.0030 

11.30 

859.624 

44.308 

44.325 

+0.017 

0.0004 

13.00 

999.236 

37.851 

38.132 

+0.281 

0.0074 

16.50 

1,262.000 

30.119 

30.192 

+0.073 

0.0024 

17.00 

1,324.506 

28.664 

28.770 

+0.106 

0.0037 

19.00 

1,466.736 

25.885 

25.978 

+0.093 

0.0036 

21.70 

1,653.490 

22.968 

23.044 

+0.076 

0.0033 

21.70 

1,658.440 

22.879 

22.972 

+0.093 

0.0040 

24.00 

1,843.850 

20.547 

20.665 

+0.118 

0.0059 

26.50 

2,023.666 

18.833 

18.872 

+0.039 

0.0020 

27.00 

2,049.868 

18.525 

18.588 

+0.063 

0.0035 

The  first  column  gives  the  pressure  approximatively  in  atmos- 
pheres equal  each  to  seventy-six  centimetres  of  mercury.  The 
second  gives  the  exact  pressure,  as  observed  by  measuring  the 
difference  of  level,  and  subsequently  corrected  for  temperature 
and  the  compressibility  of  mercury.  The  third  column  gives 
the  observed  volume  of  gas  in  the  measuring-tube  under  the 
given  pressure,  which  was  kept  at  the  same  temperature  dur- 
ing the  whole  series  of  experiments.  The  fourth  column  gives 
the  volume  which  the  gas  would  have  under  the  given  pressure 
if  Mariotte's  law  were  absolutely  true.  The  fifth  column  gives 
the  difference  between  the  observed  and  calculated  volumes. 
And,  finally,  the  sixth  column  gives  the  proportion  of  these  dif- 
ferences to  the  observed  volume.  It  will  be  noticed  that  the  dif- 
ferences are  in  all  cases  very  small,  seldom  greater  than  one  two- 
hundredth  of  the  observed  volume,  and  frequently  almost  nothing. 
Moreover,  it  will  also  be  noticed  that,  although  the  differences  are 
always  in  the  same  direction,  indicating  in  every  case  a  greater 
compression  than  that  required  by  Mariotte's  law,  yet  the  propor- 
tion of  these  differences  to  the  observed  volume  does  not  increase 


THE   THREE   STATES   OP   MATTER.  295 

with  the  pressure,  as  would  naturally  be  expected,  if  they  were 
owing  to  an  actual  deviation  from  the  law. 

As  in  any  investigation  of  natural  phenomena  it  is  impossible  to 
measure  quantities  with  absolute  accuracy,  a  limited  amount  of 
error  in  the  observations  is  to  be  expected ;  and  since  the  differen- 
ces just  mentioned  are  very  small,  it  was  natural  to  conclude  that 
they  would  have  disappeared  if  the  measurements  could  have  been 
made  with  absolute  accuracy.  So  concluded  Dulong  and  Arago, 
and  it  was  generally  conceded  that  the  validity  of  the  law  of 
Mariotte  in  regard  to  air  had  been  fully  established  by  their  in- 
vestigations. There  were,  nevertheless,  strong  grounds  for  ques- 
tioning the  accuracy  of  this  conclusion.  In  the  first  place,  there 
was  no  reason,  in  the  nature  of  things,  for  supposing  that  the  law 
of  Mariotte  was  absolutely  true  ;  and  since  it  was  not  exact  in 
the  case  of  so  many  gases,  it  was  reasonable  to  conclude  that  it 
was  not  absolutely  so  in  the  case  of  the  air.  In  the  second  place, 
the  volumes  observed  by  Dulong  and  Arago  were  in  every  case  less 
than  the  calculated  volumes,  a  fact  not  sufficiently  accounted  for  by 
the  construction  of  their  apparatus,  though  they  were  inclined  to 
believe  that  it  was.  Then,  lastly,  their  method  of  experimenting 
was  open  to  serious  objections.  They  measured  the  volume  of  the 
air,  by  means  of  a  graduated  scale  at  the  side  of  the  tube,  with  a 
degree  of  accuracy  which  was  evidently  entirely  independent  of  the 
volume  occupied  by  the  gas  in  the  tube,  whether  large  or  small. 
At  the  commencement  of  the  experiment,  this  volume  occupied 
a  length  of  nearly  two  metres  ;  and  hence  any  error  which  could 
be  made  in  reading  the  scale  would  be  an  insensible  portion  of 
the  whole  ;  but  when,  at  the  end  of  the  experiment,  the  pressure 
was  equal  to  thirty  atmospheres,  the  volume  occupied  in  the 
tube  a  length  of  only  one  fifteenth  of  a  metre,  so  that  the  same 
error  in  reading  the  scale  would  now  correspond  to  a  portion  of 
the  whole  volume  thirty  times  as  great  as  before,  and  might  be 
very  important. 

The  results  of  Dulong  and  Arago  were  not  destined  long  to  re- 
main the  last  word  of  physical  science  on  this  subject.  The  French 
government,  in  1841,  ordered  a  revision  of  the  principal  laws 
and  numerical  data  connected  with  the  theory  of  the  steam- 
engine.  This  work  was  intrusted  to  Victor  Regnault,  and  the 
results  of  his  investigation  occupy  nearly  the  whole  of  the  twenty- 
first  volume  of  the  Memoirs  of  the  French  Academy  of  Sciences. 


296 


CHEMICAL  PHYSICS. 


This  volume  is  a  monument  of  scientific  industry  and  skill,  and 
marks  an  epoch  in  the  history  of  physical  science.  Among  the 
other  numerical  data,  Regnault  carefully  redetermined  the 
amount  of  diminution  of  volume  of  atmospheric  air  under  in- 
creasing pressure.  He  repeated  the  experiments  of  Dulong  and 
Arago  with  a  greatly  improved  apparatus,  and  extended  his  in- 
vestigations to  other  gases.  It  will  not  be  possible,  in  this  text- 
book, to  enter  into  a  description  either  of  the  method  or  of  the 
apparatus  employed.  Suffice  it  to  say,  that,  although  they  were 
similar  in  general  to  those  adopted  by  Dulong  and  Arago,  they 
differed  in  one  important  detail.  Instead  of  keeping  the  quan- 
tity of  the  gas  in  the  measuring-tube  constant  during  the  whole 
experiment,  as  his  predecessors  in  the  same  line  of  investigation 
had  done,  he  continually  forced  fresh  gas,  by  means  of  a  condens- 
ing-pump,  into  the  measuring-tube  as  the  pressure  increased,  and 
thus  had  the  volume  of  gas  in  the  tube  the  same  preparatory  to 
each  measurement.  The  apparatus  was  so  delicately  constructed, 
that  he  could  measure  the  difference  of  level  of  the  mercury  in  the 
two  tubes  to  nearly  the  half  of  a  millimetre,  and  also  the  volume 
of  the  gas  in  the  measuring-tube  with  as  great  an  accuracy  at  the 
highest  as  at  the  lowest  pressures.  We  would  most  earnestly 
recommend  the  student  to  examine  the  original  memoir  of 
Regnault,*  as  one  of  the  best  examples  of  a  successful  scientific 
investigation  on  record.  From  the  results  which  Regnault  ob- 
tained, the  following  table  has  been  calculated  :  — 


Volumes. 

Pressures. 

Air. 

Difference. 

Carbonic 
Acid. 

Difference. 

Hydrogen. 

Difference. 

1 

m. 

1.0000 

m. 
+0.0000 

m. 

1.0000 

m. 

+0.0000 

iToooo 

in. 

-0.0000 

A 

4.9794 
9.9162 

+0.0206 
+0.0838 

4.8288 
9.2262 

+0.1722 
+0.7738 

5.0116 
10.0560 

-0.0116 
-0.0560 

TV 

14.8248 

+0.1752 

13.1869 

+1.8131 

15.1395 

-0.1395 

sV 

19.7198 

+0.2802 

16.7054 

43.2946 

20.2687 

-0.2687 

This  table  supposes  that  a  given  volume  of  gas  is  taken,  not,  as 
usual,  under  the  atmospheric  pressure,  but  under  an  initial  pres- 
sure represented  by  a  column  of  mercury  one  metre  in  height, 
and  then,  by  increasing  the  height  of  the  column  of  mercury,  suc- 
cessively condensed  to  one  fifth,  one  tenth,  one  fifteenth,  and  one 


*  Memoires  de  1'Acade'mie  des  Sciences,  Tom.  XXL  p.  329. 


THE   THREE   STATES    OF   MATTER.  297 

twentieth  of  its  primitive  volume.  It  is  evident,  that,  if  Mari- 
otte's  law  were  invariable,  it  would  require,  in  the  case  of  any  gas, 
pressures  corresponding  to  columns  of  mercury  respectively  five, 
ten,  fifteen,  and  twenty  metres  high  to  produce  this  result.  Now, 
in  the  table,  opposite  to  each  volume,  are  given  the  heights  of 
the  columns  of  mercury  in  metres,  which  are  actually  required, 
as  deduced  from  the  experiments  of  Regnault  on  air,  carbonic 
acid,  and  hydrogen.  In  the  case  of  air  and  carbonic  acid, 
it  will  be  noticed  that  less  pressure  is  required  than  that  indi- 
cated by  the  law.  In  the  case  of  hydrogen,  on  the  other  hand, 
more  is  required.  We  might  put  these  results  in  a  form  simi- 
lar to  that  of  the  table  on  page  294,  and  give  opposite  to  each 
pressure  the  observed  volume  and  the  calculated  volume.  It 
would  then  appear  that  air  and  carbonic  acid  are  condensed 
more  by  a  given  pressure,  and  hydrogen  less,  than  the  amount 
required  by  Mariotte's  law. 

It  appears,  then,  from  these  experiments,  that  Mariotte's  law  is 
not  an  exact  expression  of  the  truth,  even  for  air.  The  deviation 
from  the  law  in  the  case  of  air,  however,  is  exceedingly  small, 
and  it  required  all  the  precautions  with  which  Regnault  guarded 
his  experiments  to  detect  and  measure  it.  In  a  theoretical  point 
of  view,  this  deviation  is  of  the  greatest  importance ;  but  in  the 
practical  application  of  Mariotte's  law  in  the  manometer,  and  in 
the  determination  of  the  volumes  of  gases,  it  may  be  entirely 
overlooked. 

By  carefully  examining  the  table  on  page  296,  it  will  be  noticed 
that  the  deviation  from  the  law,  in  the  case  of  all  three  of  the 
gases,  increases  rapidly  with  the  increase  of  the  pressure.  This 
is  the  general  law  in  regard  to  all  gases  which  have  been  studied. 
Hence  we  may  conclude  that,  as  the  pressure  diminishes  and  the 
gas  expands,  the  deviation  from  the  law  of  Mariotte  becomes 
gradually  less,  until,  at  an  infinite  degree  of  expansion,  this  law 
would  be  the  exact  expression  of  the  truth.  Regnault  did  not, 
however,  extend  his  experiments  to  pressures  less  than  that  of 
the  atmosphere,  because  the  precision  of  his  method  was  not 
sufficient  to  detect  at  such  pressures  any  deviation  from  the 
law. 

The  table  will  also  lead  us  to  another  important  conclusion. 
On  comparing  the  numbers  of  hydrogen  and  of  air,  it  will  be 
found,  as  we  have  already  remarked,  that  they  deviate  from 


298  CHEMICAL   PHYSICS. 

the  law  of  Mariotte  in  opposite  directions.  Starting  from  a 
state  of  infinite  expansion,  at  which  both  would  exactly  obey, 
as  just  stated,  the  law,  it  would  be  found,  on  gradually  in- 
creasing the  pressure,  that  the  volume  of  the  air  diminished  in  a 
greater  proportion,  but  that  of  hydrogen  in  a  less  proportion,  than 
the  pressure.  Here,  then,  are  two  gases,  one  varying  from  the 
law  on  one  side,  and  the  other  on  the  opposite  side.  Between 
these  two  we  may  conceive  of  a  gas  which  should  have  a  com- 
pressibility exactly  conforming  to  the  law.  This  hypothetical 
gas  being  taken  as  the  limit,  we  have  on  the  one  side  a  class  of 
gases,  comprising  air,  nitrogen,  oxygen,  carbonic  acid,  etc.,  which 
have  a  greater  and  constantly  increasing  compressibility,  and  on 
the  other  side  a  single  gas,  hydrogen,  forming  a  class  by  itself, 
and  having  a  less  and  constantly  diminishing  compressibility. 
The  law  of  Mariotte  may,  therefore,  be  regarded  as  a  limit,  not 
realized  in  nature,  from  which  the  different  gases  deviate  on 
either  side  more  or  less,  according  to  their  nature,  as  well  as  ac- 
cording to  the  pressure  to  which  they  are  exposed. 

Some  experiments  of  Kegnault  seem  to  show  that  the  class  to 
which  a  gas  belongs  depends  upon  the  temperature.  He  noticed 
that,  although  carbonic  acid,  as  shown  by  the  table,  deviates  very 
markedly  from  the  law  of  Mariotte  at  the  temperature  of  0°,  yet 
that  it  conforms  almost  precisely  to  it  at  the  temperature  of  100°. 
He  also  noticed  a  similar  fact  in  regard  to  air,  which  was  found 
to  deviate  from  the  law  much  less  at  an  elevated  temperature 
than  at  the  ordinary  temperature  of  the  atmosphere  ;  and  he 
concludes  that  a  temperature  could  easily  be  attained,  at  which 
the  deviation  would  become  insensible  to  our  means  of  observa- 
tion. He  even  thinks  it  probable,  that,  at  a  very  high  tempera- 
ture, the  air  would  again  deviate  from  the  law  of  Mariotte,  but 
in  the  opposite  direction,  namely,  that  in  which  hydrogen  devi- 
ates at  the  ordinary  temperature.* 

Generalizing  these  observations,  it  is  supposed  that  the  same 
would  be  true  of  all  the  gases  belonging  to  the  first  class.  As 
the  temperature  is  increased,  it  is  supposed  that  their  compres- 
sibility would  gradually  diminish,  and  that  they  would  finally 
conform  exactly  to  Mariotte's  law,  at  different  temperatures, 
determinate  for  each  one.  If  the  temperature  were  pushed 

*  Memoires  de  1'Acade'mie  des  Sciences,  Tom.  XXI.  p.  403. 


THE   THREE    STATES    OF    MATTER. 


299 


beyond  this  limit,  it  is  supposed  that  they  would  deviate  anew 
from  the  law,  but  in  an  opposite  direction,  passing  over  into 
the  class  of  gases  of  which  at  the  ordinary  temperature  we  have 
but  one  example,  hydrogen.  On  the  other  hand,  since  hydrogen 
possesses  at  the  ordinary  temperature  of  the  air  the  character 
which  those  gases  have  at  a  high  temperature,  it  is  natural  to 
conclude  that,  by  lowering  the  temperature  sufficiently,  we  should 
bring  this  gas  to  the  condition  in  which  they  exist  at  the  ordinary 
temperature.  We  should  expect  to  find,  that,  at  a  certain  degree 
of  cold,  it  would  conform  exactly  to  the  law  of  Mariotte ;  and  that, 
at  a  still  lower  temperature,  it  would  deviate  from  that  law  again, 
but  in  an  opposite  direction.  It  must  be  admitted,  however,  that, 
although  these  conclusions  are  in  conformity  with  the  analogies 
of  science,  they  are  based  upon  too  slight  experimental  data  to 
make  them  of  much  value  ;  and  further  experiments  on  the  com- 
pressibility of  gases  at  high  temperatures  are  among  the  most 
important  desiderata  of  this  branch  of  science. 

Within  the  last  few  years,  further  experiments  on  the  condensa- 
tion of  air,  nitrogen,  oxygen,  hydrogen,  and  oxide  of  carbon  have 
been  made  by  Natterer  with  a  very  powerful  condensing-appara- 
tus,  with  which  he  has  been  able  to  exert  a  pressure  of  nearly  three 
thousand  atmospheres.  Even  with  this  immense  pressure,  he  did 
not  succeed  in  condensing  these  gases  to  liquids ;  but,  on  the 
contrary,  he  found  that  the  compressibility  in  all  the  five  cases 
was  less  than  that  required  by  Mariotte's  law.  From  his  results, 
the  following  table  *  has  been  calculated  by  interpolation  :  — 


Pressure  in 
Atmospheres. 

Number  of  Volumes  condensed  into  One. 

Hydrogen. 

Oxygen. 

Nitrogen. 

Air. 

Oxide  of 
Nitrogen. 

1 

1 

1 

1 

1 

1 

50 

50 

50 

50 

50 

50 

100 

98 

100 

99 

100 

100 

500 

396 

439 

381 

396 

412 

1,000 

623 

595 

519 

527 

544 

1,354 

.   . 

657 

.  . 

.  . 

.  . 

1,500 

776 

.  . 

590 

607 

617 

2,00& 

899 

.  . 

641 

661 

669 

2,500 

977.5 

.  . 

684 

704 

708 

2,790 

1008 

705 

726 

727 

*  This  table  is  taken  from  Liebig  und  Kopp,  Jahresbericht  fur  1854,  Seite  88.    For 
the  full  results,  see  Wien  Acad.  Ber.  XIL  199,  or  Fogg.  Ann.,  XCIV.  436. 


300  CHEMICAL  PHYSICS. 

Opposite  to  the  number  of  atmospheres  of  pressure  is  given  for 
each  of  the  five  gases  the  number  of  volumes  which  are  con- 
densed by  the  different  pressures  into  one  volume.  In  other  words, 
these  numbers  represent  the  number  of  volumes  into  which  one 
volume  of  the  condensed  gas  would  expand,  if  allowed  to  expand 
freely  under  the  pressure  of  the  atmosphere.  If  the  gases  fol- 
lowed the  law  of  Mariotte,  the  number  of  volumes  would  always 
be  equal  to  the  number  of  atmospheres  of  pressure.  According 
to  these  experiments,  the  number  is  very  much  less  than  this, 
showing  that  at  these  high  pressures  the  compressibility  is  very 
greatly  diminished.  It  will  be  noticed  that  these  results  are  in 
accordance  with  those  of  Regnault  in  regard  to  hydrogen,  but 
directly  opposite  to  them  in  regard  to  the  other  gases.  Since, 
however,  the  experiments  of  Naterer  were  conducted  in  a  man- 
ner not  calculated  to  give  accurate  numerical  results,  they  re- 
quire further  confirmation. 

We  have  dwelt  at  some  length  on  the  history  of  Mariotte's  law, 
both  because  it  furnishes  one  of  the  best  examples  of  refined  sci- 
entific investigation,  and  also  because  it  illustrates  in  a  very 
forcible  manner  the  character  of  a  very  large  class  of  the  so-called 
laws  of  nature.  The  compressibility  of  gases  was  in  the  first 
place  studied  with  a  comparatively  rude  apparatus,  and  a  simple 
law  was  discovered,  which  was  accepted  as  the  absolute  truth. 
Later,  when  the  methods  of  investigation  had  become  more  ac- 
curate, it  was  found  that  the  law  was  not  general,  but  it  was  still 
maintained  in  regard  to  air,  until  finally  the  refined  experiments 
of  Regnault  proved  that  it  failed  here  also.  Still  the  law  remains 
as  an  ideal  truth  towards  which  nature  tends,  but  which  is  never 
fully  reached,  and  we  can  even  trace  the  action  of  the  agents 
which  produce  the  perturbations.  So  is  it  with  most  physical  laws. 
They  are  not  relations  realized  with  mathematical  exactness,  but 
ideal  truths  always  more  or  less  false  in  each  particular  case.  In 
another  place,*  the  author  has  termed  this  class  of  laws,  which 
are  merely  expressions  of  external  phenomena,  phenomenal  laws. 
In  some  few  cases,  as  in  the  law  of  gravitation,  we  have  been 
able  to  go  behind  the  phenomena  to  their  proximate  cause  ;  and 
in  such  cases  the  very  variations  have  been  seen  to  be  neces- 
sary consequences  of  the  law  itself.  So,  possibly,  it  will  be  with 

*  Memoirs  of  the  American  Academy  of  Arts  and  Sciences,  Vol.  V.  p.  369. 


THE   THREE   STATES   OF   MATTER.  301 

the  law  of  Mariotte,  when  we  understand  the  constitution  of  the 
gaseous  condition  of  matter.  But  even  in  regard  to  the  law  of 
gravitation,  there  always  have  been  residual  phenomena  unex- 
plained by  the  law,  and  so  probably  there  always  will  be ;  until, 
as  we  go  on  widening  our  generalizations,  the  last  generaliza- 
tion of  all  brings  us  into  that  Presence  of  which  all  natural  phe- 
nomena are  the  direct  manifestation. 

(166.)  Limit  to  the  Compressibility  of  Gases.  —  It  has  been 
shown  that  all  gases,  when  submitted  to  pressure,  are,  with  one 
exception,  compressed  to  a  smaller  volume  than  that  calculated 
from  the  law  of  Mariotte ;  and  we  have  also  seen  that  the  devia- 
tion from  the  law  increases  rapidly  with  the  pressure.  With  most 
gases,  however,  experiments  prove  that  the  compressibility  does 
not  increase  indefinitely  ;  but  that,  when  the  pressure  reaches  a 
certain  point,  the  gas  changes  into  a  liquid.  This  change  of  state 
takes  place  suddenly,  but  it  is  preceded  by  the  increase  of  the 
compressibility  of  the  gas,  which  has  just  been  noticed,  and  which 
becomes  very  rapid  as  the  point  of  condensation  is  approached. 
Some  persons  have  been  led  by  this  fact  to  the  opinion  that 
the  deviation  from  the  law. of  Mariotte  is  owing  to  a  partial 
liquefaction  of  the  gas  ;  but  the  experiments  of  Regnault  and 
Despretz,  already  cited,  tend  to  disprove  this  theory.  The  pres- 
sure under  which  the  condensation  to  the  liquid  state  takes  place 
depends  upon  the  nature  of  the  gas,  and  also  especially  on  the 
temperature.  We  shall,  therefore,  defer  the  consideration  of  this 
subject  to  the  chapter  on  Heat. 

Application  of  Mariotte1  s  Law. 

(167.)  Pressure  of  the  Atmosphere  at  different  Heights.  — 
Having  become  familiar  with  Mariotte's  law,  we  are  prepared  to 
study  the  variation  of  pressure  as  we  rise  in  the  atmosphere, 
which  has  been  already  noticed  in  (156.  3).  This  question  is 
evidently  one  of  great  importance ;  because,  if  we  can  discover 
the  law  by  which  the  pressure  varies,  we  can  easily  deduce  from 
two  observations  of  the  barometer  made  at  different  heights  the 
difference  of  level  of  the  two  stations. 

It  is  evident,  from  the  nature  of  the  case,  that  the  density  of 

the  atmosphere  must  vary  constantly  with  the  elevation  above 

the  surface  of  the  earth,  and  hence  that  it  is  not  absolutely  the 

same  at  any  two  levels,  however  near  to  each  other.     Neverthe- 

26 


302  CHEMICAL   PHYSICS. 

less,  for  convenience,  we  will  suppose  that  the  atmosphere  con- 
sists  of  a  series  of  very  thin  concentric  layers,  having  a  common 
thickness,  which  we  will  represent  by  d  ;  and  that  the  density  is 
uniform  throughout  each  layer,  changing  abruptly  as  we  pass 
from  one  to  the  next.  Moreover,  in  order  to  reduce  the  ques- 
tion to  its  simplest  form,  we  will  suppose  that  the  temperature 
of  the  atmosphere  at  the  different  elevations  is  the  same,  and  at 
0°  C.  We  may  now  represent  the  different  quantities  to  be  used 
in  our  problem  thus  :  — 

d  =  the  common  thickness  of  the  concentric  layers. 

o?i,  #2,  x3  .  .  .  .  xn  =  the  distances  of  the  lower  surfaces  of  the  successive 

layers  from  the  centre  of  the  earth. 

ffl9  ff2,  Jf2  .  .  .  .  Hn  =  the  heights  of  the  barometer  in  the  successive  layers. 
(iSp.  £r.)b  (Sp.  GV.)a  ....  (Sp.  Gr.)n  =  the  specific  gravity  of  the  air  in 

the  successive  layers,  referred  to  mercury. 

We  have,  then,  for  the  thickness  of  the  first  layer,  #2  —  x\  =  d, 
and  for  the  fall  of  the  column  of  mercury  in  the  height  of  the  first 
layer,  JHi  —  Ht.  It  is  therefore  evident,  that  a  column  of  atmos- 
pheric air  equal  to  x*  —  x{  supports  a  column  of  mercury  equal 
to  Hi  —  HI.  Now,  since  the  air  acts  in  all  respects,  so  far  as 
regards  pressure,  like  a  liquid  of  a  very  small  specific  gravity 
(151),  it  follows  that  the  proportion  [81]  is  true  for  these  two 
columns  of  air  and  mercury.  Eepresenting,  then,  the  specific 
gravity  of  mercury  by  unity,  we  have 


TT  TT  TT 

/•  cr  **  —  ^*  -«  — 

(  o».  L 


Moreover,  since  the  pressure  is  proportional  to  the  density  [99]  , 
it  is  also  proportional  to  the  specific  gravity  ;  and  we  have,  for 
any  two  layers,  such  as  the  first  and  the  wth, 

(Sp.  £r.)i 
or 


Representing  by  C  a  constant  quantity,  we  may  evidently  put 

(Sp.Gr.^=CHh     and      (Sp.Gr.)n=  C  Hn.        [102.] 

The  value  of  C  depends  upon  the  latitude  of  the  place  and  on 
the  conditions  of  the  atmosphere,  as  will  hereafter  be  shown. 


r 

THE   THREE   STATES    OP   MATTER.  303 

Comparing  the  two  values  of  (Sp.  <2r.),,  [101]  and  [102],  we 
obtain 

?^J^  =  CH19      or      H,  =  Hl(l  —  Cd). 
By  the  same  course  of  reasoning  we  should  obtain 

g--#3  =CH^    or  H,=  H2(l  —  Cd)  =  Hl(l—Cdy. 
"We  can  in  like  manner  readily  form  the  following  table  :  — 

X  =  0  ffl  =  ffi' 


x-x,  =  nd,        ffn+l  =  Hn  (l  —  Cd)  =  H,  (1  -  Cd)\ 

The  values  d,  2  c?,  3  d  ----  nd,  which  represent  the  elevations 
above  any  given  level,  are  evidently  terms  of  an  increasing  arith- 
metical progression  ;  and  the  values  of  JETi,  H^  H^  .  .  .  .  HnJ  which 
represent  the  pressures  at  these  elevations,  are  evidently  terms  of 
a  geometrical  progression,  —  since  each  value  is  formed  from  the 
preceding  by  multiplying  by  the  constant  quantity  (1  —  <7d). 
Moreover,  since  the  value  of  this  quantity  is  less  than  unity,  the 
progression  is  decreasing. 

From  the  equation  Hn  +  ,=  HY  (1  —  C  d)n,  we  can  easily  ob- 
tain a  formula  for  calculating  the  difference  of  elevation  from  the 
height  of  the  barometer  at  any  two  stations.  Taking  the  loga- 
rithms of  the  two  members,  this  equation  becomes 

log  Hn+l  —  log  .Hi  =  n  log  (1  —  C  d),  or,  developing, 


"We  have  assumed  that  the  common  thickness  of  the  atmospheric 
layers  (d)  was  only  very  small.  We  may  now  pass  at  once  to  the 
actual  condition  of  the  atmosphere  by  making  d  infinitely  small. 
The  d2,  d3  .  .  .  .,  being  all  infinitely  less  than  d,  may  be  taken  at 
zero,  and  the  equation  becomes 

0 
log  Hn+  l  —  loQHl  =  —nd-^f-9 

or,  changing  the  signs  of  all  the  terms,, 

log  H,  —  log  Hn  +  !  =  n  d  -^  ; 


304  CHEMICAL  PHYSICS. 

from  which  can  be  easily  deduced 

,       ,        H,       M 


In  this  formula,  n  d  is  obviously  the  sum  of  the  thicknesses  of  the 
infinitely  thin  layers  between  the  levels  of  the  two  stations,  and 
is  therefore  the  quantity  required.  We  will  represent  it  by  x. 
M  is  the  modulus  of  the  common  tables  of  logarithms,  or 
2.302585.*  C  is  the  constant  already  mentioned.  Hn_l  is  the 
height  of  the  barometer  of  the  upper  station,  which  we  can  more 
conveniently  represent  simply  by  h  ;  and  HI  the  height  at  the 
lower  station,  which  we  can  more  conveniently  represent  by  H. 
The  formula  then  becomes 


The  constant,  (7,  in  this  equation  is  a  quantity  which,  multi- 
plied by  the  height  of  the  barometer,  will  give  the  specific  grav- 
ity (relatively  to  mercury)  of  the  air  in  which  the  barometer  is 
immersed  [102].  "We  shall  hereafter  have  occasion  to  show  that 
the  weight  of  one  cubic  centimetre  of  air,  and  hence  also  its  spe- 
cific gravity,  varies  not  only  with  the  pressure  H9  but  also  with 
the  elastic  force  of  the  vapor  which  it  contains,  with  the  tempera- 
ture, and  with  the  intensity  of  the  force  of  gravity  at  the  place 
of  observation.  All  these  circumstances  must,  therefore,  modify 
the  value  of  the  constant  C.  If,  however,  we  reduce  the  condi- 
tions to  their  simplest  form,  and  suppose  that  the  temperature 
is  0°  C.  at  both  stations,  that  the  place  of  observation  is  on  the 
parallel  of  45°,  and  that  the  atmosphere  is  one  half  saturated 

with  vapor,  we  have,  for  the  value  of  the  constant,  -^  =  18,336 

metres  ;  and,  neglecting  the  variation  of  the  intensity  of  gravity 
with  the  elevation,  [103]  becomes  f 

x  =  log  ^18336  =  log  H  18336  —  log  h  18333  ;        [104.] 

*  Some  writers  use  as  M  the  reciprocal  of  this  value. 

t  It  is  evident  that  these  conditions  are  never  realized  in  the  atmosphere.  The  tem- 
perature diminishes  very  rapidly  as  we  ascend  ;  and  the  force  of  gravity  varies  with  the 
elevation,  as  well  as  with  the  latitude  of  the  place  of  observation.  In  the  practical 
application  of  this  method  in  determining  differences  of  level,  it  is  necessary  to  pay  re- 
gard to  all  these  circumstances.  The  eminent  mathematician  La  Place  calculated  a 
formula  for  finding  the  value  of  x,  in  which  all  the  causes  which  may  modify  the  pres- 


THE   THREE   STATES   OF    MATTER.  305 

in  which  H  and  h  denote  the  height  of  the  barometer  in  millime- 
tres. If,  further,  we  suppose  that  the  lower  station  is  at  the  sea 
level,  and  that  the  barometer  at  this  level  is  at  its  mean  height, 
or  TGO  m.  m.,  the  formula  becomes 

x  =  52,822.6  metres  —  log  h  18336.  [105.] 

sure  of  the  different  layers  of  the  atmosphere  have  been  considered.     In  this  formula, 
the  letters  denote  the  following  values  :  — 
H  =  height  of  barometer  at  the  lower  station. 

T  =  temperature  of  barometer  at  the  lower  station. 

t  =  temperature  of  the  air  at  the  lower  station. 

k>  =  height  of  barometer  at  the  upper  station. 
T'  =  temperature  of  barometer  at  the  upper  station. 

t1  =  temperature  of  the  air  at  the  upper  station. 

A  =  latitude  of  the  place  of  observation. 

x  =  in  the  fourth  factor  the  approximate  height  determined  from  the  previous  factors. 

The  formula  of  La  Place  is  then  as  follows  :  — 

4. 


1  2.  3 

[log  //  18336  — log  h'  18336  —  (T—  T')  1.2843]  X  \    (1  +  0.00265  cos  2  A), 

6. 

'          z  + 15926% 
.  6366198  /' 

which  does  not  differ  materially  from  the  complex  equation  of  the  Mtamiqne  Celeste 
(CEuvres  de  La  Place,  Tom.  IV.  p.  328,  Paris,  1845).  The  terms  and  factors  of 
the  formula  have  been  numbered  for  the  sake  of  reference.  The  first  two  terms  are  the 
same  as  in  [104],  and  give  the  approximate  elevation.  The  third  term  is  a  correction 
for  the  difference  of  temperature  of  the  mercury  columns  at  the  stations.  The  correct- 
ed altitude  is  now  to  be  multiplied  by  three  factors.  The  first  (marked  4)  corrects  it 
for  the  difference  of  temperature  of  the  air  at  the  two  stations  ;  the  second  (5),  for  the 
variation  of  gravity  with  the  latitude ;  and  the  third  (6),  for  the  variation  of  gravity 
with  the  elevation.  The  calculation  of  the  value  of  x  is  rendered  exceedingly  easy  by 
means  of  a  set  of  tables,  originally  prepared  by  Oltmans,  which  are  given  in  the  Annu- 
aire  du  Bureau  des  Longitudes  of  Paris.  Similar  but  more  extended  tables,  calculated 
by  Delcros,  Guyot,  and  Loomis,  are  contained  in  the  collection  of  Meteorological 
Tables  prepared  by  Professor  Arnold  Guyot,  and  published  by  the  Smithsonian  Insti- 
tution. 

M.  Babinet  (Comptes  Rendus  de  TAcade'mie  des  Sciences  for  March,  1857)  has  pro- 
posed a  modification  of  La  Place's  formula,  which  dispenses  both  with  the  use  of  loga- 
rithms and  with  tables  of  any  kind.  The  notation  is  the  same  as  before,  but  the  two 
.barometers  are  supposed  to  be  reduced  to  the  same  temperature,  and  the  small  correc- 
tion for  the  latitude  is  omitted.  The  modified  formula  is  as  follows  :  — 

Hi  —  A'o     /      .    2(f  +  tf)\ 

x  =  16,000  metres   rr^r-r:     ( 1  H WA—^  j« 

x/o  ~r « o     ^  1000      / 

In  using  this  formula,  the  two  heights  of  the  barometer  must  first  be  reduced  to  zero, 
and  it  will  then  give  accurate  results  for  elevations  of  less  than  1000  metres,  and  ap- 
proximate results  even  for  much  greater  elevations.  For  further  information  on  thia 

26* 


Bulk  of  equal 
Weight  of  Air. 

Specific  Gravity. 
Air  at  76  c.  m.  =  1 

Height  of 
Barometer. 

1  c.  m.3 

1 

76.00 

2    " 

i 

38.00 

4    « 

i 

19.00 

8    « 

^ 

9.50 

16    " 

TV 

4.75 

32    « 

2.38 

306  CHEMICAL   PHYSICS. 

From  this  formula,  it  is  easy  to  calculate  the  pressure  and  spe- 
cific gravity  of  the  atmosphere  at  different  elevations,  on  the 
assumption  that  its  condition  is  as  just  supposed ;  and  by  means 
of  it  the  following  table  has  been  constructed. 

Pressure  and  Specific  Gravity  of  the  Air  at  increasing  Altitudes. 

Metres  above 
the  Sea. 

0 
5,520 

11,040 
16,560 
22,080 
27,600 

This  table  illustrates  the  fact  already  stated  on  page  303  ;  for 
while  the  elevation  above  the  sea  level  increases  in  an  arithmeti- 
cal progression,  the  height  of  the  barometer  and  the  specific 
gravity  diminish  in  a  geometrical  progression.  Dr.  Young  has 
calculated  that,  if  the  air  continues  to  diminish  in  specific  gravity 
according  to  the  law  indicated  in  the  above  table,  one  cubic  inch 
of  air,  of  the  mean  specific  gravity  at  the  earth's  surface,  would, 
at  a  distance  of  four  thousand  miles  from  the  earth  (a  distance 

subject,  we  would  refer  the  student  to  the  excellent  collection  of  tables  by  Professor 
Guyot,  already  mentioned. 

In  taking  observations  of  the  barometer  for  the  purpose  of  measuring  heights,  certain 
precautions  are  indispensable,  in  order  to  obtain  good  results.  If  the  horizontal  distance 
between  the  stations  is  considerable,  it  is  necessary  to  make  the  two  observations  si- 
multaneously, in  order  to  eliminate  the  effect  of  the  accidental  changes  to  which  the 
barometer  is  liable ;  or,  if  this  is  impossible,  to  return  to  the  first  station,  and  ascertain 
whether  the  pressure  has  changed  in  the  interval.  If  it  has,  the  observation  should  be 
•rejected.  But  even  this  method  of  observing  will  not  eliminate  the  effects  of  the  regu- 
lar changes,  because  these  are  not  necessarily  the  same  at  the  two  stations,  and  do  not 
take  place  at  precisely  the  same  moment,  especially  when  the  difference  of  elevation  is 
considerable.  The  same  is  also  more  or  less  true  of  the  accidental  changes.  In 
order  to  eliminate  all  these  causes  of  error,  it  is  best  to  make  a  great  number  of  obser- 
vations simultaneously  at  both  stations,  and  to  take  the  mean  ;  and  this  course  is  es- 
sential when  the  two  stations  are  several  miles  apart.  For  example,  in  finding  the 
elevation  of  a  place  above  the  sea  level,  it  is  best  to  take  the  barometric  mean  of  the 
place,  calculated  from  observations  extending  over  several  years,  and  compare  it  with 
a  similar  mean  taken  at  the  sea  level.  In  the  tropics,  where  the  accidental  variations 
barely  exist,  and  where  the  regular  variations  follow  well-known  laws,  accurate  results 
can  be  obtained  by  taking  successive  observations  at  the  different  stations.  With  good 
instruments  and  careful  observation,  the  difference  of  level  can  be  ascertained,  from 
the  formula  of  La  Place,  within  a  metre. 


• 

THE   THREE   STATES   OF   MATTEB.  307 

equal  to  the  earth's  radius),  fill  the  whole  orbit  of  Saturn  ;  and, 
on  the  other  hand,  if  a  mine  could  be  dug  forty-six  miles  deep 
into  the  earth,  that  the  air  at  the  bottom  would  be  as  dense  as 
quicksilver. 

It  has  already  been  stated,  that  there  is  probably  a  limit  to  the 
upper  surface  of  our  atmosphere,  as  definite  as  that  of  the  sur- 
face of  the  ocean.  At  this  elevation,  the  repulsive  force  of  the 
particles  is  supposed  to  be  balanced  by  their  gravitation  towards 
the  earth.  If  we  assume  that,  at  this  point,  the  repulsive  force 
is  equal  to  a  column  of  mercury  one  millimetre  high,  we  can 
easily  calculate  the  height  of  the  atmosphere.  The  second  term 
of  the  second  member  of  [105]  disappears,  since  log  1  =  0,  and 
we  obtain  x  =  52,822.6  metres.  But  this  assumes  that  the  tem- 
perature is  the  same  at  this  high  elevation  as  at  the  surface, 
namely,  0°.  The  probability  is  that  the  temperature  is  about 
— 60°  C.  We  must,  therefore,  make  a  correction  for  this  differ- 
ence, amounting,  as  follows  from  La  Place's  formula,  (see  note, 
p.  304,)  to  0.12  of  the  whole,  which  reduces  the  height  to 
46,483.9  metres. 

Instruments  illustrating'  the  Properties  of  Gases. 

(168.)  Manometers.  —  This  name  (derived  from  Awnxk,  rare, 
and  perpov,  measure)  is  applied  to  a  class  of  instruments  which 
are  used  for  measuring  the  elastic  force  or  pressure  of  confined 
gases  and  vapors.  Of  the  numerous  forms  of  the  manometer, 
we  shall  describe  but  three. 

1.  For  pressures  less  than  the  atmosphere,  the  most  convenient 
form  of  manometer  for  the  laboratory  is  that  represented  in  Fig. 
272,  at  the  side  of  the  barometer.  It  consists  simply  of  a  tube, 
open  at  both  ends.  The  lower  end  dips  into  a  reservoir  of  mer- 
cury, and  the  upper  end  connects,  by  a  flexible  hose,  with  the 
vessel  containing  the  gas  or  vapor  whose  pressure  we  wish  to 
measure.  If  the  gas  exerts  no  pressure,  or,  in  other  words,  if 
there  is  a  vacuum  in  the  vessel,  it  is  evident  that  the  mercury 
will  stand  at  the  same  height  in  the  tube  as  in  the  barometer ; 
and,  on  the  other  hand,  if  the  gas  exerts  pressure,  the  mercury 
will  be  depressed  by  the  exact  amount  of  this  pressure.  By 
measuring  with  a  cathetometer  the  difference  of  level  in  the 
barometer  and  manometer  tubes,  we  can  ascertain  the  exact 
amount  of  the  pressure,  or  tension,  of  the  confined  gas. 


308 


CHEMICAL  PHYSICS. 


Fig.  272. 

2.  The  form  of  manometer  represented  in  Fig.  273,  which  we 
owe  to  Regnault,  may  be  used  both  for  pressures  greater  and  less 
than  that  of  the  atmosphere.  It  consists  of  two  glass  tubes,  g  h 
and  i  k,  which  are  cemented  into  an  iron  U,  (made  as  represent- 
ed in  Figs.  276,  277,  and  278,)  and  form  together  an  inverted 
siphon.  Between  the  two  arms  of  the  siphon,  and  forming  a 
part  of  the  iron  U,  is  placed  a  three-way  cock,  whose  construc- 
tion is  sufficiently  explained  by  the  figures.  According  to  the 
position  which  we  give  to  this  cock,  we  may  either  open  or  close 
the  communication  between  the  glass  tubes,  or  vent  the  mercury 


THE   THREE   STATES   OF   MATTER. 


309 


from  either  tube  alone,  or  from  both  together,  at  pleasure.  The 
tube  i  k  is  open  at  the  top,  and  the  mercury  column  which  it 
contains  receives  the  pressure  of  the  atmosphere.  The  tube  g*  h 


Fig.  273.  Fig   276. 

terminates  in  a  capillary  tube,  which  is  bent  at  right  angles,  and 
connected  with  the  vessel,  a  6,  containing  the  gas  or  vapor  whose 
elasticity  we  wish  to  measure,  by  a  connection  of  peculiar  con- 
struction, and  admirably  adapted  for  experiments  of  this  kind. 
To  the  end  of  the  tube  b  g  is  cemented  the  steel  cap  a1  b'  d, 
which  is  represented  in  Fig.  274.  The  face  of  this  cap  is  formed 


276. 


Fig.  277. 


Fig.  278. 


by  a  plane  surface,  a'  b',  and  by  a  hollow  cone,  o'.  On  the  other 
hand,  the  face  of  the  stopcock  which  closes  the  reservoir  has 
exactly  a  reverse  form,  and  the  two  are  carefully  ground  to- 
gether. In  order  to  secure  a  joint  which  is  absolutely  hermeti- 
cal,  it  is  only  necessary  to  press  the  two  together  by  means  of 


310 


CHEMICAL   PHYSICS. 


a  brass  collar  (Fig.  275),  which  is  tightened  by  means  of  the 
screws,  after  having  interposed  a  little  melted  India-rubber. 
The  elasticity  of  the  gas  in  the  reservoir  a  b  is  measured  by 
the  difference  of  the  level  of  the  mercury  in  the  two  arms  of  the 
tube,  and  by  the  height  of  the  barometer.  If  the  level  is  the 
same,  then  it  is  evident  that  the  elasticity  is  exactly  equal  to 
the  atmospheric  pressure,  and  is  measured  by  the  height  of  the 
barometer.  If  the  level  is  higher  in  the  tube  h  g-  than  in  i  k, 
then  the  elasticity  is  measured  by  the  height  of  the  barometer 
less  the  difference  of  level.  On  the  other  hand,  if  the  level  is 
highest  in  the  tube  *  &,  then  the  elasticity  is  measured  by  the 
height  of  the  barometer  plus  the  difference  of  level.  Represent- 
ing the  elasticity  by  $,  the  height  of  the  barometer  reduced  to 
0°  by  H,  and  the  difference  of  level,  also  reduced  to  the  stand- 
ard temperature,  by  h0,  we  have  in  every  case 

%  =  H0  ±  h0.  [106.] 

3.  The  form  of  manometer  just  described,  although  an  ex- 
ceedingly accurate  instrument,  cannot  be  conveniently  used 
when  the  elasticity  is  greater  than  two  atmospheres,  because, 
when  the  difference  of  level  exceeds  76  c.  m., 
the  tube  i  k  must  be  made  inconveniently  long, 
and  the  instrument  becomes  difficult  to  manage. 
Where  great  accuracy  is  not  necessary,  we  can 
then  use  with  advantage  a  form  of  the  manom- 
eter which  is  represented  in  Fig.  279,  and  which 
is  based  on  Mariotte's  law ;  for  although,  as  we 
have  seen,  this  law  is  not  rigorously  true,  even 
in  regard  to  air,  yet  the  deviation  is  so  small 
that  it  may  be  regarded  as  exact  for  all  prac- 
tical purposes. 

This  third  form  of  manometer  consists  of  a 
cylindrical  glass  tube,  closed  at  the  top  and 
filled  with  dry  air.  The  lower  end  of  the  tube 
passes  through  the  collar  of  a  cast-iron  reservoir, 
and  dips  under  the  surface  of  the  mercury,  with 
which  it  is  in  part  filled.  At  the  side  of  the 
rig.  279.  reservoir  is  an  opening  which  connects  by  the 

tube  A  with  the  closed  vessel  or  boiler  contain- 
ing the  gas  or  vapor  whose  elastic  force  is  to  be  measured. 


THE  THREE   STATES   OF   MATTER. 


311 


The  whole  apparatus  is  fastened   to  a  wooden  plank  for  con- 
venience and  security. 

The  quantity  of  the  air  contained  in  the  glass  tube  is  such 
that,  when  the  opening  at  A  communicates  with  the  atmosphere, 
the  mercury  stands  at  the  same  level  in  the  tube  and  reservoir. 
Consequently,  opposite  to  this  level  on  the  plank  is  marked  the 
figure  1.  If,  now,  a  pressure  is  transmitted  through  A  equal  to 
two  atmospheres,  the  mercury  will  rise  in  the  tube  until  the  ten- 
sion of  the  confined  air,  added  to  the  pressure  of  the  mercury 
column,  just  balances  it.  Were  it  not  for  the  weight  of  the  mer- 
cury, it  would  rise  to  just  one  half  of  the  height  of  the  tube  ;  but 
in  fact  it  rises  .to  somewhat  less,  because  a  part  of  the  pressure  is 
supported  by  the  mercury  column  itself.  In  like  manner,  if  the 
pressure  is  increased  to  four  atmospheres,  the  mercury  does  not 
rise  to  three  quarters  of  the  height  of  the  tube,  because  the  pres- 
sure is  in  part  sustained  by  the  column  of  mercury,  and  is  not, 
therefore,  all  transmitted  to  the  confined  gas.  It  is  easy  to  cal- 
culate the  exact  point  to  which  it  will  rise  when  the  height  of  the 
tube  is  known,  and  to  graduate  the  instrument  by  inscribing  the 
number  of  atmospheres  at  the  side  of  the  tube.  This  instrument 
is  not  sufficiently  delicate  for  high  pressures  ;  for,  the  volume  of 
the  air  becoming  smaller  and  smaller,  the  divisions  become  pro- 
portionally close  together. 

The  metallic  manometer  of  Bourdon,  based  on  the  elasticity  of 
metals,  has  been  already  described  (104). 

(169.)  Pneumatic  Trough,  —  This  simple  contrivance,  which 
we  owe  to  Dr.  c 

Priestley,  for  col- 
lecting and  trans- 
ferring gases,  is 
one  of  the  most 
valuable  instru- 
ments of  chemis- 
try. It  consists 
usually  of  a  rec- 
tangular trough, 
made  of  glass  or 
of  any  other  suit- 

,  ,  .    ,       .  Fig.  280. 

able   material,   in 

which  is  suspended  a  shelf,  as  represented  in  Fig.  280.     The 


312 


CHEMICAL   PHYSICS. 


shelf  is  perforated  with  one  or  more  holes,  and  its  under  surface 
is  concave.  When  in  use,  the  trough  is  filled  with  water  to  a 
level  which  is  one  or  two  inches  above  the  shelf.  In  order  to  col- 
lect a  gas,  a  glass  jar  or  bell  is  first  filled  with  water,  and  then 
placed  on  the  shelf  with  its  mouth  downwards  and  over  the  hole. 
The  tube  conducting  the  gas  is  now  adjusted  so  that  its  mouth 
shall  open  under  the  shelf,  when  the  gas,  as  it  escapes,  will  bubble 
up  and  displace  the  water  sustained  in  the  jar  by  the  pressure  of 
the  air.  After  one  jar  is  filled  with  gas,  it  may  be  moved  to  one 
side,  and  its  place  supplied  with  another,  previously  filled  with 
water,  as  before ;  or  the  jar  may  be  removed  from  the  trough  by 
sliding  under  its  open  mouth,  still  immersed  in  water,  a  plate. 
On  lifting  the  plate  from  the  trough,  it  will  hold  sufficient  water 
to  retain  the  gas  in  the  bell  standing  on  it.  We  can  also  readily 
transfer  gases  from  one  jar  to  another  by  filling  the  jar  to  receive 
the  gas  with  water,  placing  its  mouth  over  the  hole  in  the  shelf, 
and  then  pouring  up  the  gas  from  the  other  jar. 

A  very  simple  pneumatic  trough  may  be  made  with  an  earthen- 


281. 


.V        " 


ware  basin  of  water,  as  represented  in  Fig.  281.     The  jar  in 
which  the  gas  is  to  be  collected  can  be  readily  put  in  its  place  in 
the  following  way.      It   is   first   filled   with 
water,  and   a  glass  plate   pressed  with  the 
hand  over  the  mouth.     It  is  then  inverted, 
the  mouth  plunged  under  the  water  of  the 
basin,  and  the  glass  plate  removed.      The 
mouth  of  the  jar  may  be  conveniently  supported  on  an  inverted 


Fig.  282. 


THE   THREE   STATES   OF   MATTER. 


313 


saucer,  in  which  two  holes  have  been  perforated,  as  represented  in 
Fig.  282.  Through  the  hole  at  the  side  passes  the  end  of  the 
tube  conducting  the  gas. 

There  are  many  gases  which  are  absorbed  by  water,  and  in  ex- 
perimenting on  these  we  use  a  trough  filled  with  mercury.  Such 
a  trough  is  represented  in  Fig. 
283,  and  two  vertical  sections 
of  the  same  in  Fig.  284.  On 
account  of  the  cost  of  mer- 
cury, the  mercury  trough  is 
made  in  such  a  form  as  to 
economize  as  far  as  possible 
the  metal.  In  other  respects, 
it  is  precisely  similar  to  the 
water-trough,  and  does  not 
require  a  detailed  descrip-  Fig.  288. 

tion. 


Fig.  284. 


In  measuring  the  volume  of  a  gas  standing  in  a  graduated  bell 
over  the  pneumatic  trough,  it  must  be  remembered  that  the  gas 
is  ndt  exposed  to  the  pressure  of  the  atmosphere  as  indicated  by 
the  barometer,  except  when  the  level  of  the  liquid  is  the  same 
both  in  the  bell  and  in  the  trough.  When  the  level  is  higher  in 
the  bell,  then  the  pressure  exerted  on  the  gas  is  evidently  meas- 
ured by  the  height  of  the  barometer  H0  less  the  height  of  a  col- 
umn of  mercury  A0,  which  is  equivalent  to  the  difference  of  level. 
If  the  trough  is  filled  with  mercury,  this  height  is  equal  to  the 
difference  of  level ;  if  with  water,  we  can  always  easily  find,  by 
[81],  the  height  of  the  column  of  mercury,  which  is  equivalent 
to  the  difference  of  water  level,  or,  more  readily,  by  inspection 
from  Table  XIX.  Let  us  call  this  difference  of  level,  reduced  to 
centimetres  of  mercury  at  0°  C.,  h0.  In  order,  then,  to  reduce  the 
27 


314 


CHEMICAL   PHYSICS. 


volume  of  gas  to  the  standard  pressure  of  76  c.  m.,  we  have,  by 
[98J,  the  proportion 


'=H0—h0:  76, 


or 


[107.] 


The  difference  of  level  may  always  be  measured  by  a  cathe- 
tometer,  or  more  rudely  by  a  graduated  scale.     We  can   also 

avoid  this  measurement  by  sinking 
or  raising  the  bell  in  the  trough 
until  the  level  is  the  same  in  both 
(see  Fig.  285).  This  is  not,  how- 
ever, so  accurate  a  method. 


Fig.  285. 


Fig-  286. 


(170.)  Gasometers.  —  These  are  instruments  for  collecting 
and  preserving  larger  volumes  of  gas.  They  have  various  forms, 
but  that  represented  in  Fig.  286  is  one  of  the  most  useful.  It 
consists  of  a  closed  and  air-tight  cylindrical  vessel,  A,  made  of 
copper  or  zinc,  which  is  surmounted  by  a  basin,  C.  This  basin  is 
supported  on  the  cylinder  by  five  columns  of  copper,  two  of  which, 
a  and  6,  are  hollow,  and  furnished  with  stopcocks.  The  tube  a 
opens  at  once  into  the  the  top  of  the  cylinder ;  but  the  tube  b,  on 
the  contrary,  descends  quite  to  the  bottom.  At  c,  there  is  a  small 
stopcock  for  drawing  off  the  gas ;  and  at  d,  a  short  curved  tube, 
which  can  be  hermetically  closed  by  the  screw-plug  k. 

In  order  to  use  the  instrument,  we  commence  by  pouring 
water  into  the  basin  C,  having  first  closed  the  opening  d,  and 
opened  the  stopcocks  a  and  b.  The  water  now  flows  into  the 
cylinder  by  the  long  tube  ft,  and  the  air  escapes  by  the  tube  «, 
and  we  continue  pouring  water  into  C  until  the  cylinder  A  is 


THE   THREE   STATES    OF   MATTER. 


315 


completely  filled,  when  we  close  the  stopcocks  a  and  b.  In  order, 
now,  to  fill  the  cylinder  with  gas,  we  open  the  tubulature  &,  and 
introduce  the  mouth  of  the  tube  connecting  with  the  vessel  from 
which  the  gas  is  evolved.  The  pressure  of  the  air  sustains  the 
water  in  the  gasometer,  and  the  gas,  as  it  bubbles  up,  collects  in 
the  upper  part,  displacing  the  water,  which  slowly  flows  from  the 
tubulature.  When  the  evolution  of  gas  has  ceased,  we  remove 
the  tube  and  close  the  tubulature  d. 

If  now  we  open  the  cock  &,  a  portion  of  the  water  from  the 
vessel  C  descends  into  the  cylinder,  and  the  confined  gas  is  com- 
pressed by  the  force  of  a  column  of  water  equal  in  height  to  the  dif- 
ference of  level  of  the  water  in  the  two  vessels  A  and  C.  Hence, 
on  opening  the  cock  c,  the  gas  will  flow  out,  and  its  place  will  be 
supplied  with  water  from  the  vessel  C.  Or,  if  we  wish  to  fill  a 
bell  with  gas,  we  first  fill  it  with  water,  cover  the  mouth  with  a 
glass  plate,  and,  having  inverted  it  in  the  vessel  C,  place  it  over 
the  tube  a.  On  opening  the  cock,  the  gas  will  rise  into  the  bell 
and  displace  the  water  it  contains,  while  an  equivalent  amount 
of  water  will  descend  by  the  tube  b  into  the  cylinder. 

(171.)  Safety- Tubes.  —  These  tubes,  which  are  frequently 
connected  with  chemical  apparatus  for  the  purpose  of  avoiding 
explosions,  or  preventing  the  mixing  of  liquids  which  the  vessels 
composing  the  apparatus  contain,  are  excellent  illustrations  of  the 
properties  of  gases.  Let  us  suppose,  for  example,  that  we  are 
preparing  chlorine  gas  from  hyperoxide  of  manganese  and  chlo- 
rohydric  acid,  in  the  flask  A  (Fig.  287), 
and  that  connected  with  this  flask  by  the 
bent  tube  a  b  c  is  a  test-glass  filled  with 
a  solution  of  caustic  soda,  on  which  we 
wish  the  gas  to  act,  and  which  absorbs 
it  rapidly.  So  long  as  the  chlorine  is 
evolved  with  great  rapidity  the  process 
goes  on  with  regularity,  and  the  gas  bub- 
bles up  through  the  solution. 

The  elastic  force  of  the  chlorine  gas  in 
the  flask  is  evidently  greater  than  the 
pressure  of  the  atmosphere ;  because  it 

balances  not  only  the  atmospheric  pressure  on  the  solution  of 
caustic  soda,  but  also  a  column  of  this  solution  whose  height, 
a  (Fig.  287),  is  equal  to  the  difference  of  level  between  the  surface 
of  the  liquid  in  the  test-glass  and  the  open  mouth  of  the  gas- 


Fig.  287. 


816 


CHEMICAL   PHYSICS. 


tube  c.  The  pressure  of  the  atmosphere  is  measured  by  H^  the 
height  of  the  column  of  mercury  which  it  supports.  We  may 
also  measure  the  pressure  exerted  by  the  column  of  liquid  a  in 
the  same  way  ;  for  when  we  know  its  specific  gravity,  it  is  easy, 
by  [81],  to  find  the  height  of  a  column  of  mercury  which 
would  exert  the  same  pressure.  Let  hQ  represent  the  height  of 
this  column  of  mercury,  and  (Sp.Gr.)  and  (Sp.  Gr.y  the  specific 
gravities  of  mercury  and  the  solution  respectively ;  we  shall 

have  a  :  h0  =  (  Sp.  Gr.)  :  (  Sp.  Gr.y,  and  h0  =  a  ^|£y  •      Then 

the  elastic  force  of  the  gas  in  the  balloon  is  equivalent  to  a  col- 
umn of  mercury  whose  height  equals  the  sum  of  H0  and  //„,  or 

fi--7!  +  <,(*•<*••>'  nofti 

^  —  H0  +  a  -^s~Gr)  •  [108.] 

Let  us  suppose,  now,  that  from  any  cause,  such  as  the  exhaus- 
tion of  the  materials,  or  the  cooling  of  the  flask,  the  evolution  of 
chlorine  ceases ;  it  is  evident  that,  if  the  solution  continues  to 
absorb  the  gas  contained  in  the  flask  A,  the  elastic  force  of  this 
gas  will  constantly  diminish,  and  the  pressure  of  the  atmosphere, 
remaining  constant,  will  cause  the  liquid  to  rise  in  the  tube  b  c. 
If  the  experimenter  is  present,  he  can  prevent  accident  by  uncork- 
ing the  flask  ;  but  if  the  absorption  continues,  the  greater  part  of 
the  solution  may  be  pressed  over  into  the  flask,  and  the  experi- 
ment defeated. 

Such  an  accident  can  be  prevented  by  adjusting  to  the  flask 
the  safety-tube  efg^  having  the  form  rep- 
resented in  Fig.  288.  Into  this  tube  we 
pour  a  quantity  of  the  same  liquid  which 
is  contained  in  the  flask,  and  which  in  the 
present  case  would  be  chlorohydric  acid. 
When  the  process  is  going  on  regularly, 
and  the  gas  is  escaping  from  the  mouth  of 
the  tube  c,  the  tension  of  the  gas  in  the 
flask  will  raise  a  column,  A,  of  chlorohy- 
dric acid  in  the  tube/£%  which  must  ne- 
cessarily exert  a  pressure  equal  to  this 
tension  less  the  pressure  of  the  air  on 
^g  288.  the  top  of  the  column.  Hence  by  [108] 

this  pressure  is  measured  by  a  column  of  mercury  which  equals 

a  VfaGr-Y-f      Moreover,   if  (Sp.  Gr.y  represents   the    specific 
(bp.Gr.) 


THE   THREE   STATES   OF   MATTER.  817 

gravity  of  the  acid,  a  column  of  mercury  exerting  an  equiva- 
lent pressure  will  also  be  equal  to  h    £'  ^  ,  and  we  shall  have 

h(Sp.Gr.)"  _         (Sp.Gr.y  h__a(^Gr.y 

h  (S^)   '      a  (^Gr.)  '  a  (Sp7Gr.)« ' 

If  now  the  evolution  of  gas  ceases,  and  the  tension  of  the  gas 
in  the  flask  becomes  less  than  the  pressure  of  the  atmosphere,  as 
before,  the  liquid  will  rise  in  the  tube  b  c.  But  it  will  also  fall 
in  the  tubeg*/;  and  if  the  parts  are  properly  proportioned,  the 
chlorohydric  acid  will  fall  to  the  lowest  point,  /,  of  the  safety- 
tube,  before  the  solution  reaches  the  point  6,  when  air  will  enter 
the  flask  by  the  safety-tube  and  prevent  any  accident.  A  bulb  is 
blown,  at  the  point  u,  sufficiently  large  to  hold  all  the  liquid  con- 
tained in  the  tube/g* ;  and  the  air,  in  entering  the  flask,  bubbles 
through  the  liquid  in  this  bulb. 

This  safety-tube  is  also  a  security  against  the  bursting  of  the 
flask.  It  not  unfrequently  happens,  in  experiments  similar  to 
the  one  just  described,  that  the  mouth  of  the  exit-tube  becomes 
clogged  by  a  deposition  of  solid  matter.  If,  now,  the  evolution  of 
gas  continues,  the  pressure  rapidly  increases  on  the  interior  of 
the  flask,  and  soon  becomes  greater  than  the  thin  walls  of  the 
vessel  can  resist,  when  an  accident  would  result.  A  safety-tube 
effectually  prevents  such  a  possibility ;  for  when  the  tension  of  the 
gas-  becomes  much  greater  than  the  pressure  of  the  atmosphere, 
the  liquid  will  be  driven  out  of  the  safety-tube,  and  the  gas  can 
then  escape  freely  into  the  atmosphere. 

The  safety-tube  also  enables 
us  to  introduce  liquids  into  the 
flasks  during  the  experiment, 
without  removing  the  cork. 

When  the  vessel  used  for  mak- 
ing gas  is  a  retort,  the  safety- 
tube  may  be  attached  to  the  exit- 
tube,  as  represented  in  Fig.  289. 
This  peculiar  form  of  safety-tube 
is  called  Welter's  tube,  from  the 
name  of  the  chemist  who  in- 

vented   U- 

In  making  hydrogen  or  car- 
bonic acid,  we  frequently  use  a  two-necked  bottle,  such  as  is 

27* 


318 


CHEMICAL   PHYSICS. 


represented  in  Fig.  290.  The  safety-tube  may  then  be  a  simple 
straight  tube  surmounted  by  a  funnel,  and  dipping  a  few  milli- 
metres below  the  surface  of  the  liquid  in  the  bottle.  If,  as  be- 


Fig.  290.  Fig.  291. 

fore,  we  pass  the  gas  into  some  solution  contained  in  a  test-glass 
(Fig.  291),  the  tension  of  the  gas  in  the  bottle  will  raise  a  column 
of  liquid,  A,  in  the  safety-tube,  whose  height  will  bear  the  same 
proportion  to  that  of  the  column  a  (Fig.  289)  which  the  specific 
gravity  of  the  liquid  in  the  test-glass  has  to  that  in  the  bottle. 

It  not  unfrequently  happens,  that  we  wish  to  transmit  the  same 
gas  through  a  series  of  flasks  containing  the  same  or  different 
solutions.  Let  us  suppose  that  we  used  the  arrangement  of 
three-necked  bottles  represented  in  Fig.  292,  containing  solutions 


Fig.  292. 

which  absorb  the  gas  evolved  from  the  flask  A,  and  let  us  exam- 
ine what  would  be  the  tension  of  the  gas  in  the  successive  jars. 
The  gas  in  the  jar  E  communicates  directly  with  the  atmosphere 
through  the  tube  o,  and  its  tension  is  therefore  represented  by 
the  height  of  the  barometer,  or  H0.  The  tension  of  the  gas  in 
the  jar  D  must  evidently  be  measured  by  the  height  H0  plus  the 
height  of  a  column  of  mercury  which  is  equivalent  to  the  column 


THE   THREE    STATES    OF   MATTER.  319 

of  the  liquid  in  the  jar  72,  indicated  by  a""  in  the  figure.  In  like 
manner,  the  tension  of  the  gas  in  the  jar  C  will  be  equal  to  the 
tension  in  D  plus  a  quantity  which  is  measured  by  a  column  of 
mercury  equivalent  to  a"' ;  and  so  on  for  C  and  B.  Finally,  the 
tension  of  the  gas  in  the  flask  will  be  equal  to  the  tension  in  B  plus 
a  quantity  which  is  measured  by  a  column  of  mercury  equivalent 
to  a1.  If,  then,  we  represent  the  specific  gravities  of  the  liquids  in 
the  four  bottles  by  d1,  d" ',  d'",  and  d"",  and  that  of  mercury  by  #, 

d1          d" 
we  shall  have  for  the  equivalent  mercury  columns,  a1  --,  a"  — , 

d1"  d"" 

a'"  — ,  and  a""  —  .     The  measures  of  the  tension  of  the  gas  in 

the  four  bottles  and  the  flask  are,  then,  as  follows  :  — 
In  the  bottle  E....H<>. 

«      D       H.-\-a*"'—. 

tjini  jin 

«       C        770  +  a""  —  -f  a'"  -- . 
d  d 

fjnii  jit  i  Jn 

«      B        770  +  a""  —  +  a'"  —  +a"-. 

d  d  d 

In  the  flask  A         ff0  +  a""  —  +  a'"  —  +  alldL-+a'  -.    [110.] 

If,  now,  the  evolution  of  gas  ceases  in  the  flask,  while  the  ab- 
sorption continues  in  the  bottles,  it  is  evident  that  there  will  be 
a  transfer  of  liquid  from  right  to  left  through  the  bottles,  and 
from  the  first  bottle  to  the  flask ;  or,  on  the  other  hand,  if  either 

of  the  tubes  be ,  b'c' ,  should  become  clogged,  the  pressure 

would  increase  indefinitely  in  the  apparatus,  until  one  of  the  ves- 
sels in  front  of  the  obstruction  bursts.  This  would  usually  be 
the  flask,  because  it  is  weaker  than  the  rest.  Both  of  these  dan- 
gers may  be  avoided,  by  arranging  the  apparatus  with  safety- 
tubes,  as  represented  in  Fig.  293  ;  for  then,  if  the  pressure  in 
the  bottles  or  flask  becomes  considerable,  a  portion  of  the  liquid 
will  be  forced  out  at  these  tubes ;  or,  on  the  other  hand,  if  it  be- 
comes much  less  than  that  of  the  atmosphere,  air  will  bubble  in 
through  the  same  channels. 

When  the  gas  is  flowing  freely  from  the  flask  through  the 
apparatus,  and  bubbling  in  each  bottle,  it  is  easy  to  calculate 
the  heights  to  which  the  liquid  will  rise  in  the  safety-tubes, 
since,  the  tension  of  the  gas  in  the  different  parts  of  this  ap- 
paratus must  be  the  same  as  in  the  other.  For  example,  the 

d"" 

tension  of  the  gas  in  D  is  measured  by  H>  +  a""  —  ;   but  it 


320 


CHEMICAL   PHYSICS. 


Fig.  293. 


must  also  be  measured  by  H0  plus  a  column  of  mercury  equiv- 
alent to  the  column  of  liquid  h1"  in  the  safety-tube.  This 
column  of  mercury,  as  is  evident  from  what  has  been  said, 

d"1    '  d1"  d"" 

is  equal  to  h'"  — ;  and  hence  we  have  h"1  ~  =  a""  — , 


or 


And  in  like  manner  we  can  easily  find 


h' 
h 


^ 

df 


d1"  ' 
tjiu 


d!" 
d1" 


[111.] 


The  apparatus  thus  constructed  is  usually  called  Woolfs  appa- 
ratus. 

(172).   Siphon.  —  The  principle  of  this  well-known  instru- 
ment is  illustrated  by  Fig.  294.     The  siphon-tube  a  b  c  is  filled 
,  with  the   same  liquid  as   the  two  beaker- 

glasses  in  which  its  ends  are  dipped,  and 
the  liquid  is  sustained  in  the  tube  by  the 
pressure  of  the  air.  If  the  level  of  the 
liquid  in  the  two  vessels  is  on  the  same  hori- 
zontal plane,  it  is  evident  that  the  columns 
Fig.  294.  of  liquids  in  the  two  legs  of  the  siphon  will 


THE   THREE   STATES   OF   MATTER.  321 

have  the  same  vertical  height,  and  will  be  in  equilibrium.  If, 
however,  the  liquid  stands  at  a  lower  level  in  one  vessel  than  in 
the  other,  as  in  the  figure,  then  the  two  columns  of  liquid  in  the 
legs  of  the  siphon  will  not  have  the  same  height,  and  a  difference 
of  pressure  will  result,  corresponding  to  the  difference  of  level. 

In  order  to  ascertain  what  will  be  the  result  of  this  difference  of 
pressure,  take  a  section  through  the  tube  at  the  highest  point,  b, 
and  consider  the  amount  of  pressure  on  the  two  faces  of  this  sec- 
tion. On  the  face  towards  the  vessel  a,  this  pressure  is  equal  to 
the  pressure  of  the  atmosphere  (measured  by  the  height  of  the 
barometer),  or  H,  less  the  pressure  of  a  column  of  the  liquid  used 
whose  height  is  equal  to  the  difference  of  level  between  b  and  the 
surface  of  the  liquid  in  the  vessel  a.  Let  us  represent  the  height 
of  a  column  of  mercury  which  is  equivalent  to  that  of  the  liquid 
by  A0,  and  the  surface  of  the  section  by  s.  "We  shall  then  have, 
for  the  pressure  on  this  surface  of  the  section,  the  value 

*  =  *(!&  —  *.)•  [112.] 

On  the  surface  of  the  section  towards  the  vessel  c,  we  have  for 
the  pressure  a  value 


in  which  h'0  represents  the  height  of  a  column  of  mercury  which  is 
equivalent  to  a  column  of  the  liquid  used  whose  height  is  equal 
to  the  difference  of  level  between  b  and  c.  When  the  level  of  the 
liquid  is  the  same  in  both  vessels,  it  is  evident  that  h0=h'0.  Hence 
the  pressures  on  the  two  surfaces  are  equal,  and,  as  already  stated, 
there  will  be  an  equilibrium.  If  the  level  in  the  vessel  c  is  lower 
than  in  «,  then  hQ  <  7i'0,  and  H^  —  h0  >  H0  —  h'0.  There  will, 
therefore,  be  an  excfess  of  pressure  in  the  direction  of  the  vessel  c 
equal  to  h'0  —  A0,  which  will  cause  a  constant  flow  of  liquid  in 
the  direction  of  the  greatest  pressure.  This  flow  will  continue 
until  h0  =  A'0,  or  until  the  level  is  the  same  in  both  vessels.  If 
the  vessel  c  is  removed,  then  h'0  represents  the  height  of  a  column 
of  mercury  equivalent  to  a  column  of  the  liquid  used  whose 
height  equals  the  vertical  distance  between  the  mouth  of  the 
tube  and  b.  If  this  mouth  is  below  the  level  of  the  bottom  of 
the  vessel  a,  it  is  evident  that  A0  can  never  equal  A'0  ;  and  hence 
the  flow  in  this  case  will  continue  until  the  surface  of  the  liquid 
in  the  vessel  falls  below  the  mouth  of  the  tube  at  a.  It  is  evi- 
dent, that,  other  things  being  equal,  the  velocity  of  the  flow  will 


322 


CHEMICAL  PHYSICS. 


depend  on  the  difference  between  7i'0  and  h0.  In  the  ordinary 
method  of  using  a  siphon,  as  represented  in  Fig.  294,  this  differ- 
ence is  constantly  diminishing ;  and  hence  the  velocity  of  the  flow 
is  constantly  diminishing. 

The  siphon  is  frequently  employed  in  the  laboratory  for  de- 
canting liquids.  Before  using  the  instrument,  it  is  necessary  to 
fill  it  with  the  liquid  to  be  decanted.  If  this  liquid  is  water,  the 
siphon  is  easily  filled  by  closing  the  end  of  the  short  leg  with  the 
finger,  and,  after  inverting  the  instrument,  by  pouring  in  water  at 
the  other  end,  the  air  being  allowed  to  escape  from  the  short  leg 
by  lifting  for  a  moment  the  finger.  When  the  tvibe  is  filled,  it 
can  easily  be  reversed,  and  the  end,  still  closed  with  the  finger, 
plunged  under  the  liquid  in  the  vessel ;  when,  on  removing  the 


Fig.  295. 

finger,  the  water  will  begin  to  flow.  The  siphon  can  also  be  filled 
by  dipping  the  end  of  the  short  leg  in  the  liquid,  and  sucking 
out  the  air  from  the  other  leg  with  the  mouth.  In  the  iabora- 
tory,  the  siphon  is  frequently  used  for  decanting  corrosive  liquid ; 
and  it  is  then  necessary  to  resort  to  various  contrivances  for  fill- 
ing it.  The  one  represented  in  Fig.  295,  which  can  easily  be 
made  of  glass  tubes  and  cork,  is  one  of  the  best.  The  short  leg 
is  plunged,  as  usual,  into  the  liquid.  The  end  of  the  long  leg  is 
then  closed  by  the  finger,  which  can  be  protected  by  a  piece  of 
India-rubber,  and  the  air  is  sucked  out  by  the  mouth  applied  at 


THE   THREE    STATES   OP   MATTER.  323 

the  end  of  the  side  tube.  As  soon  as  the  liquid  descends  into 
the  enlargement  at  the  end  of  the  long  leg,  the  finger  is  with- 
drawn. 

(173.)  Mariettas  Flask.  —  It  is  sometimes  important  to  ob- 
tain with  the  siphon  a  uniform  flow  of  liquid.  This  can  be  easily 
secured  by  means  of  the  apparatus  represented  in  Fig.  296, 
called  Mar  lottos  flask.  It  consists  of  a  bottle  with  two  necks, 
into  one  of  which  a  straight  tube,  and  into  the 
other  a  bent  tube,  have  been  adjusted  air-tight, 
both  reaching  nearly  to  the  bottom  of  the  bot- 
tle. The  siphon-tube  is  filled  by  blowing  in  air 
through  the  straight  tube,  when  the  flow  contin- 
ues of  uniform  velocity  until  the  surface  of  the 
liquid  in  the  bottle  has  fallen  to  the  level  b  c  d, 
the  air  constantly  entering  the  bottle  by  the 
straight  tube  at  b. 

It  can  easily  be  shown  that  the  flow  in  this 
case  must  be  uniform  in  velocity.  Consider,  as 
before,  a  section  through  the  siphon-tube  at  the  highest  point. 

The  pressure  on  the  surface  of  this  section  towards  o  is  evi- 
dently 

f'=  s  (HQ  —  /*'„);  [114.] 


where  h'Q  is  the  height  of  a  column  of  mercury  equivalent  to  a 
column  of  the  liquid  used  whose  height  equals  the  vertical  dis- 
tance from  o  to  the  centre  of  gravity  of  the  section. 

The  surface  of  the  section  towards  c  is  evidently  exposed  to 
the  pressure  exerted  by  the  confined  air  on  the  surface  of  the 
liquid  in  the  bottle,  less  the  pressure  of  a  column  of  the  liquid 
whose  height  equals  the  vertical  distance  between  this  surface 
and  the  centre  of  gravity  of  the  section.  If  we  represent  the 
tension  of  the  confined  air  by  |j,  and  the  height  of  a  column 
of  mercury  equivalent  to  the  column  of  liquid  by  h"09  we  easily 
obtain  for  the  pressure  on  the  surface  of  the  section, 


When  the  apparatus  is  in  use,  and  air  is  freely  entering  through 
6,  it  is  evident  that  the  pressure  of  the  atmosphere  at  b  is  bal- 
anced by  the  pressure  of  the  confined  air  on  the  surface  of  the 
liquid,  and  by  the  pressure  of  the  column  of  liquid  above  b. 


324 


CHEMICAL  PHYSICS. 


Representing  the  equivalent  of  this  column  in  centimetres  of 
mercury  by  A'"0,  and  the  height  of  the  barometer  by  H^  we  ob- 
tain H0  =  f)  +  A'"o  >  an(i  by  substitution, 

£  = 


Subtracting  from  this  value  [114],  we  obtain 

J-  -  f  '  =  »  [A'.-  (/.".+  A»0]. 

The  value  A"o-f-  A'"0  represents  the  height  of  a  column  of  mer- 
cury equivalent  to  a  column  of  the  liquid  used  whose  height 
equals  the  vertical  distance  between  c  and  the  centre  of  gravity 
of  the  section.  As  this  height  remains  constant,  and  is  indepen- 
dent of  the  height  of  the  liquid  in  the  bottle,  it  is  evident  that 
the  difference  of  pressure  [116]  which  determines  the  velocity 
of  the  flow  will  also  be  constant.  It  is  also  evident  that  the  dif- 
ference of  pressure  is  always  equal  to  a  column  of  the  liquid 
used  whose  height  equals  the  difference  of  level  between  b  and  o. 
A  very  useful  application  of  Mariotte's  bottle  is  represented  in 
Fig.  297.  It  is  frequently  necessary,  in  the  laboratory,  to  wash 

for  several  hours,  or  even 
days,  a  precipitate  which  has 
been  collected  on  a  filter. 
This  is  done  by  keeping  the 
filter  constantly  full  of  wa- 
ter, which  slowly  percolates 
through  the  porous  mass  on 
the  filter,  and  washes  out 
everything  which  is  soluble. 
Mariotte's  bottle  furnishes 
an  automatic  machine,  by 
which  the  water  in  the  fil- 
ter can  be  maintained  at  a 
constant  level.  The  disposi- 
tion of  the  apparatus  is  suf- 
ciently  explained  by  the  fig- 
Fig-  297'  ure.  The  difference  of  level 

between  b  and  o  is  made  very  small,  and  the  water  flows  from 
the  bottle  to  the  filter,  until  the  level  rises  to  the  lower  dotted 
line  in  the  figure.  Then  the  flow  ceases,  but  recommences  as 
soon  as  the  level  falls. 


THE   THREE   STATES   OP   MATTER. 


325 


Fig.  298. 


The  principle  of  Mariotte's  bottle 
is  also  applied  to  produce  a  uniform 
flow  of  air  through  the  tube  apparatus 
which  is  frequently  used  in  chemical 
analysis.  Fig.  298  represents  what  is 
termed  an  aspirator  jar.  The  tube, 
which  passes  air-tight  through  the 
cork  in  the  neck,  has  a  free  communi- 
cation with  the  atmosphere,  and  the 
current  of  air  is  caused  by  the  flow  of 
water  from  the  cock  at  r.  The  veloci- 
ty of  the  flow  of  water  from  the  cock, 
other  things  being  equal,  depends 
upon  the  pressure  exerted  on  a  sec- 
tion of  the  stopcock  ;  and  it  can  easily  be  seen  that  this  will  be 
the  same  until  the  level  of  the  water  in 
the  jar  has  fallen  below  the  mouth  of  the 
tube  V. 

(174.)  Wash-Bottle.  —  This  simple  in- 
strument (Fig.  299),  which  is  so  much 
used  in  the  laboratory,  is  one  of  the  most 
useful  applications  of  the  properties  of  gas- 
es. By  condensing  the  air  over  the  water 
in  the  bottle,  by  blowing  in  at  the  tube  a, 
the  liquid  is  forced  out  at  o  in  a  fine  jet, 

which  can  be  directed  at  pleasure. 

^••i 

Fig.  299. 

Machines  for  Rarefying  and  Condensing  Air. 

(175.)  The  Air-Pump.  —  One  of  the  simplest  forms  of  the 
air-pump  is  represented  in  Fig.  300.  It  consists  of  a  hollow 
brass  cylinder,  in  which  a  piston  moves  readily  up  and  down  by 
a  handle  attached  to  the  piston-rod  above.  The  inner  surface  of 
the  cylinder  is  perfectly  smooth  and  true,  so  that  the  piston, 
which  is  formed  of  yielding  materials,  moves  air-tight  through 
its  whole  course.  Moreover,  the  under  surface  of  the  piston  fits 
exactly  the  bottom  of  the  cylinder,  so  that,  when  the  piston  is  in 
the  lowest  position,  there  can  be  no  air  between  it  and  the  cylin- 
der bottom.  The  upper  end  of  the  piston  is  closed  by  a  brass  cov- 
er, through  which  the  piston-rod  passes  freely,  and  the  atmosphere 
28 


326 


CHEMICAL   PHYSICS. 


has  free  access  to  the  upper  surface  of  the  piston.  The  lower  end 
of  the  cylinder  opens  into  a  narrow  tube,  which  connects,  at  one 
end,  with  the  glass  bell  on  the  plate  of  the  air-pump  through  the 


Fig.  300. 

stopcock  u,  and  at  the  other,  with  the  atmosphere  through  the 
stopcock  p.  Just  below  the  bottom  of  the  cylinder  there  is 
placed  a  stopcock  of  peculiar  construction.  The  core  of  the 
cock  is  bored  with  two  holes,  one  of  which  has  the  same  position 
as  in  ordinary  stopcocks,  and  as  is  shown  in  the  figure.  The  po- 
sition of  the  second  is  shown  in  the  small  section  at  the  side. 
When  the  cock  has  the  position  indicated  in  the  main  figure, 
there  is  a  direct  connection  between  the  interior  of  the  cylinder 
and  the  glass  bell.  If  the  cock  be  now  turned  through  ninety  de- 
grees, till  it  takes  the  position  shown  in  the  small  section,  the  con- 
nection with  the  glass  bell  will  be  closed,  and  direct  communica- 
tion with  the  atmosphere  opened  through  the  channel  s  v.  The 
channel  r  m  opens  in  the  centre  of  a  round  plate  made  of  brass, 
or,  still  better  for  chemical  uses,  of  glass.  This  plate  is  ground  on 
its  upper  surface  perfectly  plane.  The  lower  edges  of  the  glass 


THE  THREE   STATES   OP   MATTER.  327 

bell-receivers  are  also  carefully  ground,  and  may  be  made  to 
adhere  air-tight  to  the  plane  by  interposing  a  little  oil. 

The  principle  of  the  air-pump  can  now  be  easily  explained. 
Let  us  suppose  that  the  piston  is  in  its  lowest  position,  and  that 
the  stopcock  is  in  the  position  represented  in  the  figure.  If  now 
we  draw  up  the  piston  by  the  hand,  the  air  contained  in  the  bell- 
receiver  and  in  the  tube  connecting  it  with  the  cylinder  will 
expand  until  it  fills  the  cylinder  ;  and  its  volume  being  thus 
increased,  its  density  will  be  proportionally  diminished.  Let  us 
next  turn  the  stopcock  q  into  the  position  represented  in  the  sec- 
tion. The  bell  is  thus  hermetically  closed,  but  a  connection  is 
opened  between  the  cylinder  and  the  atmosphere.  Now,  on  press- 
ing down  the  piston,  all  the  air  in  the  cylinder  will  be  forced 
into  the  atmosphere.  The  stopcock  may  then  be  turned  back 
to  its  first  position,  and  the  same  motion  repeated,  which  will  fur- 
ther rarefy  the  air  in  the  bell ;  and  thus  the  process  may  be  con- 
tinued until  the  required  degree  of  exhaustion  is  obtained. 

(176.)  Degree  of  Exhaustion.  —  It  is  obvious  that  the  effect 
of  the  air-pump  depends  upon  the  expansive  force  of  air,  and 
that  each  motion  of  the  piston  is  accompanied  with  a  certain 
amount  of  expansion  of  the  air  in  the  bell.  This  amount  is  evi- 
dently determined  by  the  size  of  the  cylinder,  as  compared  with 
that  of  the  bell  and  the  tube  leading  to  it.  With  these  data,  we 
can  easily  calculate  the  degree  of  exhaustion  after  each  stroke 
of  the  piston. 

Let  us  then  represent  the  volume  of  the  bell-receiver  and  of  the 
tube  connecting  it  with  the  cylinder  by  V\  and  that  of  the  cylin- 
der itself,  when  the  piston  is  at  its  highest  position,  by  v.  Let  us 
suppose  that  the  piston  starts  from  its  lowest  position,  and  let  us 
take  the  quantity  of  air  contained  in  the  receiver  and  the  tube  as 
unity.  When  now  the  piston  is  raised,  the  volume  occupied  by 
this  quantity  of  air  (taken  as  unity)  becomes  V  -{-v.  When  the 
stopcock  is  turned  and  the  piston  lowered,  the  volume  v  is  ex- 
pelled, which  is  a  portion  of  the  original  quantity  (or  unity) 

represented  by  yqj-  •     The  piston  is  now  in  its  initial  position, 

and  the  quantity  of  air  remaining  in  the  receiver  and  tube,  after 
the  first  stroke,  is 

'  •••-'•  ' 


328  CHEMICAL   PHYSICS. 

Reversing  the  stopcock,  and  raising  again  the  piston,  this  quan- 

7/ 

tity  of  air,  v  .  ,  occupying  the  volume  F,  expands  to  the  vol- 
ume F-f-  v.  When  the  piston  descends,  the  volume  v  is  ex- 
pelled, which  is  -^r-j —  of  the  whole,  or  of  -j-r-r  -  ',  that  is,  — - , — r^ 

y  -(-  v  v  -\-v  ( r-\-v) 

of  unity.     There  remains,  therefore,  after  the  second  stroke, 

y+7~~  (Y+v)2==  (K+v)2' 

At  the  third  stroke  of  the  piston,  the  same  proportion  of  the  air 
now  remaining  is  expelled  as  before ;  and  there  is  consequently 
left,  after  the  third  stroke, 

F2  v  F2  F3 


In  like  manner  there  will  remain,  after  the  ntli  stroke, 

17" -1  „    Vn—l  T7n 

y v  y  _     v  r-i  90 1 

(F+t-)'—  —  (K+t*)"--  (V+v)»- 

If,  for  example,  the  volume  of  the  receiver  is  equal  to  ten  litres, 
and  that  of  the  cylinder  to  one  litre,  we  shall  have,  for  the  amount 

1Q50 

of  air  left  after  the  fiftieth  stroke,  --To  =  0.0085   of  the  original 


quantity. 

Since  the  value  of  [120]  never  can  become  zero  until  n  =  oo , 
it  is  evident  that  we  can  never,  even  theoretically,  by  means  of 
the  air-pump,  exhaust  the  whole  of  the  air.  Nevertheless,  theo- 
retically we  ought  to  be  able  to  approach  a  perfect  vacuum  in- 
definitely by  continuing  the  process  for  a  sufficiently  long  time. 
Practically,  however,  the  limit  is  soon  reached  ;  and  even  with 
the  best  pumps,  we  can  never  obtain  a  degree  of  exhaustion 
greater  than  that  when  -njWth  of  the  original  quantity  of  air  is 
left  in  the  receiver.  It  is  not  difficult  to  explain  the  cause  of  the 
discrepancy  between  the  theoretical  and  the  practical  results. 

In  any  machine,  however  well  made,  there  must  be  a  number 
of  joints  which  are  never  absolutely  hermetical.  There  are  fre- 
quently, even  in  the  metal  itself,  imperceptible  pores  which  trans- 
mit air.  During  the  first  few  strokes  of  the  piston,  this  minute 
leakage  produces  no  perceptible  effect ;  but  when  we  attain  a  high 
degree  of  exhaustion,  the  air  enters  by  these  minute  crevices  as 
fast  as  we  can  remove  it  by  the  pump. 


THE   THREE   STATES    OF   MATTER. 


329 


But  besides  this  imperfection,  the  capability  of  the  instrument 
is  limited  in  still  another  way.  In  calculating  the  degree  of  ex- 
haustion, we  supposed  that  at  each  descent  of  the  piston  the 
whole  of  the  air  was  expelled  from  the  cylinder  ;  and  this  would 
be  the  case,  if  the  base  of  the  piston  adhered  exactly  to  the  base 
of  the  cylinder.  In  practice,  however,  there  is  never  an  absolute 
adhesion  ;  and  a  small  amount  of  air  remains  between  the  two, 
which  no  force  applied  to  the  piston  is  able  to  expel.  When, 
therefore,  after  working  the  pump  for  some  time,  this  small 
amount  of  air,  expanded  through  the  whole  interior  of  the  cylin- 
der, exerts  a  pressure  equal  to  that  of  the  air  remaining  in  the 
receiver,  it  is  evident  that  the  air  from  the  receiver  can  no  longer 
expand  into  the  cylinder,  and  the  pump  will  cease  to  exhaust. 
But  although  a  perfect  vacuum  can  never  be  obtained  with  an 
air-pump,  yet  a  sufficient  degree  of  exhaustion  for  all  practical 
purposes  is  easily  attained. 


Fig.  301. 


(177.)  Air-Pump  with  Valves.  —  The  form  of  air-pump  de- 
scribed in  (175)  is  exceedingly  simple  in  its  construction,  and  not 
liable  to  get  out  of  order.  It  is  therefore  well  adapted  for  use  in 

28* 


330 


CHEMIC*AL   PHYSICS. 


the  chemist's  laboratory,  where  it  is  exposed  to  vapors  which  are 
likely  to  injure  any  delicate  valves.  It  is  open,  however,  to  two 
serious  objections.  In  the  first  place,  the  stopcock  q  must  be 
turned  by  the  hand  at  each  stroke  of  the  piston ;  and  although 
this  motion  may  be  obtained  by  means  of  cranks  and  levers,  yet 
this  machinery  renders  the  instrument  unnecessarily  complicated. 
In  the  second  place,  the  piston  must  be  raised  through  the  whole 
length  of  each  stroke,  against  a  great  pressure  of  air,  which 

rapidly  increases  as  the 
exhaustion  proceeds,  an 
objection  which  would  be 
very  serious  in  a  large 
pump,  rendering  a  great 
force  necessary  to  work 
it.  Both  of  these  difficul- 
ties are  overcome  in  the 
pump  represented  in  Fig. 
801.  A  section  of  this 
pump  is  represented  in 
Fig.  302,  and  the  details 
of  the  upper  valve  in 
Fig.  303. 

In  this  air-pump  there 
are  three  valves,  all  open- 
ing upwards :  one  at  the 
bottom  of  the  cylinder, 
covering  the  mouth  of 
the  tube  connecting  with 
the  receiver  (a  in  Fig. 
302);  one  at  the  top  of 
the  piston,  b,  covering  the 
holes  perforated  through 
it;  and,  finally,  one  at  the 
top  of  the  cylinder,  c,  cov- 
ering the  aperture  which  opens  into  the  atmosphere.  The  piston- 
rod  passes  through  a  packing-box,  &,  in  which  it  moves  air-tight, 
and  the  power  is  applied  to  the  piston-rod  by  means  of  a  lever, 
which  facilitates  the  working  of  the  pump.  Let  us  now  sup- 
pose that  we  start  with  the  piston  at  the  bottom  of  the  cylinder, 
and  proceed  to  raise  it.  The  air  from  the  receiver  expands 


Fig.  302. 


THE   THREE   STATES   OF   MATTER.  331 

into  the  empty  space  thus  formed  in  the  cylinder,  raising  the 
valve  a.     As  now  the  piston  descends,  the  valve  a  closes  and 
prevents    the    air    from    re-  . 
turning  to  the  receiver  ;  and 
this   air  passes  up,  through 
the  holes  in  the  piston,  into 
the  upper  part  of  the  cylin- 
der,   raising    the    valve     d. 
When  next  the  piston  rises, 
this  same  air,  now  in  the  up-  F«g-  303- 

per  part  of  the  cylinder,  is  forced  out  into  the  atmosphere  by  rais- 
ing the  valve  c.  At  the  same  time,  a  fresh  amount  of  air  from 
the  receiver  expands  into  the  space  below  the  piston,  which  air  is 
forced  out  by  the  next  stroke  at  the  valve  c,  as  before,  and  thus 
continuously. 

It  is  evident  from  the  construction,  that,  as  the  piston  rises,  the 
air  above  it  is  gradually  condensed,  and  the  valve  c  does  not  open 
until  the  density  of  the  air  is  equal  to  that  of  the  atmosphere. 
D  uring  the  first  few  strokes,  the  fprce  required  to  raise  the  piston 
is  considerable  ;  but  as  the  exhaustion  proceeds,  the  effort  neces- 
sary becomes  less  and  less,  until  at  last  only  sufficient  force  is 
required  to  overcome  the  friction,  and  a  sudden  pressure  at  the 
end  of  the  stroke  to  expel  the  air  condensed  at  the  top  of  the 
cylinder.  In  pumps  like  the  one  represented  in  Fig.  300,  the 
size  of  the  piston  and  cylinder  is  necessarily  very  limited  ;  be- 
cause, if  the  area  of  the  piston  exceeds  a  very  limited  extent,  the 
pressure  of  the  air  on  the  upper  surface  becomes  so  great,  as  the 
exhaustion  proceeds,  as  to  require  an  impracticable  amount  of 
force  to  work  the  pump.  With  pumps  of  the  construction  just 
described,  this  pressure  is  in  great  measure  removed  ;  and  it  is 
possible  to  increase  very  greatly  their  size  advantageously.  Fig- 
ure 304  is  a  representation  of  a  large  air-pump  of  this  descrip- 
tion, made  by  Ritchie,*  of  Boston.  The  piston  is  10  c.  m.  in 
diameter,  and  the  length  of  the  stroke  26  c.  m.  The  ground 
brass  plate  is  37  c.  m.  in  diameter,  and"  admits  of  as  large  a  bell- 
receiver  as  can  be  readily  made.  The  efficiency  of  the  pump 
depends  in  great  measure  upon  the  valves.  These  are  best  made 


*  The  two  representations  of  air-pumps,  Fig.  301  and  Fig.  304,  are  from  the  cata- 
logue of  Mr.  E.  S.  Kitchie,  a  very  expert  philosophical-instrument  maker  of  Boston. 


332 


CHEMICAL   PHYSICS. 


of  delicate  oil-silk.     The  details  of  the  upper  valve  of  the  pump, 
as  made  by  Ritchie,  are  shown  in  Fig.  303.     The  oil-silk  disk,  a, 


Fig.  304. 


is  kept  in  its  place  by  the  pin  6,  and  the  whole  is  protected  by  the 
dome-shaped  covering  c  d.  The  tube  at  the  side  discharges  the 
air,  and  the  oil  which  escapes  with  it  is  conducted  into  a  reser- 
voir placed  below  the  basement  of  the  pump.  This  pump  is 
furnished  with  a  manometer  similar  in  principle  to  the  one  repre- 
sented in  Fig.  272,  by  which  the  degree  of  exhaustion  can  be 
ascertained.  It  is  represented  in  the  figure  on  the  left-hand  side 
of  the  pump. 

Besides  those  already  enumerated,  there  is  obviously  another 
limit  to  the  degree  of  exhaustion  which  can  be  obtained  with 
this  pump.  This  arrives  when  the  elasticity  of  the  air  left  in  the 
receiver  is  insufficient  to  raise , the  lower  valve  a,  Fig.  302.  In 
order  to  overcome  this  difficulty,  the  lower  valve  in  the  French 
form  of  air-pump*  is  opened  and  shut  mechanically.  Babinet 

*  For  a  description  of  the  French  form  of  air-pump,  see  any  of  the  French  works 
on  physics. 


THE   THREE    STATES   OF   MATTER. 


333 


lias  still  farther  improved  the  French  air-pump,  by  so  connecting 
the  two  barrels  that,  after  a  certain  degree  of  exhaustion  has 
been  attained,  the  second  is  made  to  exhaust  the  first.  There 
can  be  no  doubt  that  a  higher  degree  of  exhaustion  can  be  ob- 
tained with  the  French  pump,  thus  arranged,  than  with  the  pump 
just  described  ;  but  this  gain  is  hardly  compensated  by  the  greater 
complexity  and  consequent  liability  to  derangement,  more  espe- 
cially since  a  sufficient  degree  of  exhaustion  for  all  practical 
purposes  can  be  obtained  without  these  complications. 

(178.)  Condensing- Pump.  —  This  instrument  is  just  the  re- 
verse of  the  air-pump,  and  it  is  used  for  increasing  the  density 
of  air  in  a  receiver,  while  the  air- 
pump  is  used  for  diminishing  it.  Any 
air-pump  may  be  converted  into  a 
condensing-pump  by  changing  the 
direction  of  all  the  valves.  For  ex- 
ample, we  may  use  the  pump  repre- 
sented in  Fig.  300  as  a  condensing- 
pump.  Starting  with  the  piston  at 
the  bottom  of  the  cylinder,  we  give 
the  stopcock  the  position  represented 
in  the  section  at  the  side.  Then,  on 
raising  the  piston,  the  air  enters  at  v 
and  fills  the  cylinder.  We  now  turn 
the  cock  into  the  second  position, 
when,  on  pushing  down  the  piston, 
this  air  is  forced  into  the  receiv- 
er. We  can  then  reverse  the  stop- 
cock and  repeat  the  process,  until 
the  required  degree  of  condensation 
is  obtained.  Instead,  however,  of 
placing  the  receiver  on  the  brass 
plate,  as  before,  we  screw  it  on  be- 
yond the  stopcock  p,  opening  this 
stopcock,  and  closing  the  stopcock  u. 

The  most  convenient  form  of  con- 
densing-pump for  the   laboratory  is 

represented  in  Fig.  305.  It  consists  of  a  cylinder,  and  a  piston, 
which  is  moved  by  the  handle  M.  The  two  valves,  which  are 
both  at  the  bottom  of  the  cylinder,  are  represented  in  section  in 


Fig.  305. 


334  CHEMICAL   PHYSICS. 

Fig.  306.     They  are  made  to  fit  exactly  the  conical  openings  at 
the  bottom  of  the  cylinder,  and  are  kept  in  place  by  very  delicate 


Fig.  306. 

spiral  springs.  When  the  piston  rises,  the  valve  A  opens  and 
admits  the  air  through  the  tube  c  a  into  the  cylinder.  On  the 
other  hand,  when  the  piston  descends,  the  valve  A  closes,  while 
B  opens,  and  the  air  is  forced  out,  through  the  tube  b  d,  into  the 
receiver  placed  at  d.  It  is  evident,  that  if  two  receivers  are  con- 
nected with  the  pump,  one  at  c  and  the  other  at  d,  the  air  will 
be  exhausted  from  one  and  condensed  in  the  cither.  The  pump 
may,  therefore,  be  used  either  for  condensing  or  rarefying.  In 
using  the  pump,  it  is  fastened  firmly  to  a  table,  or  some  other 
solid  support,  and  the  handle  M  is  moved  up  and  down  alter- 
nately with  the  two  hands. 

This  simple  machine  is  sufficient  for  almost  all  purposes.  If, 
however,  a  more  powerful  apparatus  is  required  for  condensing 
gases  into  large  reservoirs,  it  is  best  not  to  increase  the  size  of  the 
pump ;  but  to  combine  several  cylinders,  connecting  them  all  with 
the  same  receiver.  The  piston-rods  of  all  these  cylinders  can  be 
united  by  cranks  to  one  axis,  and  a  handle  connected  with  a 
fly-wheel  can  be  used  to  give  this  axis  a  regular  and  uniform 
motion. 

(179.)  Water-Pump.  —  Entirely  analogous  in  its  principle  to 
the  air-pump  is  the  common  water-pump,  a  glass  model  of  which 
is  represented  in  Fig.  307.  It  consists  also  of  a  hollow  cylinder, 
in  which  moves  a  piston,  B.  It  has  two  valves,  both  opening  up- 
wards ;  one  at  the  bottom  of  the  cylinder,  covering  the  mouth  of 
the  tube  leading  to  the  water  of  the  well,  and  the  other  at  the 


THE   THREE   STATES   OF   MATTER. 


335 


top  of  the  piston,  covering  the  hole  with  which  it  is  pierced.  If 
the  piston  and  valves  are  sufficiently  tight,  this  pump  will  act  as 
an  air-pump,  and  on  moving  the  piston  by  the  handle  P  alter- 
nately up  and  down,  it  will  ex- 
haust the  air  from  the  tuhe  A. 
But  since  the  end  of  the  tube 
dips  under  water,  the  pressure 
of  the  air  will  force  up  the  water 
until  it  fills  both  the  tube  and 
the  cylinder  below  the  piston. 
Then,  on  lowering  the  piston, 
the  water  in  the  cylinder  will 
raise  the  valve  o,  and  pass  above 
the  piston.  Afterwards,  on  rais- 
ing the  piston,  this  water  will 
be  lifted  and  discharged  into  the 
pipe  C,  while  a  fresh  quantity  of 
water  will  be  forced  up  by  the 
atmospheric  pressure  through 
the  valve  S.  Thus,  at  each 
stroke  of  the  piston,  a  quantity 
of  water  is  lifted  equal  to  the 
capacity  of  the  cylinder  less  the 
volume  occupied  by  the  piston 
itself.  If  the  piston  and  valves 
are  not  sufficiently  tight  to  pump 

out  the  air,  they  can  be  made  so  by  pouring  a  little  water  into 
the  pump.  This  is  what  is  called  the  drawing  of  water,  and  the 
philosophy  of  this  well-known  process  is  evident. 

It  follows  from  this  description,  that  the  pump  will  not  work,  if 
the  bottom  of  the  piston,  in  its  highest  position,  is  over  ten  metres 
above  the  level  of  the  water  in  the  well ;  and  it  was  an  attempt 
of  some  Florentine  engineers  to  raise  water  in  the  suction-tube 
of  a  pump  above  this  height,  which  led  to  the  discovery  of  the 
pressure  of  the  atmosphere.  On  account  of  the  imperfections  of 
the  valves  and  piston,  a  pump  will  seldom  work  in  practice  higher 
than  eight  metres.  The  height  of  the  tube  (7,  in  which  the  water 
is  lifted  by  the  piston,  may  be  very  considerable,  and  the  whole 
height  through  which  the  water  is  raised  by  the  pump  is  fre- 
quently very  much  over  ten  metres ;  but  the  difficulty  of  working 


Fig.  307. 


386  CHEMICAL   PHYSICS. 

a  pump,  and  keeping  it  in  order,  increases  very  rapidly  with  the 
height  of  the  column  of  water  which  is  lifted. 

PROBLEMS. 

Unless  otherwise  stated,  the  temperature  in  all  the  following  problems  is  to  be  taken  as  0°  C., 
and  the  height  of  the  barometer  at  76  c.  m. 

Weight  of  a  Body  in  Air. 

176.  A  mass  of  metal,  whose  Sp.  Gr.  =  11.35,  weighs  0.575  gramme 
in  a  vacuum.     How  many  milligrammes  will  it  lose  when  weighed  in  air  ? 

177.  A  brass  weight  (Sp.  Gr.  —  8.55)  weighs  in  a  vacuum  one  kilo- 
gramme.    How  many  milligrammes  does  it  lose  when  weighed  in  air  ? 

178.  A  body  loses  in  carbonic  acid  gas  1.15  gramme  of  its  weight. 
What  would  be  the  loss  of  its  weight  in  air  and  in  hydrogen  ? 

179.  A  body  loses  7  grammes  of  its  weight  in  air ;  how  much  of  its 
weight  would  it  lose  in  carbonic  acid  and  in  hydrogen  ? 

1 80.  What  is  the  weight  of  hydrogen  contained  in  a  glass  globe  whose 
surface  is  equal  to  10  in.2  ? 

181.  A  glass  globe  from  which  the  air  has  been  exhausted  weighs 
254.735  gram.      When  full  of  air,   it  weighs    289.621    gram.      When 
full  of  another  gas,  308.078  gram.     What  is  the  capacity  of  the  globe, 
and  what  is  the  specific  gravity  of  the  gas  ? 

182.  A  glass  globe  30  c.  m.  in  diameter,  filled  with  air,  and  hermeti- 
cally sealed,  is  balanced  in  the  atmosphere  by  brass  weights  amounting  to 
356.225  gram.     How  much  would  it  weigh  in  a  vacuum  ?     How  much 
would  the  globe  weigh  in  a  vacuum,  if  it  were  opened  so  that  the  air 
could  be  exhausted  from  the  interior?     Sp.  Gr.  of  brass  8.55,  and  of 
glass  3.33. 

183.  A  glass  globe  hermetically  sealed  weighs  in  the  air  25.236  gram, 
and  gains  in  a  vacuum  0.632  gram.     What  is  its  diameter  ? 

Buoyancy  of  Air. 

184.  What  is  the  ascensional  force  of  a  balloon  one  metre  in  diameter, 
three  quarters  filled  with  hydrogen,  when  the  balloon  itself  weighs  one 
hundred  grammes  ? 

185.  Calculate  the  ascensional  force  of  a  spherical  balloon  made  of 
prepared  silk  and  filled  with  impure  hydrogen,  knowing  that  the  bal- 
loon itself  weighs  63,620  gram.,  that  the  prepared  silk  weighs  250  gram, 
the  square  metre,  and  that  a  cubic  metre  of  impure  hydrogen  weighs  100 
gram. 

186.  What  would  be  the  ascensional  force  of  a  spherical  balloon  seven 
metres  in  diameter,  two  thirds  filled  with  hydrogen,  when  the  balloon  and 
attachments  weigh  twenty  kilogrammes  ? 


THE   THREE   STATES   OF   MATTER.  337 

187.  The  material  of  a  balloon  containing  1229  c.  m.3  weighs  1.5  gram. 
The  balloon  is  filled  with  hydrogen,  whose  specific  gravity  referred  to 
water  is  0.00009003.     The   specific  gravity  of  the  surrounding  air  is 
0.0013105.     Will  the  balloon  rise  in  the  atmosphere  ? 

188.  The  material  of  a  spherical  balloon  and  its  attachments  weighs 
400   kilogrammes.      This    balloon    is   15   m.   in  diameter,  and  is  three 
fourths  filled  with  gas  whose  specific  gravity  equals  0.0005.     The  specific 
gravity  of  the  surrounding  air  is  0.0013.     What  is  the  ascensional  force 
of  the  balloon  ? 

Barometer. 

1 89.  When  the  surface  of  a  column  of  mercury  in  a  barometer  stands 
at  76  centimetres  above  the  mercury  in  the  basin,  with  what  weight  is  the 
atmosphere  pressing  on  every  square  centimetre  of  surface  ?     Sp.  Gr.  of 
mercury  =  13.596. 

190.  To  what  difference  of  pressure  does  a  difference  of  one  centi- 
metre in  the  barometric  column  correspond  ? 

191.  When  the  water  barometer  stands  at  ten  metres,  what  is  the 
pressure  of  the  air  if  the  temperature  is  4°  ? 

192.  How  high  would  an  alcohol  barometer,  and  how  high  a  sulphuric- 
acid  barometer,  stand  under  the  same  circumstances,  disregarding  in  each 
case  the  tension  of  the  vapor  ?     Sp.  Gr.  of  alcohol  =  0.8095  ;  Sp.  Gr. 
of  sulphuric  acid  =  1.85. 

193.  When  the  mercury  in  a  barometer  stands  75.2  c.  m.,  with  what 
weight  is  the  atmosphere  pressing  on  every  square  centimetre  of  surface  ? 
How  high  would  barometers  stand  under  the  same  circumstances,  filled 
with  liquids  of  the  following  specific  gravities,  viz.  1.12,  1.45,  2.36,  3  ? 

194.  When  the  mercury  barometer  stands  at  76  c.  m.,  what  must 
be  the  length  of  a  water  barometer  inclined  to  the  horizon  at  an  angle 
of  30°  ? 

195.  If  a  barometer,  having  its  lower  end  immersed  in  a  basin  of  mer- 
cury, be  suspended  from  the  beam  of  a  balance,  and  weighed,  is  its  weight 
altered  by  weighing  it  again  when  inverted  and  containing  the  same 
quantity  of  mercury  as  before  ? 

Pressure  of  the  Atmosphere. 

196.  When  the  barometer  stands  at  76  c.  m.,  how  great  is  the  pres- 
sure of  the  air  upon  a  plane  surface  having  an  area  of  one  square 
metre  ? 

197.  The  body  of  a  man  of  ordinary  stature  exposes  a  surface  of  about 
one  square  metre.     How  great  a  pressure  does  the  body  sustain  when  the 
barometer  stands  at  72  c.  m.  ?     If  the  barometer  rises  to  78  c.  m.,  how 
great  is  the  increase  of  pressure  ? 

29 


338  CHEMICAL   PHYSICS. 

198.  When  the  barometer  stands  at  72  c.  m.,  how  great  is  the  pres- 
sure of  the  air  on  a  sphere  whose  radius  is  equal  to  6675  c.  m.  ? 

199.  When  the  barometer  stands  at  76  c.  m.,  what  is  the  pressure  ex- 
erted in  the  vertical  direction  on  a  sphere  125  c.  m.  in  diameter  ? 

Mariotte's  Law. 
In  all  these  problems  the  law  is  to  be  regarded  as  invariable. 

200.  A  volume  of  hydrogen  gas  was  measured  and  found  to  be  equal 
to  250  cTnT.3     The  height  of  the  barometer,  observed  at  the  same  time,  was 
74.2  c.  m.     What  would  have  been  the  volume  if  observed  when  the  ba- 
rometer stood  at  76  c.  m.  ?     What  would  be  the- volume  at  an  elevation  at 
which  the  barometer  stands  at  56  c.  m.  ? 

201.  A  volume  of  nitrogen  gas  measured  756  c.  m.3  when  the  barometer 
stood  at  77.4  c.  m.     What  would  it  have  measured  if   the   barometer 
had  stood  at  76  c.  m.  ? 

202.  A  volume  of  air  standing  in  a  bell-glass  over  a  mercury  pneumatic 
trough  measured  568  c.  m.3     The  barometer  at  the  time  stood  at  75.4 
centim.,  and  the  surface  of  the  mercury  in  the  bell  was  found,  by  meas- 
urement, to  be  6.5  c.  m.  above  the  surface  of  the  mercury  in  the  trough. 
What  would  have  been  the  volume  had  the  air  been  exposed  to  the  pres- 
sure of  76  c.  m.  ? 

203.  A  volume  of  air  standing  in  a  tall  bell-glass  over  a  mercury  pneu- 
matic trough  measured  78  cTrn.3     The  barometer  at  the  time  stood  at  74.6 
c.  m.,  and  the  mercury  in  the  bell  at  57.4  c.  m.  above  the  mercury  in 
the  trough.     What  would  have  been  the  volume  had  the  pressure  been 
76  c.  m.? 

204.  What  would  be  the  answers  to  the  last  two  problems,  had  the 
pneumatic  trough  been  filled  with  water  instead  of  mercury  ? 

205.  The  specific  gravity  of  air  at  0°  and  76  c.  m.  referred  to  water 
is  0.00129206.     What  is  the  specific  gravity  when  the  barometer  stands 
at  the  following  heights,  viz.  72.65   c.  m.,  74.23  c.  m.,  75.54  c.  m., 
77.82  c.  m.  ? 

206.  The  specific  gravity  of  carbonic  acid  gas  at  0°  and  76  c.  m.  re- 
ferred to  water  is  0.00196663.     What  is  the  specific  gravity  when  the 
barometer  stands  at  the  heights  given  in  the  last  problem  ? 

207.  A  glass  globe  10  c.  m.  in  diameter  hermetically  sealed  weighs 
45.120  gram,  when  the  barometer  stands  at  74.5  c.  m.     What  would  it 
weigh  if  the  barometer  stood  at  76  c.  m.  ? 

208.  A  glass  globe  hermetically  sealed,  30  c.  m.  in  diameter,  suspended 
to  one  pan  of  a  balance,  is  poised  by  325.422  grammes  in  brass  weights 
when  the  barometer  stands  at  76.21  c.  m.     After  several  hours  it  is  found 
to  have  lost  in  weight  0.022  gram.     What  is  now  the  height  of  the  ba- 
rometer, supposing  the  temperature  not  to  have  changed  ?     Sp.  Gr.  of 
brass  8.55. 


THE   THREE    STATES    OP   MATTER.  339 

209.  A  glass  globe  hermetically  closed  was  found  to  weigh  354.567 
gram,  when  the  barometer  stood  at  73  c.  m.,    and   to  weigh   353.917 
gram,  when  the  barometer  stood  at  77  c.  m.     What  is  the  diameter  of 
the  globe? 

210.  A  glass  globe  25  c.  m.  in  diameter  contains  how  many  grammes 
of  hydrogen  at  the  following  pressures,  viz.  72.2  c.  m.,  74.6  c.  m.,  76  c.  m., 
77.2  c.  m.  ? 

211.  Two  glass  globes  are  connected  by  a  tube  in  which  there  is  a 
stopcock.    In  the  first  globe  there  are  250  cTm.3  of  air  at  a  tension  of  2  c.  m. 
In  the  second,  340  c-  m.3  of  air  at  a  tension  of  10  c.  m.     After  opening 
the  stopcock,  what  will  be  the  tension  in  both  globes  ? 

212.  Into  an  exhausted  jar  having  a  capacity  of  60  litres  there  have 
been  poured  30  litres  of  nitrogen  at  the  pressure  of  72  c.  m.,  15  litres  of 
oxygen  at  the  pressure  of  64  c.  m.,  and  5  litres  of  carbonic  acid  gas  at 
the  pressure  of  78  c.  m.     What  is  the  elastic  force  of  the  mixture  ? 

213.  A  glass  globe  contains  8.548  gram,  of  air.     It  is  afterwards  filled 
with  protoxide  of  nitrogen  whose  Sp.  Gr.  =  1.52,  that  of  air  being  unity. 
What  is  the  weight  of  the  gas,  1st.  when  the  tension  of  the  two  gases  is 
the  same,  2d.  when  the  tension  of  the  air  is  76  c.  m.  and  that  of  the  pro- 
toxide of  nitrogen  78  c.  m.  ? 

214.  A  glass  globe  weighs,  when  completely  empty,  152.475  gram. ;  full 
of  air,  it  weighs  168.386  gram.,  and  full  of  another  gas,  157.235  gram. 
What  is  the  Sp.  Gr.  of  the  gas,  supposing  the  pressure  the  same  at  all  the 
weighings  ?     Also,  what  correction  must  be  made  if  the  pressure  was  76 
c.  m.  during  the  weighing  of  the  globe,  77  c.  m.  during  the  weighing  of  the 
air,  and  74  c.  m.  during  the  weighing  of  the  gas  ?     The  tension  of  the  air 
and  gas  in  the  balloon  is  supposed  to  be  76  c.  m.,  and  the  temperature  is 
supposed  invariable  at  0°. 

Atmosphere. 
The  folloioing  prddems  may  be  solved  by  Babinefs  formula.     See  note  to  page  304. 

215.  Find  the  difference  of  level  of  two  stations  from  the  following 
data :  — 

Height  of  barometer  at  lower  station  reduced  to  0°  C.,     755  m.  m. 
Temperature  of  air         "  "  15°  C. 

Height  of  barometer  at  upper  station  reduced  to  0°  C.,     695  m.  m. 
Temperature  of  air         "  «  10°  C. 

216.  Find  the  difference  of  level  of  two  stations  from  the  following 
data :  — 

Height  of  barometer  at  lower  station  reduced  to  0°  C.,     730  m.  m. 
Temperature  of  air         «  "  20°  C. 

Height  of  barometer  at  upper  station  reduced  to  0°  C.,     635  m.  m. 
Temperature  of  air         "  "  15°  C. 

217.  Find  the  height  of  Mount  Washington  above  sea  level  from  the 
following  observations  of  Prof.  Arnold  Guyot,  Aug.  8,  1851,  4  P.  M. :  — 


340  CHEMICAL  PHYSICS. 

Height  of  barometer  at  Gorham  reduced  to  0°  C.,  740.70  m.  m. 

Temperature  of  air  at  Gorham,     ^^  <rv  ,     .  22°.25 
Height  of  barometer  near  the  summit  of  Mount 

Washington  reduced  to  0°  C.,        .         .         .  608.93  m.  m. 

Temperature  of  air  at  summit,     ....  10° .30 

Barometer  at  Gorham  above  sea  level,      .         .  251  m. 

Air-Pump* 

218.  The  capacity  of  the  cylinder  of  a  pump  is  one  tenth  of  that  of  the 
receiver.     What  will  be  the  tension  of  the  air  in  the  receiver  after  1,  2,  3, 
4,  5,  10,  and  40  strokes  of  the  piston,  the  original  tension  being  76  c.  m.? 

219.  The  capacity  of  the  cylinder  of  a  pump  is  one  third  of  the  ca- 
pacity of  the  receiver.    After  how  many  strokes  of  the  piston  will  the  ten- 
sion of  the  air  in  the  receiver  be  reduced  to  yfo  of  its  primitive  amount  ? 

220.  If  the  air  in  the  receiver  of  an  air-pump  is  by  two  strokes  of  the 
piston  made  four  times  rarer  than  it  was  at  first,  what  is  the  ratio  of  the 
capacity  of  the  receiver  to  that  of  the  barrel  ? 

221.  If  in   an  air-pump  the  density  before  is  to  the  density  after  three 
strokes  of  the  piston  as  35  is  to  8,  determine  the  ratio  of  the  capacity 
of  the  receiver  to  that  of  the  barrel. 

222.  If,  in  an  air-pump  similar  in  construction  to  Fig.  300,  an  interval 
be  left  between  the  piston  and  the  base  of  the  cylinder  at  the  lowest  pos- 
sible position  of  the   piston,  determine  the  density  of  the  air  in  the  re- 
ceiver after  n  strokes  and  after  an  infinite  number. 

223.  The  piston  of  a  common  pump  is  6  c.  m.  in  diameter,  and  the 
vertical  height  of  the  mouth  from  the  surface  of  the  water  in  the  well  is 
6.250  m.     How  great  is  the  intensity  of  the  force  required  to  raise  the 
piston,  assuming  that  there  is  no  gain  by  leverage  ?     Is  there  any  gain 
in  power  in  the  use  of  a  pump  over  a  bucket  in  raising  water  ? 

224.  What  are  the  conditions  under  which  the  common  pump  will  not 
draw,  when  the  piston  does  not  descend  to  the  fixed  valve  ? 

225.  If  a  body  when  placed  under  the  receiver  of  a  given  air-pump 
weighs  a  gram.,  and  after  n  strokes  weighs  b  gram.,  determine  the  weight 
of  the  body  in  a  vacuum ;  and,  supposing  the  specific  gravity  of  the  body 
known,  determine  the  specific  gravity  of  the  air  in  the  receiver  at  first. 

Miscellaneous. 

226.  A  cylinder,  the  height  of  which  is  6  c.  m.  and  the  radius  of  the 
base  1  c.  m.,  is  filled  with  atmospheric  air.     To  what  depth  will  a  piston 
sink  in  the  cylinder  which  weighs  10  kilogrammes?     To  what   depth 
would  it  sink  if  it  weighed  1000  kilogrammes  ? 

227.  In  the  cylinder  described  in  the  last  example,  a  piston  is  forced 
down  2  c.  m. ;  determine  the  pressure  of  the  confined  air.     Determine 
also  the  pressure  of  the  air  when  it  is  forced  down  5.64  c.  m. 


THE  THREE   STATES   OP   MATTER.  341 

228.  Calculate  the  total  weight  of  the  atmosphere  in  kilogrammes,  sup- 
posing the  height  of  the  barometer  76  c.  m.,  and  the  radius  of  the  earth 
considered  as  a  sphere  equal    to  6,366  kilometres.     Calculate  also  the 
volume  of  an  equivalent  mass  of  gold,  knowing  that  the  Sp.  Gr.  of  gold 
=  19.363,  and  that  of  mercury  =  13.596. 

229.  If  the  altitude  of  the  mercury  in  a  barometer  placed  in  an  ordi- 
nary diving-bell  be  observed  at  the  beginning  and  end  of  a  descent,  deter- 
mine the  depth  descended. 

230.  Determine  the  tension  of  the  rope  by  which  an  iron  diving-bell 
is  suspended  at  any  depth  below  the  surface. 

231.  If  a  cylindrical  tube  152  c.  m.  long  be  half  filled  with  mercury, 
and  then  inverted,  determine  how  high  the  mercury  will  stand  when  the 
barometer  stands  at  76  c.  m. 

232.  Having  given  the  quantity  of  air  left  in  a  barometer  tube  be- 
fore immersion,  find  the  height  at  which  the  mercury  is  supported  after 
immersion. 

233.  If  in  an  imperfectly  filled  barometer  tube,  of  which  the  length  is 
80  c,  m.,  the  mercury  stands  at  74  c.  m.,  when  in  a  well-filled  tube  it 
stands  at  76  c,  m.,  determine  at  what  height  it  will  stand  in  the  imperfect 
one  when  it  stands  at  70  in  the  perfect  one. 

234.  Two  barometers  of  the  same  given   length,  /,  being  imperfectly 
filled  with  mercury,  are  observed  to  stand  at  the  heights  H  and  H1  on 
one  day,  and  h  and  h1  on  another.     Determine  the  quantity  of  air  left  in 
each,  supposing  the  temperature  invariable. 

235.  A  bell  partly  filled  with  gas  is  standing  over  a  pneumatic  trough. 
Its  interior  diameter  is  6  c.  m. ;  its  weight,  one  kilogramme ;  and  the  level 
of  the  mercury  in  the  bell  is  22.8  c.  m.  above  the  level  of  the  mercury  in 
the  trough.    Neglecting  the  weight  of  the  gas,  how  much  force  in  grammes 
is  required  to  sustain  the  bell  in  its  position,  supposing  that  no  portion 
dips  under  the  mercury,  and  that  the  temperature  is  at  0°  ? 

236.  A  body  of  known  specific  gravity  is  floating  between  two  immis- 
cible fluids,  whose  specific  gravities  are  also  given.     Determine  the  por- 
tion immersed  in  each. 

237.  A  cylinder  of  known  specific  gravity  and  magnitude  floats  with 
its  axis  vertical  in  a  vessel  of  water.     What  will  be  the  effect  of  remov- 
ing the  atmospheric  pressure  ? 

238.  An  hydrometer  similar  to  Fig.  248  is  divided  into  150  parts  of 
equal  capacity,  and  so  constructed  that  when  in  vacua  it  sinks  in  pure 
water  at  4°  C.  to  the  100th  division.     When  immersed  in  sulphuric  acid, 
at  the  standard  temperature  and  pressure,  it  sinks  to  the  54th  division. 
To  what  point  would  it  sink  were  the  experiment  made  in  vacua,  and 
what  is  the  true  specific  gravity  of  the  acid  ? 

29* 


342 


CHEMICAL  PHYSICS. 


MOLECULAR  FORCES  BETWEEN  HETEROGENEOUS  MOLECULES. 

(180.)  Adhesion.  —  Having  studied  the  phenomena  caused 
by  the  action  of  molecular  forces  between  homogeneous  mole- 
cules, as  manifested  in  the  characteristic  properties  of  solids, 
liquids,  and  gases,  we  come  next  to  consider  those  phenomena 
which  are  caused  by  the  action  of  molecular  forces  between  hete- 
rogeneous molecules.  As  we  have  already  seen,  the  molecular 
forces  are  either  attractive  or  repulsive  (78).  To  the  attractive 
force,  when  exerted  between  homogeneous  molecules,  like  those 
of  the  same  body,  whether  it  be  solid,  liquid,  or  gaseous,  we  give 
the  name  of  cohesion  (79).  But  when  the  attractive  force  is 
exerted  between  heterogeneous  molecules,  like  those  of  different 
bodies,  and  still  does  not  produce  any  chemical  change,  we  call 
it  adhesion.  It  must  not,  however,  be  supposed  that  these 
attractive  forces  are  essentially  different  in  the  two  cases.  The 
distinction  between  cohesion  and  adhesion  is  only  made  for  the 
sake  of  classification,  and  it  is  at  least  possible  that  they  are 
merely  different  manifestations  of  the  one  force  of  universal 
gravitation  already  considered. 

The  phenomena  of  adhesion  are  quite  numerous,  and  they  can 
be  most  conveniently  classified  according  to  the  mechanical  con- 
dition of  the  masses  of  matter  between  which  the  force  acts. 
"We  will,  therefore,  consider  in  order  the  phenomena  caused  by 
the  action  of, — 

First,  solids  on  solids  {cements'). 

Secondly,  solids  on  liquids  (capillarity,  solution). 

Thirdly,  solids  on  gases  {absorption  of  gases'). 

Fourthly,  liquids  on  liquids  (liquid  diffusion,  osmose). 

Fifthly,  liquids  on  gases  {solution  of  gases). 

Sixthly,  gases  on  gases  {gaseous  diffusion) . 

.          Solids  on  Solids. 

(181.)  Adhesion  between  Solids.  —  Many  of  the  most  famil- 
iar phenomena  of  daily  life  are  owing  to  the  attractive  forces 
which  exist  between  heterogeneous  particles  of  solids.  Thus 
the  particles  of  dust  floating  in  a  room  adhere  to  the  ceiling  in 
opposition  to  the  force  of  gravity.  In  like  manner,  the  particles 
of  chalk  adhere  to  the  vertical  surface  of  a  blackboard,  and  the 


THE  THREE   STATES   OF   MATTER.  343 

particles  of  plumbago  abraded  from  a  lead  pencil  adhere  to  a 
sheet  of  writing-paper.  So  also  the  adhesion  of  paint  to  wood 
or  canvas,  that  of  the  tin  amalgam  to  the  backs  of  glass  mirrors, 
and  that  of  gold-leaf  to  picture-frames,  belong  to  the  same  class 
of  phenomena.  The  numerous  important  applications  of  india- 
rubber  in  the  chemical  laboratory  furnish  still  further  illustra- 
tions of  adhesive  force. 

India-rubber  adheres  very  strongly  to  glass,  and  this  property 
renders  it  invaluable  for  making  stoppers  to  glass  bottles  and  air- 
tight joints  between  glass  tubes.  The  common  method  of  unit- 
ing together  glass  tubes  in  adjusting  chemical  apparatus  consists 
in  stretching  over  the  ends  of  the  tubes  a  short  tube  of  india- 
rubber  called  a  connector,  e  /,  (Fig. 
308,)  so  that  the  ends  of  the  two  glass 
tubes  shall  meet  within  it.  On  binding 
the  india-rubber  to  the  glass  by  means  of  *£"" "  3"r "~"^' 

a  silk  cord  or  fine  copper  wire,  the  adhe- 
sion is  sufficient  to  resist  the  action  of  most  gases,  unless  the  pres- 
sure is  considerably  greater  than  that  of  the  atmosphere.     These 
connectors  can  easily  be  made  of  the  required  dimensions  from 
sheet  india-rubber.     We  apply  a  strip  of  india-rubber  previously 
softened    by    heat,    to    the 
glass  tube,  as  represented  in 
Fig.  309,  and  then  cut  the 
two   edges   with   a   pair   of 
scissors,  which  should  have 
broad,   flat  blades,   and  be 

perfectly   clean.      The    cut  Fig.  309. 

edges  immediately  unite,  and 

the  union  can  be  made  more  solid  by  pressing  them  together 
between  the  thumb-nails.  The  india-rubber  connector  will  ad- 
here at  first  firmly  to  the  glass  tube,  but  it  can  be  easily  removed 
after  dipping  the  tube  into  water.  The  water  is  drawn  up 
between  the  glass  and  the  india-rubber  by  capillary  attraction, 
and  the  adhesion  is  destroyed. 

(182.)  Cements.  —  The  use  of  cements  not  only  illustrates 
the  existence  of  an  attractive  force  between  the  molecules  of 
heterogeneous  solids,  but  also  the  additional  fact,  that  the 
strength  of  this  force  varies  with  the  nature  of  the  solids.  In 
order  to  unite  two  pieces  of  wood,  we  first  fit  together  carefully 


344  CHEMICAL  PHYSICS. 

the  surfaces  to  be  joined,  and  then  interpose  between  these  sur- 
faces, perfectly  cleaned,  a  thin  layer  of  melted  glue.  When  the 
glue  hardens,  it  firmly  cements  together  the  two  pieces  of  wood, 
—  first,  by  the  adhesion  between  the  glue  and  the  wood,  and, 
secondly,  by  the  cohesion  between  the  particles  of  the  glue  itself. 
This  same  glue,  however,  would  fail  to  cement  together  pieces  of 
glass  or  of  stone,  because  the  adhesion  of  glue  to  these  solids  is 
much  feebler  than  its  adhesion  to  wood ;  but  fragments  of  glass 
and  porcelain  may  be  united  by  some  resinous  material,  such  as 
shellac,  and  those  of  stone  and  brick  by  mortar  or  some  cal- 
careous cement.* 

It  is  evident  that  in  all  these  cases  the  phenomena  of  adhesion 
are  mixed  with  those  of  cohesion.  The  adhesion  only  takes 
place  at  the  surfaces,  where  the  heterogeneous  particles  are 
brought  in  contact,  while  the  particles  of  the  solids,  and  those 
of  the  cement,  are  alike  held  together  by  the  force  of  cohe- 
sion. The  thinner  the  layer  of  cement,  the  more  perfectly  does 
it  fulfil  its  office,  since,  when  a  thick  mass  is  used,  the  unequal 
expansion  of  the  different  solids  in  contact,  caused  by  changes  in 
temperature,  tends  to  destroy  the  cohesion  of  the  particles  of  the 
cement.  It  not  unfrequently  happens  that  the  adhesion  between 
the  particles  of  a  cement  and  the  bodies  which  it  unites,  is 
greater  than  the  cohesion  which  holds  together  the  particles  of 
the  body  itself.  On  attempting  to  separate  two  pieces  of  wood 
along  a  glued  seam,  we  often  see  a  film  of  wood  split  off  adhering 
to  the  surface  of  the  glue ;  and  the  feat  of  splitting  a  bank-note 
is  accomplished  by  cementing  it  firmly  between  two  flat  surfaces, 
and  then  forcibly  separating  them,  when,  the  cohesion  of  the 
paper  being  feebler  than  the  adhesion  of  the  cement,  the  paper  is 
split  through  the  middle. f 

Solids  and  Liquids. 

(183.)  Adhesion  of  Liquids  to  Solids.  —  That  the  surfaces  of 
solids  are  generally  wetted  when  dipped  into  a  liquid  is  a  fact 
universally  known,  arid  it  is  self-evident  that  the  liquid  mole- 
cules are  held  to  the  solid  surface  by  a  mutual  attraction  between 


*  For  a  description  of  the  various  cements  used  in  the  laboratory,  the  student  is 
referred  to  the  works  on  chemical  manipulations  by  Faraday,  Morfit,  and  others. 
t  Miller,  Elements  of  Chemistry,  page  59. 


THE   THREE   STATES   OP  MATTER.  345 

the  liquid  and  solid  particles.  The  strength  of  this  attraction, 
which  is  much  greater  than  is  generally  supposed,  can  be  made 
evident  by  a  simple  experiment.  If  a  disk  of  glass  is  suspended 
to  the  pan  of  a  hydrostatic  balance,  and,  having  been  exactly 
counterpoised  by  weights  in  the  opposite  pan,  is  applied  to  the 
surface  of  a  liquid  capable  of  wetting  it,  it  will  be  found  neces- 
sary to  add  a  very  considerable  weight  to  the  counterpoise  in 
order  to  separate  the  disk.  Moreover,  when  the  separation  takes 
place,  the  disk  will  be  found  wet,  showing  that  the  separation 
has  been  between  the  particles  of  liquid,  and  not  between  the 
solid  and  liquid  surfaces,  and  indicating  that  the  adhesion  was 
greater  than  the  cohesion  of  the  liquid. 

In  experiments  made  by  Gay-Lussac,  at  a  temperature  of  8°, 
with  a  circular  plate  118.366  m.  m.  in  diameter,  59.4  gram,  were 
required  to  separate  it  from  water,  31.08  to  separate  it  from  alco- 
hol (Sp.  Gr.  =  0.8196),  and  34.1  to  separate  it  from  oil  of  tur- 
pentine. It  was  also  found  that  the  substance  and  thickness  of 
the  plate  had  no  influence  on  the  result,  proving,  as  before,  that 
the  force  overcome  by  the  weight  was  the  cohesion  between  the 
particles  of  the  liquid,  and  further  showing  that  the  distance 
through  which  the  force  acted  was  less  than  the  thickness  of  the 
liquid  film  which  remained  adhering  to  the  plate.  These  num- 
bers cannot,  however,  be  regarded  as  a  direct  measure  of  the  rel- 
ative cohesion  of  the  three  liquids,  as  could  easily  be  shown  by  a 
further  examination  of  the  conditions  of  the  experiment. 

Adhesion  also  exists  between  liquids  and  such  solid  surfaces  as 
they  have  not  the  power  of  wetting.  Gay-Lussac  found  that  a 
disk  of  glass  adhered  to  the  surface  of  mercury  with  a  very  con- 
siderable force.  In  an  experiment  made  as  just  described,  with 
a  disk  of  glass  118  m.  m.  in  diameter,  resting  on  the  surface  of 
a  basin  of  mercury,  it  required  in  one  case  296  gram.,  and  in 
another  158  gram.,  to  effect  a  separation,  the  amount  of  weight 
required  depending  on  the  manner  in  which  the  surfaces  were 
applied  to  each  other.  In  these  experiments,  when  the  surfaces 
were  parted,  the  separation  took  place  between  the  mercury  and 
the  glass,  indicating  that  the  weight  overcame  the  adhesion  of  the 
heterogeneous  particles,  and  not  the  cohesion  of  the  liquid,  as  in 
the  other  experiments.  Moreover,  the  force  required  to  effect 
the  separation  was  no  longer  independent  of  the  material  of  tho 
disk. 


346 


CHEMICAL  PHYSICS. 


Fig.  310. 


(184.)    Capillary   Attraction.  —  When  a   solid  body  is   par- 
tially immersed  in  a  liquid,  the  force  of  adhesion  produces  im- 
portant modifications  in  the  laws  of  liquid  equilibrium  as  already 
enunciated.     Thus,  for  example,  if  we  dip  the .  end  of  a  fine 
glass  tube,  2  or  3  millimetres  in  diameter,  into  water,  the  liquid 
will  not  maintain  the  same  level  within  and  without  the  tube  as 
required  by  the  principle  of  (130),  but  will  be  elevated  in  the 
interior  of  the  tube,  and  maintained  at  a  height  which  is  very 
considerably  above  the  exterior  level,  and  which  is  the  greater  the 
smaller  the  diameter  of  the  tube.     Moreover,  the  surface  of  the 
water  does  not  remain  horizontal  near  the  walls  of  the  tube,  as 
required  by  (129),  but  on  the' outside  it  curves 
towards  the  tube,  as  represented  in  Fig.  310,  and 
in  the  interior  it  assumes  a  concave  form,  which, 
for  tubes  less  than  2  millimetres  in  diameter,  is 
sensibly  hemispherical.     If  now  we  dip  the  end 
of  the  same  tube  into  liquid  mercury,  we  shall 
obtain  a  result  equally  opposed   to  the  laws   of 
liquid   equilibrium,   but    of    a   reversed    order. 
The  column  of  mercury  in  the  interior  of  the 
tube  will  be  depressed  below  the  outside  level,  and  its  surface 
will  assume  a  convex  shape,  which  for  a  small  tube  is  as  before 
sensibly  hemispherical,  while  on  the  outside  the  surface  of  the 
liquid  will  curve  from  the  tube,  as  if  repelled  by 
it  (Fig.  311).     By  repeating  these  experiments 
with  different  liquids,  and  with  tubes  of  various 
kinds,  we  shall  obtain  results  like  the  first  when- 
ever  the  liquid   has   the   power  of  wetting  the 
walls  of  the  tube,  and  results  like  the  second 
when  the  reverse  is  the  case ;  while  in  some  few 
cases  (as,  for  example,  when  the  tube  is  polished 
steel,  and  the  liquid  is  alcohol)  the  level  will  not 
be  changed,  and  the  surface  of  the  liquid  will  remain  horizontal 
both  within  and  without  the  tube.     These  phenomena  are  termed 
in  general  capillarity,  and  the  curved  surfaces  which  the  liquids 
assume  in  the  proximity  of  solid  bodies  are  called,  respectively, 
concave  and  convex  meniscuses.     In  studying  this  subject,  we 
will  first  consider  what  changes  the  molecular  forces  must  be  ex- 
pected to  produce  a  priori  in  the  laws  of  liquid  equilibrium,  and 
afterwards  we  will  examine  the  phenomena  and  see  how  closely 


Fig  311. 


THE   THREE   STATES    OF   MATTER.  347 

the  facts  coincide  with  our  theoretical  deduction.     Let  us  com- 
mence with  the  simplest  case  possible,  and  consider  how  the  sur- 
face of  a  liquid  must  be  disturbed  by  the 
contact  of  a  solid  bar. 

Take,  for  example,  a  liquid  particle,  m 
(Fig.  312),  in  contact  with  a  solid  bar, 
dipping  under  the  surface  of  any  liquid. 
This  particle  is  evidently  acted  upon  by 
the  force  of  gravity,  g-,  and  by  three  other 
forces.  The  first  of  these,  /,  is  the  result- 
ant of  the  attractive  forces  exerted  by  the 
liquid  particles  included  in  the  quarter- 
sphere  m  a  b.  The  other  two,/'  and/",  are  the  resultants  of  the 
attractive  forces  exerted  by  the  solid  particles  included  in  the 
two  quarter-spheres  mo  c  and  m  o  b,  the  radius  of  the  sphere  in 
each  case  being  the  insensible  distance  through  which  the  mole- 
cular forces  can  act.  We  can  now  decompose  eacli  of  these  three 
forces  into  a  vertical  and  a  horizontal  component.  Considering 
the  components  which  act  in  the  directions  m  a  or  m  b  positive, 
we  shall  have  for  the  horizontal  components  (35), 

/  cos  45°,  — /'  cos  45°,  -/"  cos  45° ; 

and  remembering  that  /"  =  /',  we  shall  also  have  for  the  single 
resultant  of  the  three  horizontal  components  (/ —  2  /')  cos  45°. 
In  like  manner,  for  the  vertical  components,  including  gravity, 
we  shall  have,  — 

£•,        /  cos  45°,          —  /'  cos  45°,         /"  cos  45°, 

and  for  the  single  vertical  resultant,  g  +/  cos  45°.  Let  us  next 
inquire  what  will  be  the  direction  of  the  final  resultant  of  the 
horizontal  and  vertical  forces,  whose  values  are 

(1.)    (/  —  2  /')  cos  45° ;        (2.)  g-  +  /  cos  45.        [121.] 

It  is  evident  that  the  vertical  force  must  always  be  positive,  and 
hence  directed  downwards ;  but  the  direction  of  the  horizontal 
force  will  depend  on  the  relative  values  of /and/',  that  is,  on  the 
relative  strength  of  the  cohesive  and  adhesive  attractions.  There 
may  be  three  cases,  according  as  /  is  less  than,  is  greater  than, 
or  is  equal  to  2  /'.  We  will  consider  each  case  separately. 

1st.  When  /  <;  2  /'.  If  the  cohesive  force  is  less  than  twice 
the  adhesive  force,  then  the  horizontal  force  [121.  1]  is  negative, 
and  the  resultant  of  this  force  with  the  vertical  force  [121.  2]  will 


348  CHEMICAL   PHYSICS. 

fall  within  the  angle  b  m  0,  and  take,  for  example,  the  direction 
MR  (Fig.  313).  Now,  since  the  surface  of  a  liquid  must  at 
every  point  be  normal  to  the  resultant  of  all 
the  forces  acting  at  that  point  (129),  it  fol- 
lows that  the  liquid  surface  will  be  drawn 
up  towards  the  solid  bar,  so  as  to  be  per- 
pendicular to  the  line  MR,  and  tangent  to 
the  line  M  N,  making  with  the  bar  an  angle 
D  M  N,  which  is  constant  for  the  same  sub- 
stances, and  is  called  the  angle  of  contact. 
If  next  we  consider  the  liquid  particles  M'  M",  <fcc.  adjacent 
to  M  on  the  surface  of  the  liquid,  it  is  evident  that  on  account 
of  their  greater  distance  they  will  be  acted  upon  less  strongly 
by  the  solid  bar,  and  hence  the  resultants  M1  R,  M"R",  &c. 
will  approach  more  and  more  nearly  the  vertical,  with  which 
they  will  soon  coincide.  Thus  it  appears  that  the  liquid  surface, 
which  must  be  at  each  point  perpendicular  to  these  resultants, 
will  be  curved  up  towards  the  bar,  but  will  become  horizontal  at 
a  certain  small  distance  from  it.  It  is  easy  to  see  that,  if  a  sec- 
ond bar  is  dipped  into  the  liquid  parallel  to  the  first,  the  surface 
of  the  liquid  between  the  bars  will  take  the  form  of  a  concave 
cylindrical  surface,  in  case  the  bars  are  sufficiently  near  together, 
and  that  in  a  tube  it  would  take  the  form  of  a  concave  meniscus, 
formed  by  the  revolution  of  the  curve  MM1  M"  round  the  axis 
of  the  tube. 

2d.   When/>2/'.     If  the   cohesive   force  is  greater  than 
twice  the  adhesive  force,  then  the  horizontal  force  [121.  1]  is 
positive,  and  consequently  directed  towards  the  liquid.     Hence 
the  resultant  of  this  force  and  the  ver- 
tical force   [121.  2]  will  fall  within  the 
angle  amb  (Fig.  312),  taking,  for  ex- 
ample, the   direction  MR  (Fig.  314), 
and  the  surface  of  the  liquid  will  be  per- 
pendicular to  this  resultant,  making  with 
the  solid  bar  an  angle  D  M  N  less  than 
Fig  3U  90°.    Moreover,  for  the  particles  M',  M", 

&G.  adjacent  to  M  on  the  surface  of  the  liquid,  it  can  be  proved 
that  the  resultants  of  the  molecular  forces  and  gravity  will  ap- 
proach the  vertical  nearer  and  nearer  the  farther  we  recede  from 
the  bar,  and  will  soon  coincide  with  it.  Hence  it  follows  that 


THE   THREE   STATES   OF   MATTER.  849 

the  liquid  surface  will,  in  this  case,  be  convex,  taking  the  form 
of  a  convex  cylinder  between  two  parallel  bars,  and  of  a  convex 
meniscus  in  a  fine  tube. 

3d.  When  /  =  2  /'.  When  the  cohesive  force  exactly  equals 
twice  the  adhesive  force,  then  the  horizontal  force  [121. 1J  becomes 
zero,  and  the  resultant  of  all  the  molecular  forces  and  gravity, 
acting  on  the  particle  w,  coincides  with  the  vertical.  In  this 
case  alone  the  surface  of  the  liquid  is  horizontal,  even  to  the  line 
of  contact  with  the  solid  bar,  and  consequently,  likewise,  hori- 
zontal between  two  bars,  or  in  the  interior  of  a  tube. 

(185.)  Form  of  the  Meniscus.  —  It  is  evident  from  the  last 
section,  that  the  exact  form  of  the  meniscus,  and  the  angle  of 
contact,  depend  upon  the  relative  values  of /and  2/'  [121],  and 
hence  upon  the  nature  of  the  solids  and  liquids  used.  The  con- 
ditions are  changed,  however,  when,  as  is  usual  in  such  experi- 
ments, the  solid  bar  or  tube  lias  been  previously  rinsed  with  the 
liquid.  In  such  cases  the  action  takes  place  between  the  parti- 
cles of  the  thin  film  of  liquid  covering  the  solid,  and  those  of  the 
same  liquid  into  which  it  is  dipped,  the  solid  itself  serving  only 
to  sustain  the  liquid  film,  and  it  is  then  found  that  the  result  is 
entirely  independent  of  the  nature  of  the  solid.  Moreover,  when 
the  solid  has  not  been  previously  moistened,  the  phenomena  are 
rendered  very  irregular  by  the  film  of  air  which  covers  the  sur- 
face of  the  bar  or  tube,  and  which  it  is  almost  impossible  to 
remove  without  moistening  the  whole  surface.  So  also,  when  the 
liquid  has  not  the  power  of  wetting  the  solid  surface,  as  in  the 
case  of  mercury  and  glass,  there  may  be  a  film  of  air  between 
the  two  of  sufficient  thickness  to  keep  the  liquid  particles  beyond 
the  sphere  of  action  of  the  adhesive  force.  In  such  cases  the 
form  of  the  liquid  surface  will  be  determined  by  the  action  of 
the  cohesive  force  alone,  and  this  action  will  be  entirely  similar 
to  that  which  gives  to  the  rain-drop  its  spherical  form  (129). 

Since  it  has  been  observed  that  the  surface  of  a  liquid  in  a 
tube  is  concave  when  it  wets  the  walls  of  the  tube,  and  convex 
when  it  has  not  the  power  of  thus  wetting  them,  it  follows  from 
the  last  section  that  a  liquid  will  wet  a  solid  surface  when  the 
force  of  cohesion  between  its  particles  is  less  than  twice  the  force 
of  adhesion  of  these  particles  to  the  solid. 

(186.)  Pressure  exerted  by  the  Molecular  Forces.  —  Having 
seen  how  the  molecular  forces  may  modify  the  form  of  a  liquid 
30 


350  CHEMICAL  PHYSICS. 

surface,  and  produce  either  a  concave  or  a  convex  meniscus,  let 
us  further  inquire  how  the  form  of  the  surface  may  modify  the 
law  of  liquid  pressure  already  enunciated  (126).  In  discussing 
the  subject  of  liquid  pressure,  caused  by  the  force  of  gravity 
(123  seq.},  we  left  out  of  view  any  action  which  might  be 
exerted  by  the  molecular  forces  emanating  from  the  liquid 
particles  themselves.  This  leads  us  into  no  error,  so  long  as  the 
surface  of  the  liquid  is  horizontal ;  but  when,  as  in  capillary 
tubes,  this  surface  is  curved,  the  action  of  the  molecular  forces 
can  no  longer  be  disregarded.  In  order  to  investigate  the  man- 
ner in  which  the  molecular  forces  may  influence  the  pressure 

exerted  by  a  liquid  mass, 
terminated  by  a  given 
surface,  XY  (Fig.  315), 
lot  us  study  the  action 
which  they  would  exert 
on  any  particle  taken  on 

Fig.  315.  or  near  this  surface.     If 

this  molecule  is  on  the 

surface,  as  M,  it  will  evidently  be  attracted  by  all  the  particles 
of  liquid  comprised  within  the  hemisphere  described  round  the 
point  M,  with  a  radius  equal  to  the  distance  of  sensible  attrac- 
tion^ and  it  is  easy  to  see  that  the  res-ultant  of  all  these  attractive 
forces  will  be  in  the  direction  M  P,  normal  to  the  surface.  If 
the  molecule  is  within  the  surface,  as  at  M1,  then  the  active  por- 
tion of  the  liquid  will  be  the  mass  enclosed  by  the  sphere  of  sen- 
sible attraction,  ABC.  This  may  be  divided  into  three '  parts 
by  an  equatorial  plane,  P  Q,  and  by  a  surface,  A1  B1,  symmetrical 
with  A  B,  and  equidistant  from  the  equator.  The  attraction  ex- 
erted by  the  portion  A  B  P  Q  is  evidently  balanced  by  the  equal 
and  opposite  attraction  exerted  by  A'  B'  P  Q,  so  that  the  result  is 
the  same  as  if  the  molecule  were  only  attracted  by  the  portion 
A'  B'  C.  The  resultant  of  all  the  attractive  forces  exerted  by 
the  particles  contained  in  this  portion  of  the  sphere  is  evidently 
much  less  than  before,  but  still  it  is  normal  to  the  surface.  Fi- 
nally, if  we  take  a  molecule,  M",  at  a  distance  from  the  surface 
equal  to  the  radius  of  sensible  attraction,  it  is  evident  that  the 
attractive  forces  acting  upon  it  will  balance  each  other.  If  then 
we  draw  a  surface,  X'  Y',  parallel  to  X  Y,  and  at  a  distance  from 
it  equal  to  the  radius  of  sensible  attraction,  we  shall  have  com- 


THE   THREE   STATES   OF   MATTER.  351 

prised  between  these  two  surfaces  a  liquid  film  whose  particles 
are  under  the  influence  of  forces  acting  perpendicularly  to  the 
surfaces,  and  exerting  an  effect  similar  to  that  of  gravity.  There 
must  then  result  from  the  action  of  these  molecular  forces  a 
pressure,  which  will  be  transmitted  in  all  directions,  according  to 
the  principle  of  (120),  and  whose  effect  must  be  added  to  those 
of  gravity  and  atmospheric  pressure. 

(187.)  Amount  and  Effect  of  the  Molecular  Pressure.  — 
Let  us  now  inquire  whether  the  form  of  the  surface  exerts  any 
influence  on  the  amount  of  the  molecular  pressure.  For  this 
purpose  let  us  take  a  molecule,  M'  (Fig.  316),  at  a  distance 
below  the  surface,  M1  II,  less  than  M '  C, 
the  radius  of  sensible  attraction,  and  con- 
sider what  will  be  the  relative  amount 
of  molecular  pressure  exerted  by  this 
molecule,  —  1st,  when  the  surface  is 
plane;  2dly,  when  it  is  concave;  and 
Sdly,  when  it  is  convex. 

If  the  surface  is  plane,  as  A  B,  the 
attraction  exerted  by  the  liquid  mass 
A  BPQ  is  balanced  by  that  of  A'  B1  PQ, 
and  the  only  force  which  produces  pres- 
sure is  the  attraction  exerted  by  A'  B1  C.  Let  us  represent  the 
value  of  this  force  by  A. 

If  now  the  surface  is  concave,  as  D  E,  it  is  evident  that  the 
only  portion  of  the  liquid  within  the  sphere  of  sensible  attraction, 
whose  attractive  force  is  not  neutralized,  is  the  portion  D'  E'C, 
cut  off  by  a  surface  D'  E',  drawn  symmetrically  to  D  E.  Since 
this  liquid  mass  is  less  than  A'  B1  (7,  the  attractive  force  which 
it  exerts  must  be  less  by  an  amount  we  will  call  B,  and  it  is  evi- 
dent that  the  value  of  B  will  increase  as  the  radius  of  curvature 
of  the  surface  diminishes.  The  value  of  the  force  which  is  ex- 
erted in  molecular  pressure  may  then  be  represented  by  A  —  B, 
when  the  surface  is  concave. 

If,  lastly,  the  surface  is  convex,  as  KL,  and  we  draw  K'  L1 
symmetrical  with  this,  it  is  equally  evident  that  the  active  por- 
tion of  the  liquid  is  now  K1  L1  C\  and  since  this  mass  is  greater 
than  A1  B'  C,  the  value  of  the  molecular  pressure  may  be  repre- 
sented by  A  -f-  B1,  when  the  surface  is  convex. 

Since  what  has  been  shown  to  be  true  of  the  pressure  exerted 


352  CHEMICAL   PHYSICS. 

by  the  molecule  M1  is  true  of  all  the  molecules  contained  in  the 
thin  film  bounded  by  the  surfaces  X  Y,  and  X'  Y  (Fig.  315),  it 
follows  that,  when  the  surface  of  a  column  of  liquid  is  concave, 
it  exerts  a  less  pressure,  and  conversely,  when  the  surface  is 
convex,  it  exerts  a  greater  pressure  than  when  it  is  plane,  as- 
suming always  that  the  radius  of  curvature  of  the  surface  is 
comparable  with  the  radius  of  sensible  attraction. 

(188.)  Effects  of  Molecular  Pressure.  —  It  is  now  easy  to 
see  in  what  way  the  molecular  pressure  may  modify  the  prin- 
ciple of  (130),  when  one  of  the  vessels  is  very  small.  Let  us 
suppose,  then,  that  we  have  a  fine  tube  of 
glass,  dipping  into  a  liquid  (Fig.  317).  By 
the  principles  of  hydrostatics,  the  level  of 
the  liquid  should  be  the  same  within  and 
without  the  tube,  because  it  is  a  necessary 
condition  of  equilibrium  that  the  pressure  on 
any  given  section,  as  M 'N9  should  be  the 
same,  whether  exerted  by  the  column  of  liquid 
in  the  tube,  or  by  the  liquid  mass  outside,  and 
this  can  only  be  when 

S  .  II.  (Sp.  Gr.)  =  S  .  II' .  (Sp.  Gr.)  [122.] 

or  when  J/=  H'  (compare  130).  This  equation,  however,  only 
has  regard  to  the  pressure  exerted  by  liquids  in  consequence  of 
their  weight,  although,  as  we  have  just  said,  the  molecular  forces 
exert  a  pressure  themselves  whose  effect  must  be  added  to  that 
of  gravity.  As  the  surface  of  the  liquid  outside  the  tube  is  hori- 
zontal, the  molecular  pressure  transmitted  by  it  to  the  section 
M  N  may  be  represented  by  A,  and  the  whole  pressure  on  the 
section  will  be  S  .  JJ.  (Sp.Gr.)  -f-  A.  If,  however,  the  liquid 
wets  the  tube,  the  interior  surface  will  be  concave,  and  the  pres- 
sure transmitted  from  the  interior  of  the  tube  to  the  section  will 
be  S  .//'.(  Sp.  Gr.)  +  (A  —  B) .  Evidently  there  can  only  be 
an  equilibrium  when 


or 


that  is  to  say,  when  the  level* in  the  tube  is  above  the  level 
outside.    The  difference  of  level,  A,  measures  the  difference  of 


S'.  H.  (Sp. GV.)  +  A=*S.  II' .  (Sp.Gr.*)  +  (4  —  £), 

h;  [123.] 


THE   THREE   STATES   OP   MATTER. 


353 


pressure,  £,  caused  by  the  concavity  of  the 
surface. 

If  the  liquid  does  not  wet  the  tube  (Fig. 
318),  then  the  interior  surface  will  be  con- 
vex, and  the  pressure  transmitted  from  the 
interior  of  the  tube  to  the  section  will  be 
S.  H'  .  (Sp.Gr.)  +  (4  +  #)• 
then  have  equilibrium  when 


S. 


$>.  GV. 


.S.  dr 


or 


[124.] 


that  is  to  say,  when  the  level  in  the  tube  is  below  the  level  out- 
side ;  and  here,  as  before,  the  difference  of  level  measures  the 
difference  of  pressure,  which  is  caused  in  this  case  by  the  con- 
vexity of  the  surface. 

Between  these  two  conditions  there  is  a  third,  in  which  the 
liquid  surface  is  level  within  the  tube.  In  this  case  it  is  evident 
that  the  molecular  pressures  will  balance  eacli  other,  and  there 
can  be  equilibrium  only  when  H'  =  H \  or  when  the  level  is  the 
same  within  and  without  the  tube. 

These  results,  which  we  have  now  deduced  theoretically,  are 
fully  confirmed  by  observation  ;  for  we  find,  as  has  already  been 
stated  (184),  that  a  concave  meniscus  is  always  accompanied  by 
an  elevation  of  the  liqiiid  column  in  a  capillary  tube,  and  a  con- 
vex meniscus  by  a  corresponding  depression.  The  phenomena 
of  capillarity  may  be  illustrated  not  only 
by  means  of  a  simple  tube,  as  represented 
in  Figs.  310  and  311,  but  also  by  a  siphon 
tube,  one  of  whose  branches  is  very  small, 
while  the  other  is  at  least  20  millimetres 
in  diameter  (Figs.  319  and  320).  The 
depression  or  elevation  of  the  liquid  in 
the  smaller  tube  becomes  then  very  evi- 
dent, and  can  easily  be  measured.  A 
number  of  these  tubes  may  be  mounted 
together  for  comparison,  as  represented 
in  Fig.  321. 

These  phenomena  are   entirely  independent  of  the  pressure 
30* 


Fig  319. 


Fig-  390. 


354 


CHEMICAL   PHYSICS. 


to  which  the  apparatus  is  ex- 
posed. They  are  the  same  in 
compressed  air  as  in  a  vacuum, 
and  are  not  influenced  by  the 
thickness  of  the  walls  of  the 
tube.  They  vary,  on  the  oth- 
er hand,  with  the  material  of 
the  tube,  and  with  the  nature 
of  the  liquid.  When,  how- 
ever, the  tube  has  previously 
been  wet  with  the  liquid,  the 
phenomena  are  also  entirely 
independent  of  the  material 
of  which  it  is  formed,  and  at 
any  given  temperature  vary 
only  with  the  nature  of  the 
liquid  and  the  diameter  of 
the  tube. 

If  we  take  tubes  of  the  same 
diameter,  and  dip  their  ends 
in  different  liquids,  capable  of 
moistening  the  walls,  we  find  that  the  heights  to  which  the  liquid 
columns  are  elevated  differ  very  greatly.  If  the  tube  is  1.8  m.  m. 
in  diameter,  the  height  is  23.1  m.  m.  for  water,  9.8  m.  m.  for  oil 
of  turpentine,  7.07  m.  m.  for  alcohol,  and  still  less  for  ether.  It 
is  essential  in  these  experiments  that  the  tubes  should  be  pre- 
viously cleaned,  and  carefully  rinsed  out  with  the  liquid  to  be 
used.  Otherwise  the  phenomena  are  also  influenced  by  the  ma- 
terial of  the  tube,  and  are  rendered  very  irregular  by  the  film  of 
air  adhering  to  the  surface.  This  is  especially  true  when  the 
liquid  has  not  the  power  of  wetting  the  surface,  and  the  order  of 
the  phenomena  is  reversed.  The  amount  of  depression  in  such 
cases  not  only  varies  with  the  nature  of  the  tube  and  of  the 
liquid,  but,  moreover,  it  is  not  the  same  for  the  same  tube  and 
liquid  under  different  circumstances.  For  example,  in  the  case 
of  mercury  and  glass,  the  form  of  the  meniscus,  and  the  depres- 
sion of  the  mercury  column,  which  depends  upon  this  form,  vary 
so'  greatly  with  the  impurity  of  the  metal,  the  presence  of  the  air, 
and  the  nature  of  the  glass,  that  it  is  not  possible  to  calculate  the 
amount  from  any  general  measurements,  but  it  is  necessary  to  de- 


rig.  321. 


THE   THREE   STATES   OP   MATTER.  355 

termine  it  by  experiment  for  each  particular  instrument.  Thus, 
in  the  same  tube  the  mercury  column  will  be  more  depressed  in 
a  vacuum  than  in  the  air,  especially  when  the  air  is  moist.  So, 
also,  mercury  which  has  been  boiled  in  the  air  forms  a  less  con- 
vex meniscus  than  mercury  which  has  been  boiled  in  an  atmos- 
phere of  hydrogen  or  carbonic  acid.  And  lastly,  a  small  amount 
of  oxide  dissolved  in  the  mercury  may  even  invert  the  order  of 
the  phenomena,  causing  it  to  assume  a  plane,  or  even  a  slightly 
concave  surface. 

In  determining  the  amount  of  pressure  from  the  height  of 
a  mercury  column  in  a  barometer  tube,  or  in  other  forms  of 
tube-apparatus  used  in  experiments  on  gases,  it  is  important 
to  correct  the  observations  for  the  capillary  depression  ;  but 
since,  from  the  causes  just  stated,  the  amount  is  uncertain,  it  is 
best  either  to  use  tubes  so  large  that  it  is  rendered  insensible, 
or  else  so  to  arrange  the  apparatus  that  the  effect  of  capillarity  in 
one  arm  of  a  siphon  is  balanced  by  an  equal  effect  in  the  other. 
In  the  barometers  of  Rcgnault  and  Fortin  the  amount  of  depres- 
sion is  a  constant  quantity,  and  is  determined  once  for  each  instru- 
ment (159  and  160)  ;  but  even  in  a  well-made  barometer  the 
surface  of  the  mercury  is  liable  to  changes,  which  alter  the  form 
of  the  meniscus,  and  consequently  cause  a  variation  in  the 
amount  of  depression.  The  convexity  of  the  meniscus  can  gen- 
erally be  restored  by  tapping  on  the  glass ;  but  when  the  surface 
of  the  mercury  is  badly  soiled,  it  is  necessary  to  refill  the  tiibe. 

(189.)    Numerical  Laics.  —  Although  the  theory  of  capillarity, 
as  thus  far  developed,  explains  and  predicts  the  general  order 
of  the  phenomena,  it  does  not  yet  enable  us  to  calculate  the 
amount  of  the  elevation  and  depression  in  different 
tubes.     This,  as  we  have  seen,  varies  with  the  na- 
ture of  the  liquid,  and,  when  the  walls  of  the  tube 
have  not  been  previously  moistened  with  the  liquid, 
also  with  the  nature  of  the  tube.     But  assuming 
that  all  other   conditions    are  equal,  let   us   in- 
vestigate the  relation  between  the  capillary  effect 
and  the  size  of  the  tube. 

For  this  purpose  let  us  take  the  simple  case 
of  a  capillary  tube  (Fig.  322)  dipping  in  a  mass 
of  liquid  which  is  capable  of  wetting  its  surface, 
and  which  consequently  rises  in  its  bore  to  a  Fig  322. 


356  CHEMICAL   PHYSICS. 

mean  height  AB.  In  the  first  place,  it  is  evident  that  the 
mass  of  the  tube  just  above  this  level  must  attract  the  liquid 
molecules  below,  and  that  there  will  thus  result  a  vertical  force, 
which  will  tend  to  raise  the  liquid  column.  Since  this  force  is 
proportional  to  the  number  of  solid  particles  within  the  sphere 
of  attraction,  and  hence  to  the  perimeter  of  the  tube,  we  may 
represent  it  by  the  expression  pa,  in  which  a  is  a  constant 
quantity  depending  on  the  nature  of  the  tube  and  the  liquid,  and 
p  the  perimeter  of  the  tube.  If  now,  in  the  second  place,  we  con- 
sider the  portion  of  the  tube  between  A  B  and  CD,  it  is  equally 
evident  that  the  attractive  forces  exerted  by  the  solid  particles 
will  balance  each  other,  and  can  therefore  produce  no  effect  either 
in  elevating  or  depressing  the  column.  Finally,  the  molecules  of 
the  tube  placed  just  above  C  D  will  attract  the  particles  situated 
just  below  in  the  prolongation  of  the  liquid  column,  and  will  evi- 
dently exert  a  force  tending  to  raise  this  column,  which  equals,  as 
before,  pa,  arid  which  added  to  the  first  gives  us  2pa  as  the 
whole  value  of  the  upward  pressure. 

But  we  have  thus  far  left  out  of  view  the  liquid  mass  below 
the  end  of  the  tube.  If  we  conceive  of  the  solid  tube  as  pro- 
longed by  a  tube  of  liquid,  CDM  N,  it  is  evident  that  the 
liquid  particles  forming  the  walls  of  this  tube  will  attract  those 
of  the  liquid  column  just  above  C  Z),  and  will  thus  exert  a  force 
tending  to  depress  it.  Representing  by  a'  a  constant  depending 
on  the  nature  of  the  liquid,  we  shall  have  for  this  downward 
force  the  value  p  a',  and  for  the  whole  vertical  force  the  value 
p  (2  a  —  a'),  a  force  which  will  raise  or  depress  the  column 
according  as  (2  a  —  a')  is  positive  or  negative.  This  force  must 
evidently  be  equal  to  the  weight  of  the  column  of  liquid  which 
it  elevates  or  depresses  ;  and  since  this  weight  may  be  found 
by  multiplying  together  the  area  of  the  section  of  the  tube,  s,  the 
height  of  the  column,  h,  and  the  specific  gravity  of  the  liquid, 
Sp.  Gr.j  we  obtain 

p  (2  a  —  a')  =  s  .  h  .  (Sp.  £r.), 
or 

=±£a»  [125.] 


in  which  last  a"  =   ~     ~     ,  and  is  constant  so  long  as  the  liquid 
and  substance  of  the  tube  are  the  same. 


THE   THREE   STATES   OF  MATTER.  357 

If  the  tube  is  cylindrical,  *  =  —jv  ==  n  an(^  ^  ==  ^  7T  a"' 
For  another  tube  of  the  same  material,  but  different  diameter, 
D1,  we  obtain  h1  =  db  -^/  #",  whence  we  deduce 

db  h :  db  A'  =  D1 :  D,  [126.] 

or  in  words,  The  elevations  or  depressions  of  a  given  liquid  in 
cylindrical  tubes  of  the  same  material,  but  of  different  diameters, 
are  inversely  proportional  to  the  diameters  of  the  tubes. 

If  the  tube  has  a  rectangular  section,  the  perimeter  is  equal 
to  2  (m  -\-  n),  the  lengths  m  and  n  being  those  of  the  sides  of 

the  rectangle,  and  we  have  *  =  '  .     When  the  length 

s  mn  p         2 

of  one   side   is   infinite,   we  have  also  n  =  oo  ,  *-  =  —  ,  and 

2  s        m 

h  =  ±   —  a",  from  which  we  can  deduce 
m 

dbA  :  db  h'  =m':  m.  [127.] 

The  case  supposed  is  evidently  that  of  two  plates  parallel  to  each 
other,  and  separated  by  a  distance  m.  Hence  the  elevation 
or  depression  of  a  given  liquid  between  two  parallel  plates  is 
inversely  proportional  to  their  distance  apart. 

If,  lastly,  we  compare  the  effect  produced  by  a  cylindrical  tube 

4  2 

when  h  =  =t  -~  a",  and  that  by  parallel  plates  when  h'  =  db  —  a", 

we  obtain  the  proportion 

A:/i'  =  2«i:  D,  [128.] 

by  which  we  find,  that  when  m  =  D,  then  A  —  2  /*',  or  in 
words,  The  variation  of  level  caused  by  two  plates  is  one  half 
of  that  caused  by  a  tube  of  the  same  nature,  whose  diameter  is 
equal  to  the  distance  between  the  plates. 

(190.)  Verification  of  the  Laws.  First  Law.  —  It  follows 
from  [126] ,  that,  if  the  first  of  the  three  numerical  laws,  which 
have  thus  been  deduced  theoretically,  is  correct,  the  product  of 
the  elevation  or  depression  of  the  liquid  column  into  the  diam- 
eter of  the  tube  must  be  always  a  constant  quantity  for  the  same 
liquid.  That  this  is  approximatively,  at  least,  the  case,  is  shown 
by  the  following  table,  taken  from  Jamin's  Cours  de  Physique, 


358  CHEMICAL   PHYSICS. 

to  which  we  are  indebted  also  for  the  general  method  followed 
in  the  discussion  of  this  subject. 

Diameter  D.  Elevation  h.  Product  D  h. 

in.  m.  ID.  m. 

(  1  9Q  9'-4  1  f\  9Q  ftT 

Water  J  ^o.io  ^y.o/ 

(1.90  15.58  29.GO 

A,    ,   ,  (1.29  9.18  11.84 

Alcohol,     .-_..;.,    jo()  ^  ^ 

Parallel  Plates  and  Water,    .        1.069  13.57  14.52 

This  law  is  not,  however,  exact,  when  the  diameter  of  the 
tube  is  so  large  that  we  can  no  longer  neglect  the  curvature 
of  the  surface  which  terminates  the  liquid  column  (we  assume 
always  that  the  height  of  the  column  is  measured  to  the  lowest 
point  of  the  concavity,  or  to  the  highest  point  of  the  con- 
vexity). When  the  diameter  of  the  tube  is  not  greater  than 
one  or  two  millimetres,  the  surface  is  approximatively  hemi- 
spherical, and  we  can  then  easily  estimate  the  amount  of  devi- 
ation. If,  as  above,  we  represent  by  h  and  h'  the  heights  of 
two  columns  of  the  same  liquid  in  tubes  of  different  diameters, 
measured  to  the  lowest  point,  w,  of  a  concave  meniscus,  it  is  evi- 
dent that,  in  order  to  obtain  exactly  the  weight  of  these  liquid 
columns,  we  must  add  to  the  weights  of  the  liquid  cylinders 
s  .  h  .  (Sp.Gr.)  and  s' .  h' .  (Sp.Gr.)  the  weight  of  liquid  above 
the  point  n.  The  volume  of  this  liquid  is  evidently  equal  to 
the  difference  of  volume  between  a  hemisphere  and  a  cylin- 
der of  the  same  diameter  and  of  a  height  equal  to  the  radius 
of  the  hemisphere.  Using  the  notation  of  the  last  section,  we 
find  for  this  volume  the  value  &  Z)3  n  —  rV  D3  it  =  ^  D3  it, 
and  for  the  total  weights  of  the  liquid  columns  the  values 

J  I>2  Ji  (h  +  ^\  (  Sp.  GV.),  and  *  D'*7t  (/<'  +  ®\  (  Sp.  dr.),  and 
by  the  same  course  of  reasoning  as  before  [125] ,  we  deduce 


*  +       :  ±   *'  +       =  D'  :  D.  [129.] 


The  double  sign  ±  is  used,  because,  as  can  easily  be  proved,  the 
proportion  is  equally  true  when  the  meniscus  is  convex.  Hence 
it  follows,  that,  when  the  tubes  are  not  more  than  one  or  two  mil- 
limetres in  diameter,  the  law  of  inverse  proportions  is  correct, 
when  we  add  to  the  observed  heights  one  sixth  of  the  diameter 


THE   THREE   STATES   OF   MATTER. 


359 


of  the  tube,  the  correction  required  for  the  meniscus ;  and  obser- 
vation confirms  this  result  of  theory. 

When  the  tubes  are  very  small,  and  the  elevations  or  depres- 
sions correspondingly  large,  we  can  neglect  the  very  small  value 

j,  and  regard  the  law  as  accurate  without  this  correction.  When, 

however,  the  tubes  are  extremely  small,  a  new  cause  of  devia- 
tion from  the  law  is  introduced.  In  experiments  on  capillarity, 
as  already  stated,  we  can  obtain  constant  results  only  when  the 
surfaces  of  the  tubes  have  been  previously  moistened  with  the 
liquid  to  be  used,  and  the  results  are  then  the  same  as  if  the 
experiment  were  made  with  a  liquid  tube  of  less  diameter, 
the  solid  wall  serving  only  to  support  the  liquid  particles.  If 
the  tube  is  one  or  two  millimetres  in  diameter,  the  thickness 
of  the  liquid  film  may  be  neglected ;  but  when  the  tube  is  very 
small,  this  thickness  sensibly  diminishes  its  effective  size,  and  we 
should  therefore  expect  that  it  would  raise  a  liquid  column  to  a 
greater  height  than  that  required  by  the  law,  as  we  find  to  be 
the  case. 

When,  on  the  other  hand,  the  tubes  are  more  than  three  milli- 
metres in  diameter,  the  surface  of  the  liquid  column  differs  so 
considerably  from  that  of  a  hemisphere,  that  the  proportion  [129] 
no  longer  holds  true,  and  the  deviation  from  the  law  becomes 
very  large.  Even  in  such  cases,  however,  the  heights  to  which 
liquids  will  rise  can  be  calculated  when  the  precise  form  of  the 
meniscus  is  given ;  but  the  methods  are  too  complicated  for  an 
elementary  treatise. 

Second  Law.  —  The  second  law  of  (189)  can  be  verified  by  a 
very   instructive   experiment.     If  we   take 
two  glass  plates,  united  by  hinges  at  one 
side,  and,  having  very  slightly  opened  these 
hinges,  dip  the  ends  of  the  plates,  as  repre- 
sented by  Fig.  323,  in  colored  water,  we 
find  that  the  liquid   rises   between   these 
plates  to  a  variable  height,  depending  on 
the  interval  which  separates  them,  its  up- 
per surface   taking   the   form  of  a  curve,  Fig.  323. 
known  in  geometry  under  the  name  of  an 
equilateral  hyperbola.     Let  us  inquire  whether  the  form  of  this 
curve  does  not  furnish  a  confirmation  of  the  law  under  discussion. 


360  CHEMICAL   PHYSICS. 

We  may  evidently  regard  the  two  glass  plates  as  consisting 
of  an  infinite  number  of  infinitely  narrow  parallel  strips,  as 
shown  by  Fig.  324.  If  then  the  law  is 
correct,  it  follows  [127]  that  the  heights 
to  which  the  liquid  is  elevated,  at  any  two 
points,  will  be  proportional  to  the  interval 
between  the  plates  at  these  points,  so  that 

2  of1 

at  every  point  we  must  have  h  = .       If  now  we   take   for 

m 

the  axis  of  y  the  vertical  line  of  intersection  of  the  two  planes, 

and  for  the  axis  of  x  the  line  of  contact 
of  the  water  level  with  one  of  them,  we 
shall  have  (Fig.  325),  MP=h  =  ij, 
A  P  =  x,  and  P  Q  =  m  =  C  x,  in 
which  C  is  a  constant  quantity  depend- 
ing on  the  angle  between  the  planes. 

2  ct" 
Substituting  these  values  in  h  = , 

,  .    .  2  a"  m 

we  obtain        y  =  — —  , 

Fig.  825.  2  a" 

or  x  y  =  —77-  =  a  constant, 

o 

which  is  the  equation  of  an  equilateral  hyperbola  referred  to  its 
asymptotes  as  co-ordinate  axes.  Since  this  is  the  curve  which 
the  liquid  surface  always  assumes,  it  is  evident  that  the  second 
law  is  verified  by  the  experiment. 

Third  Law.  —  When  the  ends  of  two  parallel  glass  plates, 
maintained  at  a  small  distance  from  each  other,  are  dipped  into 
water,  and  the  difference  of  level  measured,  it  lias  been  found  that 
the  product  of  the  distance  between  the  plates  by  the  elevation 
of  the  liquid  is  one  half  of  that  obtained  with  glass  tubes.  This 
fact  is  shown  in  the  table  on  page  358,  and  verifies  the  third  law. 

(191.)  Influence  of  Temperature  on  Capillary  Phenomena.  — 
The  general  expression  for  the  elevation  or  depression  of  the 
liquid  column  in  a  capillary  tube  [125]  may  be  written 

4        2  a  —  a> 
'    D    '  IS^Gr.)  ' 

and  it  is  evident  that  any  cause  which  changes  either  the  spe- 
cific gravity  of  the  liquid,  or  the  relative  values  of  the  cohesive 
and  adhesive  forces,  will  produce  variations  in  the  value  h. 
Hence  an  increase  of  temperature,  which  diminishes  the  specific 


THE   THREE   STATES   OF   MATTEB.  361 

gravity  by  expanding  the  liquid,  would  of  itself  alone  increase 
the  elevation  or  depression  of  the  column  ;  but  since  this  increase 
of  temperature  produces  changes  in  the  molecular  forces,  and 
hence  affects  the  value  of  the  term  2  a  —  a',  we  find  that  the 
elevation  or  depression,  instead  of  increasing  with  the  tempera- 
ture, actually  diminishes.  This  decrease  is  not,  however,  simply 
proportional  to  the  temperature,  but  follows  much  more  compli- 
cated laws.  The  following  table  shows  the  height  at  which  the  dif- 
ferent liquids  enumerated  stand  at  0°  C.  in  a  tube  two  millimetres 
in  diameter,  together  with  the  coefficient  of  correction  for  tempera- 
ture, which,  multiplied  by  £,  the  number  of  degrees  above  0°, 
gives  the  amount  in  millimetres  to  be  deducted  from  the  height 
at  0°,  in  order  to  find  the  height  of  the  capillary  column  at  the 
temperature  required.  The  last  column  gives  the  limits  of  tem- 
perature between  which  the  formulas  hold  true. 


Sp.  Or. 

i 

Limits  of 

at  GO. 

n 

Temperature. 

m.m. 

o               o 

"Water, 

1.0000 

15.332 

—0.0286  t 

Oto    82 

Ether, 

0.7370 

5.400 

—0.0254  1 

—6  to    35 

Olive  Oil, 

0.9150 

7.461 

—0.0105  t 

15  to  150 

Oil  of  Turpentine, 

0.8902 

6.7GO 

—0.0167* 

17  to  137 

Alcohol, 

0.8208 

6.050 

—0.0116* 

—0.000051  1*      0  to    75 

Sulphuric  Acid, 

1.840 

8.400 

—0.0153  t 

—  0.000094  <2     12  to    90 

(192.)  Spheroidal  Condition  of  Liquids.  —  When  the  adhe- 
sion of  a  liquid  to  a  solid  surface  is  more  than  twice  as  great  as 
the  cohesion  between  its  particles,  it  spreads  over  the  surface  of 
the  solid  and  wets  it  (185).  If,  however,  the  force  of  adhesion 
is  less  than  this,  the  liquid  forms  in  drops,  which  roll  round  on 
the  solid  surface  like  drops  of  mercury  on  glass,  or  drops  of  water 
on  oiled  paper.  The  form  of  these  drops  is  determined  by  the 
action  of  three  forces  ;  first,  the  cohesion  of  the  particles  of  the 
liquid,  secondly,  the  adhesion  of  the  liquid  to  the  solid,  and 
lastly,  gravity.  When  very  small,  the  drops  are  sensibly  spher- 
ical ;  but  as  they  increase,  the  sphere  becomes  flattened  by  the 
action  of  gravity,  and  they  assume  a  spheroidal  shape.  Hence 
liquids,  under  these  circumstances,  are  said  to  be  in  a  spheroidal 
condition.  Since  most  solid  surfaces  are  wet  by  water,  alcohol, 
and  similar  liquids,  the  spheroidal  condition  is  their  exceptional 
state  ;  but  it  is  familiar  to  us  in  the  cases  just  mentioned,  and 
in  several  others.  As  the  effect  of  heat  is  to  diminish  both  the 
31 


B62  CHEMICAL   PHYSICS. 

cohesive  and  adhesive  forces,  we  can  easily  conceive  how  it  may 
so  far  alter  their  relative  values  as  entirely  to  change  the  rela- 
tions of  a  liquid  to  a  solid  surface.  This  result  is  readily  ob- 
tained with  water,  alcohol,  and  similar  liquids,  which,  at  the 
ordinary  temperature,  wet  metallic  surfaces. 

It  will  hereafter  be  shown,  that  we  cannot  heat  a  liquid  in  the 
open  air  above  its  boiling  point,  and  hence  we  cannot  diminish  the 
cohesive  force,  except  to  a  limited  extent ;  while,  on  the  other  hand, 
we  can  heat  the  metals  to  a  far  higher  temperature,  and  thus  di- 
minish the  adhesion,  until  the  force  becomes  less  than  twice  that 
of  cohesion,  when  the  liquid  will  assume  the  spheroidal  state. 
Thus,  for  example,  if  water  is  dropped  into  a  metallic  vessel  heat- 
ed above  171°  C.,  it  rolls  along  the  surface  of  the  metal  like  mer- 
cury on  glass,  and  remains  in  that  state  until  the  temperature  falls 
to  142° ;  then  it  moistens  the  metallic  surface,  and  evaporates 
rapidly.  Alcohol  acts  in  the  same  way  when  the  temperature  of 
the  vessel  is  above  134°,  and  ether  when  it  is  above  61°.  The 
temperature  of  the  liquid  itself,  under  these  circumstances,  is 
nearly  constant,  being  always  several  degrees  below  its  boiling 
point :  thus  96.5  is  the  temperature  of  water,  75.8  that  of 
absolute  alcohol,  34.2  that  of  ether,  and  — 10.5  that  of  liquid 
sulphurous  acid.  The  temperature  of  the  liquid  may  there- 
fore be  several  hundred  degrees  below  that  of  the  metallic 
vessel,  as  is  well  illustrated  by  liquid  sulphurous  acid,  which  in 
the  spheroidal  state  retains  a  temperature  10.5  degrees  below 
the  freezing  point  of  water,  even  when  the  metallic  crucible 
containing  it  is  visibly  red-hot.  If  water  is  slowly  dropped 
into  this  singular  liquid  under  these  circumstances,  it  is  at  once 
congealed,  thus  exhibiting  the  apparent  paradox  of  freezing 
water  in  a  red-hot  crucible. 

One  of  the  most  instructive  illustrations  of  the  spheroidal  con- 
dition of  water  is  the  rude  method  used  in  laundries  for  testing 
the  degree  of  heat  of  a  flat-iron.  If  a  drop  of  water  let  fall  upon 
it  does  not  boil,  but  runs  along  the  surface  of  the  metal,  the  iron 
is  considered  sufficiently  hot ;  but  if  the  drop  adheres,  and  rapidly 
boils  away,  the  temperature  is  known  to  be  too  low.  We  shall 
have  occasion  to  return  to  this  subject  in  the  chapter  on  Heat. 

(193.)  Examples  and  Illustrations  of  Capillarity.  —  One 
of  the  most  familiar  examples  of  capillary  action  is  seen  in 
the  wicks  of  lamps  and  candles.  These  consist  of  very  fine 


THE   THREE   STATES   OF   MATTER.  363 

vegetable  tubes,  through  which  the  oil  or  melted  combustible  is 
elevated  to  the  flame,  and  supplied  as  fast  as  it  is  burnt.  This 
same  principle  also  influences  the  circulation  of  the  liquid  juices 
in  the  porous  tissues  of  organized  beings,  and  it  is  the  principal 
means  by  which  water,  with  the  substances  it  holds  in  solution,  is 
supplied  to  the  growing  plant.  It  is  the  capillary  action,  which, 
during  the  droughts  of  summer,  draws  up  to  the  surface  of  the 
soil  the  water  necessary  for  vegetation,  which  had  penetrated  into 
it  during  the  heavy  rains  of  spring.  When  the  water  holds  salts 
in  solution,  these  are  deposited  as  it  subsequently  evaporates, 
forming  those  incrustations  which  are  frequently  seen  on  the 
brick  walls  of  old  houses  and  on  the  surfaces  of  saltpetre  beds. 

The  laws  of  capillary  action  furnish  the  explanation  of  many 
other  remarkable  phenomena.  A  platinum  wire  will  float  on  the 
surface  of  mercury,  although  its  specific  gravity  is  very  much 
greater  than  that  of  the  liquid  metal.  So  also  a  very  fine  metal- 
lic wire,  which  has  been  slightly  greased  by  passing  it  between  the 
fingers,  can  be  made  to  float  upon  water,  and  the  same  is  true  of 
many  metallic  powders.  This  singular  result  is  explained  by 
the  fact,  that  the  floating  body  is  not  wet  by  the  liquid,  and  con- 
sequently there  forms  around  it  a  meniscus,  which  displaces  a 
large  volume  of  liquid  in  comparison  with  that  of  the  solid ; 
and  since  the  volume  of  water  thus  displaced  weighs  as  much 
as  the  floating  body,  it  cannot  sink.  There  are  some  insects 
which  walk  on  the  surface  of  water,  but  which  would  almost 
entirely  sink  in  the  liquid  were  it  not  that  the  capillary  depres- 
sion formed  by  their  extended  feet  (which  are  kept  from  being 
wet  by  a  greasy  coating)  displaces  a  weight  of  water  equal  to 
that  of  the  insect. 

(194.)  Absorption.  —  The  power  which  porous  solids,  like 
wood,  cloth,  paper,  or  animal  membrane,  possess  of  absorbing 
liquids,  is  also  a  phase  of  capillary  action.  These  solid  bodies 
are  filled  with  minute  channels,  into  which  the  liquid  is  drawn 
with  great  force,  as  before  explained.  We  may  gain  an  idea  of 
the  intensity  of  this  force  by  reflecting  that  in  a  tube  1  millimetre 
in  diameter  it  is  measured  by  a  column  of  water  80  m.m.  high, 
and  hence  in  a  tube  T^a  millimetre  in  diameter  by  a  column  of 
water  3  metres  in  height.  Now  since  the  minute  channels  with 
which  these  porous  solids  are  filled  are  as  small  as  this,  or  even 
smaller,  it  is  evident  that  they  will  absorb  water  with  an  almost 


8G4  CHEMICAL  PHYSICS. 

irresistible  force  ;  hence  the  difficulty  of  pressing  out  the  liquid 
when  it  has  once  been  imbibed.  In  many  cases  the  absorp- 
tion of  a  liquid  is  attended  with  an  increase  of  volume,  and 
the  intensity  of  the  capillary  force  is  rendered  evident  by  the 
expansive  power  which  is  thus  exhibited.  A  common  method 
of  splitting  granite  rock  consists  in  drilling  a  number  of  holes 
along  the  line  of  fracture,  and  subsequently  plugging  them  up 
with  dry  wood.  Water  is  then  poured  over  the  plugs,  which 
expand  and  split  the  stone. 

The  amount  of  liquid  absorbed  by  a  given  solid  varies  with  the 
nature  of  the  liquid  used ;  thus  it  has  been  found  that  100  parts 
by  weight  of  the  dried  bladder  of  an  ox  absorbed  in  twenty-four 
hours 

2G8  parts  of  pure  water, 

133      "         water  saturated  with  common  salt, 
38      "         alcohol,  84  per  cent. 
17      "         bone  oil. 

It  has  also  been  found,  that,  if  the  bladder  saturated  with  oil  is 
soaked  in  water,  the  oil  is  after  a  while  entirely  replaced  by  water, 
and  by  as  much  water  as  the  bladder  is  capable  of  absorbing. 
These  facts  indicate  not  only  that  porous  solids  exert  an  unequal 
attraction  for  different  liquids,  but  also  that  they  attract  most 
powerfully  those  of  which  they  absorb  the.  greatest  volume. 

In  connection  with  these  facts  may  be  mentioned  the  singular 
property  which  many  kinds  of  charcoal  possess,  of  absorbing  color- 
ing-matters and  other  organic  principles.  Thus,  if  water  colored 
by  litmus  is  shaken  up  with  pulverized  charcoal,  nearly  the  whole 
of  the  coloring-matter  will  be  retained  by  the  charcoal,  and,  on 
filtering,  the  liquid  will  run  through  colorless.  A  variety  of  char- 
coal called  bone-black  possesses  this  power  in  a  high  degree,  and 
is  used  for  removing  the  color  from  the  brown  syrups  in  the  pro- 
cess of  refining  sugar.  The  syrups  are  filtered  through  a  layer  of 
charcoal  twelve  or  thirteen  feet  in  thickness,  contained  in  a  tall 
iron  cylinder,  and  are  thus  obtained  perfectly  colorless.  Bone- 
black  is  prepared  by  calcining  bones  in  close  vessels,  and  does  not 
contain  more  than  one  tenth  or  one  twelfth  of  its  weight  of  char- 
coal ;  the  remainder  consists  of  earthy  matter,  chiefly  phosphate 
of  lime.  Whether  the  peculiar  property  under  consideration  is 
due  to  the  charcoal  alone,  or  whether  it  is  also  shared  by  the 
earthy  salts,  is  not  known.  Other  animal  substances,  especially 


THE  THREE   STATES   OP   MATTER.  365 

dried  blood,  furnish  when  calcined  a  charcoal,  which,  if  well 
washed,  is  even  more  efficacious  than  bone-black,  and  the  addi- 
tion of  carbonate  of  potash  to  the  mass  before  calcining  still 
further  increases  the  decolorizing  power  of  the  charcoal. 

The  absorbing  power  of  charcoal  is  not,  however,  confined  to 
the  coloring  principles  alone.  Many  inorganic  substances  when 
in  solution,  especially  of  feeble  solubility,  are  absorbed  in  the 
same  way.  Professor  Graham  has  shown  that  this  is  the  case 
with  the  metallic  oxides  when  dissolved  in  potash  or  ammonia, 
and  with  arsenious  acid  when  dissolved  in  water.  It  is  also  true 
of  most  organic  extractive  matters.  Thus,  if  porter  is  filtered 
through  lampblack,  it  will  be  found  to  have  lost  the  greater  part 
of  its  bitterness,  as  well  as  its  color,  and  in  the  preparation  of 
organic  extracts  much  of  the  active  principle  is  lost,  if,  as  is  not 
unfrequently  the  case,  the  liquid  is  digested  with  animal  char- 
coal for  the  purpose  of  removing  the  color. 

(195.)  Solution.  —  When  the  adhesion  of  a  liquid  to  a  solid  is 
sufficiently  strong  to  overcome  the  force  of  cohesion,  the  solid 
enters  into  solution ;  that  is,  it  diffuses  throughout  the  mass  of 
the  liquid,  without  destroying  its  transparency.  Thus  salt  or 
sugar  dissolves  in  water,  resins  dissolve  in  alcohol,  fats  dissolve  in 
ether,  and  most  of  the  metals  dissolve  in  mercury.  The  solvent 
power  of  a  given  liquid  for  different  solids  varies  almost  indefi- 
nitely. Thus  sulphate  of  baryta  is  almost  insoluble  in  water ; 
sulphate  of  lime  dissolves  in  the  proportion  of  about  one  part  in 
400  parts  of  water,  and  sugar  in  one  third  of  its  weight  of  water, 
while  hydrate  of  potassa  may  be  dissolved  in  this  liquid  to  almost 
any  extent. 

If  we  add  a  solid  body,  in  successive  portions,  to  a  liquid 
capable  of  dissolving  it,  we  find  that  the  first  portions  disap- 
pear very  rapidly,  but  each  succeeding  portion  dissolves  less 
rapidly,  until  at  length  a  point  is  reached  when  the  solid  is  no 
longer  dissolved.  The  liquid  is  then  said  to  be  saturated  with 
the  particular  solid.  It  would  appear  that  the  adhesion  of  the 
liquid  had  the  power  of  overcoming  the  cohesion  of  the  solid  to 
a  limited  extent,  until  the  two  forces  were  in  a  condition  of 
equilibrium.  A  liquid,  however,  which  is  saturated  with  one 
substance  may  still  continue  to  dissolve  others. 

The  solvent  power  of  a  given  liquid  for  the  same  solid,  as  a 
general  rule,  varies  very  greatly  with  the  temperature.  Since 
31* 


3GG  CHEMICAL   PHYSICS. 

heat  tends  to  weaken  the  force  of  cohesion,  we  should  naturally 
expect  that  it  would  increase  the  solvent  power  of  a  liquid,  and 
we  find  that  in  most  cases  it  does.  There  are,  however,  many 
striking  exceptions  to  this  rule.  Thus  water  at  the  freezing 
point  dissolves  nearly  twice  as  much  lime  as  it  does  when  boiling  ; 
and  in  like  manner  sulphate  of  lime,  citrate  of  lime,  sulphate  of 
lanthanum,  and  several  other  substances,  are  known  to  be  more 
soluble  in  cold  than  in  hot  water. 

The  increase  of  solubility  with  the  temperature  is  very  unequal 
in  different  cases.  The  solubility  of  common  salt  scarcely  in- 
creases between  0°  and  100°.  Thus  100  parts  of  water  dissolve 
at  the  ordinary  temperature  36  parts  of  common  salt,  and  at  the 
boiling  point  a  little  over  39  parts.  With  a  few  salts  the  increase 
of  solubility  is  exactly  proportional  to  the  temperature,  and  may 
be  represented  by  the  general  formula,  S  =  A  +  B  £,  in  which 
A  represents  the  solubility  at  0°,  and  B  the  increase  of  solubility 
for  each  degree  of  temperature.  This  is  the  case  with  the  fol- 
lowing three  salts.  One  hundred  parts  of  water  dissolve  at  t°, 

Parts. 

of  Sulphate  of  Potash,  S  =    8.36          +  0.1741  1, 

"  Chloride  of  Potassium,          S  =  29.23  -f-  0.2738  *, 

«  Chloride  of  Barium,  S  =  32.62          +  °-2711  '• 

In  most  cases,  however,  the  solubility  increases  more  rapidly  than 
the  temperature.  This  is  the  case  with  common  nitre,  as  may  be 
seen  in  the  following  table,  in  which  the  solubilities  both  of  nitre 
and  chloride  of  potassium  are  given  side  by  side  for  every  20°  be- 
tween the  freezing  and  boiling  points  of  water. 

Chloride  of  Potassium.  Nitre. 

Temperature.   *$$%%£      Difference.  Temperature.      ^^^  Difference. 


0°  29.23                                       0°  13.32                  „ 

20  34.70  J£                   20  31.70  gg 

40  40.18  5AS                  40  63.97  4O6 

60  45.66  5                        60  110.33  59  ^ 

80  51.14                                     80  170.25 

100  56.62  100 

Since  the  solubility  of  a  salt  is  always  some  function  of  the  tem- 
perature, it  can  in  every  case  be  expressed  by  the  general  formula, 
into  which  every  algebraic  function  may  be  developed  : 

Dt*  +  &c.  [130.] 


THE   THREE   STATES   OP   MATTER.  367 

In  this  formula,  A  is  the  solubility  at  0°,  and  B,  Gf,  D,  <fcc.  are 
empirical  coefficients,  which  can  be  easily  calculated  in  any  given 
case  from  the  results  of  experiment.  Thus,  for  example,  100 
parts  of  water  dissolve  at  the  temperature  t  an  amount  of  nitre 
represented  by 

S  =  13.32  +  0.5T38 1  +  0.017168 1*  +  0.0000035977  /3, 
and  of  nitrate  of  baryta  an  amount 

S=  5.00  +  0.17179  £  +  0.0017406 19—  0.0000050035 19. 

The  values  of  the  coefficients  of  the  powers  of  t  are  calculated 
by  substituting  in  the  general  equation  [130]  the  value  of  A, 
and  also  the  values  of  S  and  £,  for  each  temperature  at  which 
the  solubility  has  been  determined.  We  shall  thus  obtain  as 
many  separate  equations  as  there  are  separate  determinations, 
and,  by  combining  them  together  according  to  the  well-known 
methods  of  algebra,  we  can  easily  calculate  the  coefficients  re- 
quired. It  is  evident  that  we  can  only  ascertain  as  many  co- 
efficients as  there  are  equations,  and  also  that  the  resulting 
formula  is  purely  empirical,  and  can  only  be  trusted  for  tem- 
peratures between  those  at  which  the  experiments  were  made. 

The  solubility  of  a  salt  at  different  temperatures  can  be  also 
expressed  graphically,  according  to  the  method  of  analytical 
geometry,  as  represented  in  Fig.  326.  The  horizontal  axis, 


which  corresponds  to  the  axis  of  abscissas,  is  divided  into  equal 
parts,  which  indicate  degrees  of  temperature,  and  the  vertical 


368  CHEMICAL  PHYSICS. 

axis,  which  corresponds  to  the  axis  of  ordinates,  is  also  divided 
into  equal  parts,  which  indicate  the  number  of  grammes  of  salt 
soluble  at  the  given  temperatures  in  100  parts  of  water.  In 
order  to  form  the  curve,  we  fix  as  many  points  as  possible  from 
the  experimental  data,  and  then  through  the  points  thus  deter- 
mined we  draw  a  line,  which  is  the  curve  required.  We  can  now, 
by  inspection,  easily  determine  the  solubility  of  the  salt  at  any 
temperature  which  is  within  the  limits  of  our  experiments.  Sup- 
pose, for  example,  we  wish  to  know  the  solubility  of  nitre  at  40°, 
we  follow  up  the  vertical  line  marked  40°  until  it  crosses  the 
curve  ;  and  then,  opposite  to  the  point  of  intersection,  we  find  on 
the  axis  of  ordinates  the  number  64,  indicating  that  at  this  tem- 
perature 64  parts  of  salt  dissolve  in  100  parts  of  water.  Such 
curves  convey  at  a  glance  a  general  idea  of  the  law  which  the 
solubility  of  a  given  salt  follows,  and  also  the  relative  solubility  of 
different  salts  at  any  given  temperature.  Thus  it  will  be  noticed 
that  the  curve  of  common  salt  is  a  straight  line  parallel  to  the 
horizontal  axis,  indicating  that  its  solubility  does  not  vary  with 
the  temperature.  The  curves  of  chloride  of  barium  and  chloride 
of  potassium  are  also  straight  lines,  inclined  at  a  certain  angle 
to  the  horizontal  axis,  showing  that  the  increase  of  solubility  is 
directly  proportional  to  the  temperature.  The  curve  of  sul- 
phate of  magnesia  is  also  a  straight  line,  but  more  inclined  to 
the  horizontal  than  the  last,  proving  that  the  solubility  of  this 
salt  increases  proportionally  to  the  temperature,  but  at  a  more 
rapid  ratio  than  that  of  the  last  two.  The  curves  of  nitrate 
of  baryta,  of  chlorate  of  potassa,  and  of  nitrate  of  potassa,  in- 
dicate that  their  solubility  increases  more  rapidly  than  the  tem- 
perature, and  according  to  very  different  laws.  Lastly,  it  will 
be  noticed  that  the  order  of  relative  solubility  of  the  three  salts, 
sulphate  of  potassa,  nitrate  of  baryta,  and  chlorate  of  potassa,  is 
completely  inverted  in  passing  from  35°  to  55°. 

The  relative  solubility  of  chemical  compounds  is  one  of  the 
most  important  circumstances  in  determining  chemical  changes ; 
and  it  can  be  easily  seen  how  important  these  tables  of  curves 
must  be  to  the  chemist.  Unfortunately,  full  determinations 
of  the  solubility  of  substances  at  different  temperatures  have 
only  been  made  in  a  few  cases,  and  these  have  been  mostly 
limited  to  solubility  in  water. 

From  a  knowledge  of  the  solubility  of  a  solid  in  one  liquid, 
we  can  draw  no  conclusions  in  regard  to  its  solubility  in  an- 


THE   THREE   STATES   OF   MATTER.  369 

other,  and  this  is  also  true  in  regard  to  the  law  according  to 
which  the  solubility  changes  with  the  temperature.  This  gener- 
ally differs  entirely  for  different  liquids,  even  when  the  solid  is 
the  same,  and  must  therefore  be  determined  separately  for  each. 

In  several  cases  the  solubility  of  substances  has  been  deter- 
mined both  above  and  below  their  melting  point ;  but  no  sud- 
den change  of  solubility  has  been  noticed  at  this  point,  as  might 
have  been  expected.  Thus  the  melting  points  of  spermaceti, 
paraffine,  and  of  several  other  similar  solids,  are  below  the  boil- 
ing point  of  alcohol,  so  that  we  can  determine  the  solubility  of 
these  substances  in  alcohol,  both  above  and  below  their  melting 
points.  In  each  case,  the  solubility  has  been  found  to  increase 
gradually  throughout  the  whole  range  of  temperature,  and  the 
melting  of  the  solid  does  not  appear  by  itself  alone  to  produce 
any  change. 

(196.)  Determination  of  Solubilities.  —  In  order  to  deter- 
mine the  solubility  of  a  substance  at  a  given  temperature,  a 
saturated  solution  is  first  prepared  at  the  temperature  required. 
This  may  be  prepared  in  one  of  two  ways.  We  may  either  keep  the 
liquid  in  contact  with  a  large  excess  of  the  solid  for  a  long  time, 
at  the  given  temperature,  until  it  has  dissolved  all  that  it  can,  or 
we  may  prepare  a  saturated  solution  at  a  slightly  higher  temper- 
ature, and,  after  having  cooled  it  to  the  required  temperature, 
keep  it  at  that  point  until  the  excess  of  the  solid  has  been  depos- 
ited. Experiments  have  proved  that  we  obtain  the  same  result 
by  both  methods ;  but  in  employing  the  second,  it  is  necessary  to 
take  certain  precautions.  It  has  been  observed,  that  a  liquid, 
when  not  in  contact  with  the  solid  particles  themselves,  will 
retain  in  solution  an  amount  of  the  solid  which  is  greater  than 
it  can  normally  dissolve  at  the  given  temperature.  But  if  a  few 
crystals  of  the  solid  are  dropped  into  it,  the  excess  will  be  at  once 
deposited.  Violent  agitation  favors  the  separation,  but  we  can- 
not in  any  case  be  certain  that  the  excess  has  been  completely 
removed  until  after  several  hours. 

Having  prepared  a  saturated  solution,  by  either  of  these  pro- 
cesses, we  next  transfer  a  quantity  of  it  to  a  tared  flask,  and  care- 
fully determine  its  weight,  which  should  be  about  50  grammes. 
We  then  evaporate  the  liquid  by  placing  the  flask  over  a  sand- 
bath  or  a  small  furnace,  as  represented  in  Fig.  327,  taking  care 
to  keep  the  neck  of  the  flask,  which  should  be  quite  long,  in- 


370  CHEMICAL  PHYSICS.^ 

clined  at  an  angle  of  about  45°,  in  order  to  prevent  loss  by  spirt- 
ing. The  evaporation  is  continued  until  both  the  water  of  crys- 
tallization and  that  of  solution  have  been  driven  off,  and  the  salt 
left  in  an  anhydrous  condition.  The  last  traces  of  moisture 
are  best  removed  by  blowing  into  the  flask  a  stream  of  dry  air, 
through  a  glass  tube  attached  to  the  nozzle  of  a  pair  of  bellows. 
When  the  flask  is  cold,  we  weigh  it,  and  thus  obtain  the  weight 
of  the  anhydrous  salt  which  the  solution  contained,  and  from 


Fig.  327. 

this  weight  it  is  easy  to  calculate  the  weight  of  salt  dissolved  by 
100  parts  of  water  at  the  given  temperature. 

Let  us  represent  the  weight  of  solution  used  in  our  ex- 
periment by  W,  and  the  weight  of  dry  salt  obtained  by  W'. 
W  —  W  is  then  the  weight  of  water  which  dissolves  a  weight 
W  of  the  anhydrous  salt.  The  amount  of  salt  which  100  parts 
of  water  will  dissolve  may  then  be  ascertained  by  the  proportion, 

W—W:W'=  100  :  X,  from  which  we  get  X  =  100  w^_w,- 

If  the  salt  contains  water  of  crystallization,  we  shall  wish  to  cal- 
culate from  the  weight  of  the  anhydrous  residue  the  weight  of 
crystallized  salt  which  100  parts  of  water  dissolved  at  the  tem- 
perature of  the  experiment.  Let  us  represent  by  w  the  weight 
of  water  of  crystallization  with  which  the  weight  W  of  anhy- 
drous salt  combines.  W1  -f-  w  then  evidently  represents  the 
weight  of  crystallized  salt  which  was  dissolved  in  the  weight  of 
water  W  -—  (  W1  -f-  w).  Hence  we  get  the  proportion,  as  before, 


the  amount  of  crystallized  salt  which  will  dissolve  at  the  given 
temperature  in  100  parts  of  water. 


THE   THREE    STATES   OF   MATTER.  371 

Instead  of  evaporating  the  solution,  it  is  frequently  more  con- 
venient to  determine  the  weight  of  salt  dissolved  by  precipitating 
one  of  its  constituents,  as  in  the  ordinary  method  of  chemical 
analysis.  Thus  the  amount  of  sulphate  of  soda  in  a  solution 
may  be  ascertained  by  precipitating  the  sulphuric  acid  as  sul- 
phate of  baryta,  and  afterwards  collecting  and  weighing  the  pre- 
cipitate in  the  usual  way ;  and  the  same  method  may  be  followed 
with  any  sulphate.  In  like  manner,  the  solubility  of  any  chloride 
in  water  may  be  determined  by  precipitating  the  chlorine  as 
chloride  of  silver.  In  either  case,  from  the  weight  of  the  pre- 
cipitate we  can  easily  calculate,  by  the  rules  of  stochiometry,  the 
weight  of  salt  which  was  in  solution,  whether  in  an  anhydrous  or 
a  crystalline  condition.  When  a  salt  is  easily  decomposed  by 
heat,  this  chemical  method  of  determining  its  solubility  is  always 
to  be  preferred. 

(197.)  Solution  and  Chemical  Change.  —  Solution  is  gener- 
ally regarded  as  merely  a  mechanical  separation  of  the  particles 
of  a  solid,  which  are  diffused  through  the  liquid  solvent.  Thus, 
when  sugar  dissolves  in  water,  its  particles  are  diffused  through- 
out the  liquid ;  but  they  are  not  supposed  to  undergo  any  essen- 
tial change,  for  the  syrup  retains  the  sweetness  of  the  sugar,  and 
on  evaporation  yields  -solid  sugar,  with  all  its  peculiar  properties. 
So  also  a  solution  of  camphor  in  alcohol  partakes  of  the  proper- 
ties of  both  substances,  and  when  evaporated  deposits  the  solid 
camphor  entirely  unchanged.  Such  a  change  is  supposed  to  be 
entirely  mechanical,  and  to  differ  widely  from  true  chemical  com- 
bination, in  which  the  properties  of  the  combining  substances 
are  entirely  merged  and  lost  in  those  of  the  compound.  Thus, 
when  we  add  lime  to  dilute  nitric  acid,  it  apparently  dissolves, 
as  sugar  dissolves  in  water,  and  the  result  is  a  clear  solution  ;  if, 
however,  we  examine  the  solution,  we  find  that  the  properties  of 
lime  have  disappeared,  and  on  evaporating  it  we  obtain,  not  lime, 
but  a  new  substance  called  nitrate  of  lime.  These  examples 
would  seem  to  indicate  that  there  is  a  very  marked  distinction 
between  solution  and  chemical  combination,  and  this  conclusion 
is  apparently  confirmed  by  the  fact,  that  whereas  chemical  com- 
bination takes  place  most  easily  between  those  substances  which 
are  most  unlike,  solution  generally  occurs  most  readily  when 
the  solvent  is  more  or  less  closely  allied  in  its  properties  to 
the  body  dissolved ;  thus  mercury  dissolves  the  metals,  alcohol 


372  CHEMICAL   PHYSICS. 

the  resins,  and  oils  dissolve  the  fats.  Bat  if,  instead  of  compar- 
ing these  extreme  cases,  we  study  the  whole  range  of  chemical 
phenomena,  we  shall  find  that  the  distinction  between  solution 
and  chemical  combination  is  by  no  means  so  clearly  marked,  and 
that  it  is  impossible  to  say  where  the  one  ends  and  the  other  begins. 
In  many  cases,  what  seems  to  be  an  example  of  simple  solution 
can  be  shown  to  be  a  mixed  effect,  at  least,  of  solution  and  chem- 
ical combination  ;  and  between  this  condition  of  things,  where  the 
evidence  of  chemical  combination  is  unmistakable,  and  a  simple 
solution  like  that  of  sugar  in  water,  we  have  every  degree  of 
gradation.  To  such  an  extent  is  this  true,  that  the  facts  seem  to 
justify  the  opinion  that  solution  is  in  every  case  a  chemical  com- 
bination of  the  substance  dissolved  with  the  solvent,  and  that 
it  differs  from  other  examples  of  chemical  change  only  in  the 
weakness  of  the  combining  force.  There  are  many  remarkable 
phenomena  connected  with  the  solution  of  salts  in  water,  which 
are  probably  caused  by  the  intervention  of  chemical  affinity. 

There  are  but  few  anhydrous  salts  which  dissolve  in  water 
without  entering  into  chemical  combination  with  it  ;  in  such 
cases  we  obtain,  not,  properly  speaking,  a  solution  of  the  anhy- 
drous salt,  but  a  solution  of  a  compound  of  the  anhydrous  salt 
and  water.  Thus,  for  example,  if  we  dissolve  anhydrous  sul- 
phate of  soda  in  water,  every  44.2  parts  of  the  salt  combine  with 
55.8  parts  of  water,  and  we  obtain  a  solution,  not  of  Na  0,  S03, 
but  of  Na  0,  S  Oj  .  10  HO ;  and  on  evaporating  the  solution  at 
the  ordinary  tempsrature,  crystals  of  the  hydrated  salt  are  de- 
posited. The  water  which  is  thus  combined  with  the  salt  is 
termed  water  of  crystallization.  It  is  combined  in  definite  pro- 
portions, but  is  united  by  so  feeble  an  affinity,  that  it  is  entirely 
driven  off  when  the  crystallized  salt  is  heated  to  33°  in  the  open 
air.  It  is  true  that  it  is  difficult,  and  frequently  impossible,  to 
ascertain  the  condition  in  which  a  salt  exists  when  in  solution, 
and  that  the  condition  in  which  it  is  deposited  on  evaporation 
is  not  necessarily  the  same  as  that  in  which  it  was  dissolved. 
Even  in  the  case  just  cited,  it  is  impossible  to  determine  with 
certainty  whether  the  hydrated  salt  exists  as  such,  in  solution, 
or  whether  it  is  first  formed  at  the  moment  of  crystallization. 
Several  facts,  however,  seem  to  support  the  first  hypothesis. 

On  examining  the  curve  of  solubility  of  anhydrous  sulphate 
of  soda  (Fig.  328),  it  will  be  noticed  that  the  solubility  rapidly 


THE   THREE   STATES    OF   MATTER.  373 

increases  with  the  temperature  up  to  33°,  where  it  reaches  its 
maximum,  and  then  diminishes  as  the  temperature  rises  above  this 
point.  Such  a  sudden  break  in  the  continuity  of  the  curve  as 
this  is  inexplicable,  at  least  with  our  present  knowledge,  if  we 
suppose  that  the  water  holds  in  solution  one  and  the  same  body 
throughout  the  whole  range  of  temperature  ;  while  it  is  easily 
explained,  if  we  assume  that  the  composition,  of  the  salt  in  solu- 
tion changes  with  the  temperature  ;  —  for  if,  as  would  naturally 
be  the  case,  the  solubility  of  the  salt  is  different  in  its  hydrated 


Fig.  328. 

and  its  anhydrous  conditions,  the  sudden  change  in  its  solubility 
may  be  caused  by  a  change  of  composition  commencing  at  a  par- 
ticular point.  That  this  is  the  case  with  sulphate  of  soda  is 
substantiated  by  the  fact,  that  the  sudden  change  in  the  law  of 
its  solubility  takes  place  at  £3°,  the  temperature  at  which  the 
hydrated  salt  loses  its  water  in  the  air.  It  is  not  supposed,  how- 
ever, that  the  change  of  composition  is  completed  at  that  tem- 
perature, but  only  that  it  commences  at  that  point,  and  becomes 
more  complete  as  the  temperature  rises.  Below  33°,  the  change 
of  solubility  is  owing  to  the  natural  effect  of  heat  in  increasing 
the  solubility  of  the  hydrated  salt.  Above  33°,  the  change  is 
a  mixed  effect  of  the  cause  just  mentioned  and  of  the  change  of 
the  hydrated  into  the  less  soluble  anhydrous  salt. 

It  is  obvious,  from  what  has  been  stated,  that  the  curve  of 
solubility  of  anhydrous  sulphate  of  soda  given  in  Fig.  328  is  a 
32 


374  CHEMICAL  PHYSICS. 

pure  fiction,  since  below  33°  it  is  NaO,  S03  .  10  HO,  and  not 
Na  0,  S03,  which  is  in  solution  ;  and  the  same  is  true  also  of  sul- 
phate of  magnesia  and  chloride  of  barium,  both  of  which  form 
crystalline  compounds  in  water.  Indeed,  in  order  that  such  a 
curve  should  be  a  representation  of  actual  facts,  it  is  essential 
to  know  in  what  condition  the  salt  exists  in  solution  at  each  tem- 
perature, and  to  calculate  the  solubility  solely  for  the  hydrate 
which  is  known  to  be  present.  A  separate  curve  should  then  be 
constructed  for  each  definite  compound,  between  the  limits  of 
temperature  at  which  it  is  known  to  exist.  This  has  been  done 
in  the  case  of  sulphate  of  soda,  by  Loewel,*  who  has  determined 
separately  the  solubility  of  the  three  compounds  Na  0,  S03, 
NaO,  S03  .  7 HO,  and  NaO,  S03  .  10 HO,  between  the  limits  of 
temperature  at  which  they  are  capable  of  existing.  His  numer- 
ical results  are  given  in  the  table  on  page  375,f  and  from  them 
the  curve  may  easily  be  drawn. 

In  the  case  of  the  two  hydrates,  the  table  gives  in  each  in- 
stance the  amount  of  anhydrous  salt  corresponding  to  the  hydrate 
dissolved,  and  by  comparing  the  three  columns  headed  "  anhy- 
drous salt,"  it  will  be  seen  that  the  amount  of  NaO,  S03  which 
100  parts  of  water  will  dissolve  at  20°,  for  example,  varies  very 
considerably  with  the  condition  of  hydration  in  which  it  exists. 
It  will  also  be  noticed,  that  the  change  of  solubility  for  each  com- 
pound follows  a  uniform  law  throughout ;  the  solubility  increas- 
ing with  the  temperature  in  the  case  of  the  two  hydrates,  and 
diminishing  with  the  temperature  in  that  of  the  anhydrous  salt. 
It  is  the  combination  of  these  two  phenomena  which  causes  the 
seeming  irregularity  in  the  curve  of  anhydrous  sulphate  of  soda, 
as  determined  by  Gay-Lussac,  and  represented  in  the  figure  above. 
Similar  irregularities,  which  have  been  observed  in  seleniate  of 
soda,  carbonate  of  soda,  and  many  other  salts,  are  probably  to  bo 
explained  in  the  same  way,  although  the  subject  has  not  been 
as  yet  sufficiently  investigated  to  furnish  the  data  for  a  satisfac- 
tory conclusion  in  all  cases. 

Loewel,  whose  memoirs  on  the  solubility  of  sulphate  of  soda 
we  have  just  cited,  has  investigated  with  equal  care  the  solubil- 
ity of  a  few  other  salts.  J  In  the  case  both  of  carbonate  of  soda 

*  Annalcs  de  Cliimie  et  dc  Physique,  Tom.  XXIX.  p.  62  ;  Tom.  XXXIII.  p.  334. 

t  Il)id.,  Tom.  XLIX.  p.  32. 

J  Ibid.,  Tom.  XXXIII.  p.  334  ;    Tom.  XLIII.  p.  405  ;    Tom.  XLIV.  p.  313. 


THE   THREE   STATES    OF    MATTER. 


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376  CHEMICAL   PHYSICS. 

and  sulphate  of  magnesia,  he  found,  very  remarkably,  that  the 
solubility  not  only  differed  for  the  different  hydrates,  but  also 
was  different  for  the  different  states  of  the  same  hydrate.  Thus 
the  salt  NaO,  CO*  .  7  HO  can  be  obtained  in  two  different  con- 
ditions or  allotropic  modifications,  which  we  may  distinguish  as 
a  and  6,  the  salt  a  crystallizing  in  rhombohedrons,  the  salt  b  in 
tabular  prisms.  Loewel  observed  that  the  solubility  of  the  salt 
was  very  different  in  these  two  modifications,  that  of  a  being  nearly 
twice  as  great  as  that  of  b.  The  table  on  page  377,  which  has 
been  taken  from  the  original  memoir,*  gives  the  solubility  at  dif- 
ferent temperatures,  not  only  of  these  two  modifications,  but  also 
of  the  ordinary  crystallized  carbonate  of  soda,  which  contains 
ten  equivalents  of  water  of  crystallization.  In  the  case  of  each 
salt,  the  corresponding  amounts  of  anhydrous  salt  are  given  for 
the  sake  of  comparison. 

This  table  illustrates  even  in  a  more  marked  manner  than  the 
last  the  fact  on  which  we  have  insisted  so  strongly  in  this  section, 
that  the  solubility  of  a  salt  varies  not  only  with  the  temperature, 
but  also  with  its  state  of  hydration ;  and  it  illustrates  an  addition- 
al fact,  that  the  solubility  may  also  be  altered  by  a  mere  change 
of  molecular  condition,  without  any  change  in  composition.  Phe- 
nomena analogous  to  those  just  described  were  also  observed  by 
Loewel  in  the  case  of  sulphate  of  magnesia,  but  for  the  details  in 
regard  to  them  we  must  refer  to  the  original  memoir. f 

(198.)  Supersaturated  Solutions.  —  Water  is  said  to  be  su- 
persaturated when  it  contains  in  solution  more  of  a  salt  than  it 
would  dissolve  if  presented  to  the  salt  at  the  given  temperature. 
That  saturated  solutions  do  not  at  once  deposit  the  excess  of  salt 
which  they  hold  in  solution,  when  cooled  to  a  lower  temperature, 
is  a  fact  familiar  to  every  one  who  has  experimented  on  this  sub- 
ject ;  but  there  can  be  also  no  doubt  that  the  prominent  exam- 
ples, which  are  frequently  cited  as  illustrations  of  this  fact,  are 
to  be  referred  to  the  intervention  of  the  force  of  chemical  affinity 
in  a  manner  similar  to  that  explained  in  the  last  section. 

If  we  prepare  a  boiling  saturated  solution  of  sulphate  of  soda 
in  a  glass  flask,  and,  having  corked  the  flask  while  the  solution  is 
boiling,  allow  it  to  cool  to  the  temperature  of  the  air,  it  may  be 


*  Annales  de  Chimie  et  de  Physique,  Tom.  XXXIII.  p.  334. 
t  Ibid.,  Tom.  XLIII.  p.  405. 


THE   THREE   STATES   OF   MATTER. 


377 


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In  100  Parts  of 
Water  of  Salt 
crystallized  with 
7  HO  ft. 

P 

s    3    8    s    s    § 

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d           Ol           CM           CO           CO           •<* 

s 

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§ 

g 

32 


378  CHEMICAL   PHYSICS. 

kept  for  months  without  crystallizing ;  but  the  moment  a  glass 
rod  or  a  crystal  of  Glauber's  salt  is  dipped  into  it,  the  whole  mass 
becomes  semi-solid  from  the  sudden  formation  of  crystals,  which 
ray  out  from  the  solid  nucleus  in  every  direction.  This  singular 
phenomenon  was  formerly  supposed  to  be  similar  to  what  is  fre- 
quently observed  during  the  freezing  of  water  and  the  solidify- 
ing of  monohydrated  acetic  acid,  melted  phosphorus,  and  many 
other  substances.  It  is  well  known  that  these  liquids,  if  kept 
perfectly  still,  may  be  cooled  several  degrees  below  the  melting 
point  without  losing  their  liquid  condition,  but  that  if  disturbed 
when  in  this  state,  they  at  once  become  solid.  These  phenomena 
have  been  referred  to  the  inertia  of  the  particles,  which  tends 
to  retain  the  substance  in  a  liquid  condition  below  the  usual 
temperature,  and  the  same  explanation  has  been  extended  to  the 
sudden  crystallization  of  sulphate  of  soda,  as  above  described. 

Loewel,  in  the  memoir  already  referred  to,*  has  investigated 
this  subject  with  great  care.  He  found  that,  if  a  supersatu- 
rated solution  of  sulphate  of  soda  is  cooled  to  a  low  tempera- 
ture, it  deposits  crystals  containing  seven  equivalents  of  water, 
which  are  much  more  soluble  than  the  ordinary  crystals  of 
Glauber's  saltf  (Na  0,  S03  .  10  HO).  From  this  fact  he  con- 
cluded that  the  so-called  supersaturated  solution  is  not  a  super- 
saturated solution  of  Glauber's  salt,  but  merely  a  saturated  solu- 
tion of  the  more  soluble  hydrate  (Na  0,  S03  .  7  HO).  That  the 
solution  is  not  at  all  changed  by  the  deposition  of  the  crystals 
Na  0,  S03  .  7  HO,  is  proved  by  the  fact,  that,  if  it  is  exposed  to 
the  air  or  touched  by  a  glass  rod,  it  becomes  suddenly  semi-solid 
from  the  deposition  of  Glauber's  salt.  These,  and  a  large  number 
of  additional  facts  which  Loewel  $  has  observed,  all  tend  to  sup- 

*  Annales  de  Chimie  et  de  Physique,  Tom.  XXIX.  p.  62. 

t  See  table  on  page  375. 

$  In  a  more  recent  memoir,  Loewel  inclines  to  the  opinion,  that  sulphate  of  soda 
always  dissolves  in  water  as  an  anhydrous  salt,  and  hence  that  in  a  solution  made 
with  Na  0,  SOa  .  10  HO,  or  Na  O,  SOa  .  7  HO,  none  of  the  water  is  combined  chemi- 
cally with  the  salt  as  water  of  crystallization.  Such  a  change  of  views  does  not,  how- 
ever, seem  to  be  a  necessary  inference  from  the  facts  cited,  and,  as  he  admits,  the  new 
hypothesis  leaves  the  unequal  solubilities  of  the  different  hydrates  entirely  unexplained. 
The  author,  therefore,  does  not  think  it  necessary  to  change  the  opinion  expressed 
above  in  the  text,  although  it  is  true  that  these  later  investigations  of  Loewel  seem  to 
show  that  at  certain  temperatures  sulphate  of  soda  exists  in  the  so-called  supersaturated 
solutions  in  an  anhydrous  condition.  See  Annales  de  Chimie  et  de  Physique,  (3e  Se'rie,) 
Tom.  XXIX.  p.  32,  and  compare  Jahresbericht  der  Chimie,  &c.  fur  1857,  S.  321.  See 
also  an  article  by  Dr.  Hugo  Schiff,  Ann.  der  Chem.  und  Pharm.,  Band  CXI.  S.  68. 


THE   THREE   STATES   OF   MATTER.  379 

port  the  conclusion,  that  in  the  so-called  supersaturated  solution 
of  sulphate  of  soda  the  salt  exists  in  solution  combined  with 
seven  equivalents  of  water,  and  does  not  crystallize  until  some 
circumstance  causes  it  to  combine  with  three  equivalents  more  of 
water,  and  to  change  into  the  less  soluble  compound  which  we 
have  called  Glauber's  salt.  What  the  circumstances  are  which 
produce  this  singular  change,  or  in  what  way  they  act,  we  do 
not  yet  fully  understand.  Some  very  remarkable  facts  in  con- 
nection with  it  have  been  noticed  by  Loewel  and  others.  Thus 
a  glass  rod,  if  heated  and  afterwards  cooled,  loses  its  power  of 
causing  the  crystallization.  Alcohol,  if  poured  into  the  flask  so 
as  to  form  a  layer  over  the  solution,  generally  causes  it  to  crys- 
tallize ;  but  if  previously  boiled,  it  no  longer  produces  this  effect. 
It  slowly,  however,  withdraws  the  water  from  the  solution,  and 
causes  it  to  deposit  crystals  of  Na  0,  S03  .  7  HO ;  and  it  was  in 
this  way  that  Loewel  obtained  the  largest  and  purest  crystals  of 
this  hydrate.  The  opinion  has  been  advanced  by  Lieben,*  that 
it  is  the  dust  floating  in  the  air,  or  adhering  to  the  glass  rod, 
which  causes  the  sudden  crystallization  of  supersaturated  solu- 
tion ;  and  he  has  endeavored  to  show  that  neither  the  air  nor  a 
solid  body  will  produce  the  effect  after  they  have  been  freed  from 
dust,  by  heating,  by  washing  with  sulphuric  acid,  or  by  any 
other  means.  This  theory,  although  ingenious,  and  supported 
by  experiment,  does  not  meet  all  the  facts  of  the  case,  and  the 
subject  requires  further  investigation. 

The  phenomena  of  "  supersaturated "  solutions,  which  are 
so  marked  in  the  case  of  Glauber's  salt,  have  also  been  noticed  in 
the  case  of  carbonate  of  soda,  of  sulphate  of  magnesia,  of  acetate 
of  soda,  of  chloride  of  calcium,  and  of  many  other  salts.f  In  some 
of  these  cases,  they  are  to  be  explained  as  in  the  case  of  Glauber's 
salts,  by  the  formation  x>f  a  hydrate  more  soluble  than  the  one 
dissolved,  while  in  others  they  may  be  caused  by  the  formation 
of  a  more  soluble  modification  of  the  same  hydrate;  but  the 
whole  subject  is  still  involved  in  great  obscurity. 

Solids  on  Gases. 

(199.)  Absorption  of  Gases  by  Porous  Solids.  —  If  apiece 
of  well-burnt  boxwood  charcoal  is  plunged  while  red-hot  under 
mercury,  and  when  cold  passed  up  into  a  jar  of  gas  confined  over 

*  Wien.  Acad.  Ber.,  XII.  771  and  1087. 
t  See  the  memoirs  of  Loewel,  just  cited. 


380  CHEMICAL  PHYSICS. 

the  same  liquid,  it  will  be  found  to  absorb  the  gas  to  a  greater 
or  less  extent,  varying  with  the  nature  of  the  gas  used.  Accord- 
ing to  Saussure's  experiments,  one  cubic  centimetre  of  charcoal 
will  absorb  the  number  of  cubic  centimetres  of  the  different  gases 
given  in  the  following  table  :  — 

Absorption  of  Gases  by   Charcoal. 
Ammonia,       .         .         .90  cTirT3      Olefiant  Gas,       .         .     35  c~in.3 


Chlorohydric  Acid,       .  85  " 

Sulphurous  Acid,    .  .     65  " 

Sulphide  of  Hydrogen,  55  " 

Protoxide  of  Nitrogen,  .     40  " 

Carbonic  Acid,    .         .  35  " 


Carbonic  Oxide,  .         9.4  " 

Oxygen,     .         .  .9.2  " 

Nitrogen,        .  .         7.2  " 

Marsh  Gas,        .  .     5.0  « 

Hydrogen,      .  .         1.7  " 


In  some  cases  the  volume  of  the  gases  thus  condensed  is  less 
than  that  which  they  would  occupy  in  a  liquid  state,  and  as 
a  general  rule,  the  more  readily  a  gas  can  be  condensed  to  a 
liquid,  the  greater  is  the  volume  absorbed  by  the  charcoal.  It 
will  also  be  noticed,  that  the  above  results  follow  very  nearly  the 
same  order  as  the  solubility  of  the  gases  in  water. 

A  piece  of  freshly  burnt  charcoal,  if  exposed  to  the  air,  con- 
denses the  gases  and  moisture  of  the  atmosphere  to  such  an 
extent,  that  its  weight  frequently  increases  one  fifth  in  a  few  days. 
The  presence  of  condensed  air  in  common  wood  charcoal  can 
easily  be  made  evident  by  plunging  it  under  hot  water.  The 
heat  of  the  water  expands  the  confined  air,  which  is  thus  driven 
out  of  the  pores  of  the  wood,  and  bubbles  up  through  the  water. 
Owing  to  this  absorbing  power  of  charcoal,  water  saturated  with 
many  gases  may  be  freed  from  them  by  filtering  it  through  ivory- 
black.  Water  impregnated  with  sulphide  of  hydrogen  may  be 
in  this  way  so  perfectly  purified,  that  its  presence  cannot  be  de- 
tected either  by  the  nauseous  odor  or  by  the  ordinary  tests. 

This  power  of  absorbing  gases  is  not  confined  to  charcoal,  but 
belongs  in  a  greater  or  less  degree  to  other  porous  solids.  The 
following  table  gives  the  number  of  cubic  centimetres  of  different 
gases  absorbed  respectively  by  one  cubic  centimetre  of  Meer- 
schaum, plaster  of  Paris,  and  silk,  when  the  temperature  is  15° 
and  the  pressure  of  the  air  73  c.  m.  By  comparing  this  table 
with  the  last,  it  will  be  noticed  that  not  only  the  absolute  quan- 
tities of  the  gases  absorbed  are  different  for  different  solids,  but 
also  that  the  relative  power  of  absorption  of  these  solids  for  the 
different  gases  is  different  in  every  case. 


THE   THREE   STATES   OP   MATTER.  381 

Absorption  of  Gases  by  Meerschaum,  Plaster  of  Pan's,  and  Silk. 

Meerschaum.  Plaster  of  Paris.                    Silk. 

Ammonia,  15.      cTm.3  78.1    cTm.3 

Protoxide  of  Nitrogen,  3.75     " 

Carbonic  Acid,                5.26     "  0.43  cTm.3  1.1        " 

Oxide  of  Carbon,  1.17     "  0.3       « 

Oxygen,                          1.49     «  0.58     "  0.44     « 

Nitrogen,                         1.60     «  0.53     "  0.13     " 

Hydrogen,                          .44     "  0.50     «  0.3  v    « 

In  like  manner  the  metals  in  the  state  of  fine  powder,  lead, 
iron,  and  platinum,  for  example,  absorb  gases  in  very  large 
amounts.  The  finely  divided  platinum  called  platinum-black, 
which  is  obtained  by  precipitating  a  solution  of  chloride  of  plati- 
num with  alcohol,  absorbs,  according  to  Doebereiner,  250  times 
its  own  volume  of  oxygen.  The  latent  heat  which  is  set  free  by 
this  great  condensation  is  sufficient  to  ignite  the  metallic  mass. 
Platinum  sponge,  and  even  platinum  plate,  possess  the  same  power, 
although  to  a  less  degree,  and  it  is  probable  that  all  solid  surfaces 
exert  a  similar  influence  to  a  limited  extent. 

The  absorption  of  gases  by  solids  is  very  greatly  influenced 
both  by  the  temperature  and  the  pressure  to  which  they  are 
exposed.  The  higher  the  temperature,  the  smaller  is  the  amount 
of  gas  absorbed,  and  the  most  efficient  means  of  expelling  the 
gas  from  a  porous  solid  is  to  expose  it  to  a  red  heat.  It  is  how- 
ever uncertain  whether  even  in  this  way  we  can  remove  all  the 
gas  condensed  on  the  surfaces  of  solid  substances,  and  at  all 
events  to  do  this  requires  a  considerable  time.  Charcoal  and 
other  porous  solids  absorb  the  largest  amount  of  gas  only  after 
a  prolonged  ignition  in  a  vacuum.  In  filling  a  barometer  tube 
the  mercury  is  boiled  in  the  tube  in  order  to  remove  the  air 
and  moisture,  not  only  from  the  mercury,  but  also  from  the 
surface  of  the  glass. 

The  greater  the  pressure  to  which  a  gas  is  exposed,  the  great- 
er is  the  quantity  which  is  absorbed  by  a  solid  ;  but  then  the 
quantity  does  not  increase  so  rapidly  as  the  pressure.  On  the 
other  hand,  under  a  diminished  pressure  a  solid  body  absorbs 
a  less  quantity  of  gas,  but  a  greater  volume.  Hence  it  is  not 
possible  by  means  of  an  air-pump  to  remove  all  the  air  from 
a  porous  solid. 

If  a  porous  body,  which  is  saturated  with  one  gas,  is  put  into 


382  CHEMICAL  PHYSICS. 

a  different  gas,  it  gives  up  a  portion  of  the  gas  which  it  had 
first  absorbed,  and  takes  in  its  place  a  quantity  of  the  second. 
Sometimes  the  presence  of  one  gas  increases  the  power  of  a 
solid  for  absorbing  a  second.  Tims  charcoal  saturated  with 
oxygen  will  absorb  more  hydrogen,  and  charcoal  saturated  with 
hydrogen  will  absorb  more  nitrogen,  than  it  would  if  the  other 
gas  was  not  present.  But  as  a  general  rule,  the  presence  of 
one  gas  diminishes  the  power  of  a  solid  for  absorbing  others. 
Thus  charcoal,  which  after  ignition  will  absorb  thirty-five  times 
its  volume  of  carbonic  acid,  will  only  absorb  about  fifteen  times 
its  volume  if  it  has  been  previously  exposed  to  the  atmosphere, 
and  thus  saturated  with  air  and  moisture. 

From  the  analogous  constitution  of  liquids  and  gases,  we 
should  naturally  expect  that  solids  would  act  on  these  two 
forms  of  fluid  matter  in  an  analogous  way.  The  same  adhesive 
force  which  attracts  liquids  to  the  surfaces  of  solids  we  should  ex- 
pect would  also  attract  gases ;  and,  moreover,  since  gases  are 
very  compressible,  we  should  further  expect  that  the  adhesion 
would  condense  the  gas  upon  the  surface  in  proportion  to  the 
strength  of  the  attraction.  Moreover,  as  in  the  case  of  liquids, 
we  should  expect  that  the  amount  of  gas  adhering  to  the  sur- 
face or  absorbed  into  the  pores  of  a  solid  would  vary  with  the 
nature  both  of  the  solid  and  of  the  gas,  with  the  extent  of  the 
surface,  with  the  fineness  of  the  pores,  and,  lastly,  with  the  tem- 
perature, becoming  less  as  the  temperature  rose. 

The  phenomena  just  described,  it  will  be  noticed,  coincide 
perfectly,  as  far  as  they  go,  with  these  natural  inferences,  thus 
showing  that  they  are  merely  phases  of  adhesion  and  capillary 
action.  The  force  of  surface  attraction,  and  hence  the  amount 
of  gas  absorbed,  varies  even  more  markedly  than  in  the  case  of 
liquids,  both  with  the  nature  of  the  solid  and  that  of  the  gas. 
It  varies  also  with  the  extent  of  the  surface ;  and,  other  things 
being  equal,  it  is  greatest  with  porous  bodies  or  fine  powders,  which 
expose  the  greatest  surface ;  finally  heat,  which  lessens  the  at- 
tractive force,  diminishes  the  amount  of  gas  absorbed  by  a  solid, 
as  it  does  the  amount  of  liquid.  There  are,  it  is  true,  phenomena 
connected  with  the  adhesion  of  gases  to  solids  which  liquids  do 
not  present,  but  these  are  such  as  may  be  supposed  to  arise 
from  the  special  law  of  compressibility,  which  all  gases  obey. 

The  phenomena  described  in  this  section,  like  those  both  of 


THE   THREE    STATES    OF   MATTER.  383 

capillarity  and  solution,  are  greatly  influenced,  it  will  be  noticed, 
by  the  chemical  nature  of  the  bodies  concerned,  and  in  fact 
pass  by  insensible  gradations  into  those  which  we  should  class 
among  purely  chemical  changes.  Like  most  phenomena  which 
occupy  the  debatable  ground  between  chemistry  and  physics, 
they  present  great  complexity,  and  are  difficult  to  investigate, 
so  that  our  knowledge  in  regard  to  them  is  exceedingly  in- 
complete.* 

There  are  many  phenomena  besides  those  of  absorption  which 
are  connected  with  the  adhesion  of  gases  to  solids.  The  fact 
that  iron  filings,  and  many  other  fine  powders,  sifted  over  the 
surface  of  water,  will  float,  though  very  much  heavier  than  the 
liquid,  has  already  been  mentioned.  This  was  then  explained 
by  the  principles  of  capillary  action.  The  water  is  prevented 
from  wetting  the  solid,  and  therefore  forms  around  the  particles 
a  concave  meniscus  which  buoys  them  up.  But  it  is  solely  the 
thin  film  of  air  adhering  to  these  particles  which  prevents  them 
from  becoming  wet,  when  they  would  at  once  sink.  The  same 
is  true  also  of  the  platinum  wire  floating  on  mercury/ and  of 
other  seemingly  paradoxical  phenomena.  In  all  cases,  if  the 
liquid  is  boiled,  the  film  of  air  is  removed  and  the  paradox 
disappears. 

Liquids  on  Liquids. 

(200.)  Liquid  Diffusion.  —  As  a  general  rule,  the  adhesion 
between  the  particles  of  different  liquids  is  so  much  greater  than 
the  cohesion  between  their  own  molecules,  that  they  may  be  mixed 
together  in  any  proportion.  This  is  not,  however,  always  the 
case ;  for  after  the  liquids  have  been  mixed  to  a  limited  extent, 
the  cohesion  may  balance  the  adhesion,  and  the  liquids  will  then 
be  mutually  saturated.  Thus  ether  and  water  cannot  be  mixed 
indefinitely,  and  if  shaken  up  together,  they  will  separate  in  a 
great  measure  on  being  allowed  to  stand,  the  water  dissolving 
only  about  one  eighth  or  one  tenth  of  its  bulk  of  ether,  and 
the  ether  dissolving  about  the  same  amount  of  water.  So  also 
the  volatile  oils,  if  shaken  up  with  water,  separate  from  it  al- 
most entirely  if  the  mixture  is  allowed  to  stand,  although  the 
water  retains  in  solution  a  sufficient  amount  to  acquire  the 
flavor  and  odor  of  the  essence. 

*  See  a  recent  paper  by  Quincke,  Fogg.  Ann.,  CVIII.  326. 


384  CHEMICAL  PHYSICS. 

The  tendency  of  liquids  to  mix  with  each  other  has  been 
termed  liquid  diffusion,  and  can  be  made  evident  by  a  simple 
experiment.  A  tall  glass  jar  is  about  two  thirds  filled  with  a 
solution  of  blue  litmus,  and  then,  by  means  of  a  tube  funnel 
reaching  to  the  bottom,  oil  of  vitriol  is  cautiously  poured  in,  so 
as  to  occupy  the  lower  portion  of  the  jar.  The  plane  of  separa- 
tion of  the  two  liquids  will  be  at  first  distinctly  marked.  But 
this  will  soon  disappear :  the  colored  water,  will  sink,  and  the 
acid  will  rise,  until  the  two  liquids  have  become  perfectly  incor- 
porated. This  will  require,  however,  two  or  three  days,  and,  if 
watched  at  intervals,  the  progress  of  the  diffusion  may  be  traced 
by  the  gradual  change  of  color  in  the  water  from  blue  to  red, 
commencing  at  the  bottom  and  slowly  progressing  towards  the 
top.  A  similar  experiment  can  be  made  with  alcohol,  or  with 
brine,  and  water ;  also  with  oil  of  turpentine  and  alcohol,  and 
indeed  with  almost  any  two  liquids  which  differ  considerably  in 
their  specific  gravities.  By  coloring  one  of  the  liquids,  the  pro- 
cess may  be  readily  traced. 

(201.)  Experiments  of  Professor  Graham.  —  The  subject  of 
liquid  diffusion  has  been  investigated  with  care  in  regard  to  sa- 
line solutions,  and  we  are  chiefly  indebted  to  Professor  Graham 
of  London  for  our  knowledge  on  the  subject.  His  experiments 
were  made  with  a  very  simple  apparatus.  "  It  consisted  of  a  set 
of  phials  of  nearly  equal  capacity,  cast  in  the  same  mould,  and 
further  adjusted  by  grinding  to  a  uniform  size  of  aperture.  The 
phials  were  3.8  inches  high,  with  a  neck 
0.5  inch  in  depth,  and  aperture  1.25  inch 
wide,  capacity  to  base  of  neck  equal  to 
2080  grains  of  water,  or  between  4  and  5 
ounces.  For  each  diffusion-phial  a  plain 
glass  water-jar  was  also  provided,  4  inches 
in  diameter  and  T  inches  deep."*  (Fig. 
329.) 

The  diffusion-phial  was  in  the  first  place 
filled  with  the  saline  solution  to  the  base  of 
the  neck,  or,  more   accurately,  to  a  level 
exactly  half  an  inch  below  the  ground  surface  of  the  lip.     The 
neck  was  then  filled  with  distilled  water,  and  a  light  float 

*  Graham's  Elements  of  Chemistry,  edited  by  Watts,  Vol.  II.  p.  604. 


THE   THREE   STATES   OF   MATTER.  385 

placed  upon  the  surface.  Thus  prepared,  the  phial  was  trans- 
ferred to  the  jar,  which  was  then  filled  with  water  to  the  height 
of  an  inch  above  the  mouth  of  the  phial,  which  was  opened  by 
the  floating  of  the  cover.  This  required  about  20  ounces  of 
water.  The  apparatus  was  then  left  undisturbed,  and  kept  at  a 
constant  temperature  for  several  days.  At  the  end  of  the  re- 
quired time,  the  diffusion  was  interrupted  by  closing  the  mouth 
of  the  phial  with  a  ground-glass  plate,  and  the  amount  of  salt 
diffused  ascertained,  by  evaporating  the  water  in  the  jar  to  dry- 
ness,  and  weighing  the  residue. 

From  these  experiments,  and  a  number  of  others  made  in  a 
similar  manner,  the  following  important  conclusions  have  been 
deduced. 

1.  With  solutions   of  the   same   substance,  but  of  different 
strengths,  the  quantity  of  salt  diffused  in  equal  times  is  propor- 
tioned to  the  quantity  in  solution.     For  example,  four  solutions 
of  common  salt  were  prepared,  containing,  respectively,  1,  2,  3, 
and  4  parts  of  salt  to  100  of  water.     The  experiments  continued 
for  eight  days,  and  the  quantities  diffused  were  respectively  2.78 
grains,  5.54  grains,  8.37  grains,  and  11.11  grains.     These  num- 
bers are  almost  exactly  proportional  to  the  first. 

2.  With  solutions  of  different  substances  of  the  same  strength, 
the  quantity  diffused  varies  with  the  chemical  nature  of  the  sub- 
stance.    This  is  shown  by  the  following  table,  which  gives  the 
weight  in  grains  of  the  substance  diffused  in  eight  days,  from 
solutions  containing,  in  each  case,   20   parts  of  the  solid  dis- 
solved in  100  parts  of  water,  and  exposed  to  a  temperature 
of  60°.5  F. 

Diffusion  of  Solids  in  Solution. 

Substances  used.  Sp.  Gr.  at  60o  F.  Weight  in  Grains  diffused. 

Sulphate  of  Magnesia,  1.185  27.42 

Chloride  of  Sodium,  1.126  58.68 

Nitrate  of  Soda,  1.120  51.56 

Oil  of  Vitriol,  1.108  69.32 

Sugar-Candy,  1.070  26.74 

Barley  Sugar,  1.066  26.21 

Starch  Sugar,  1.061  26.94 

Gum  Arabic,  1.060  13.24 

Albumen,  1.053  3.08 
33 


386  CHEMICAL   PHYSICS. 

The  substances  have  been  arranged  in  the  order  of  the  specific 
gravities  of  the  solution,  and  the  table  also  shows  that  there  is 
no  apparent  connection  between  the  amount  of  diffusion  and  the 
specific  gravity  of  the  solution. 

3.  If,  instead  of  comparing  together,  as  in  the  last  table,  the 
amounts  of  different  substances  diffused  in  equal  times,  we  com- 
pare together  the  times  required  for  the  equal  diffusion  of  these 
same  substances,  we  discover  some  remarkable  numerical  rela- 
tions.    There  exist  classes  of  equi-diffusive  substances,  and,  as  a 
general  rule,  those  substances  which  have  an  analogous  chemical 
composition,  and  crystallize  in  closely  allied  forms,  have  equal 
rates  of  diffusion.     Several  such  groups  have  been  distinguished, 
and  the  rate  of  diffusion  in  each  group  is  connected  with  the  rate 
of  diffusion  in  the  other  groups  by  a  simple  numerical  relation, 
as  is  shown  in  the  following  table.     The  first  column  gives  the 
number  of  the  group,  with  the  name  of  the  most  characteristic 
substance  belonging  to  it.     The  second  gives  the  relative  diffu- 
sion of  these  substances  in  equal  times,  in  other  words,  the  rate 
of  diffusion.     The  third  gives  the  times  of  equal  diffusion ;  and 
the  fourth,  the  squares  of  these  times,  which  stand  to  each  other 
very  nearly  in  the  simple  relation  expressed  in  the  last  column. 

-  Rate  of  Times  of  Equal         Squares  -,,  . . 

Groups.  Ditfusion.  Diffusion.  of  Times. 

1.  Chlorohydric  Acid,  1.000  3.960  15.682  2 

2.  Hydrate  of  Potash,  0.800  4.950  24.502  3 
8.  Nitrate  of  Potash,             0.565           7.000           49.000  6 

4.  Nitrate  of  Soda,  0.462  8.573  73.496  9 

5.  Sulphate  of  Potash,  0.400  9.900  98.010  12 

6.  Sulphate  of  Soda,  0.326  12.125  147.015  18 

7.  Sulphate  of  Magnesia,  0.200  19.800  392.040  48 

4.  The  rate  of  diffusion  increases  with  the  temperature,  but 
increases  in  an  equal  proportion  for  all  substances,  so  that  the 
ratio  between  the  diffusion  of  different  bodies  is  the  same  for  all 
temperatures. 

5.  If  two  substances,  which  do  not  combine  chemically  and 
have  different  rates  of  diffusion,  are  placed  in  the  diffusion-phial, 
they  may  be  partially  separated  by  the  process  of  diffusion,  since 
the  more  diffusible  passes  out  the  most  rapidly,  although  the 
relative  rate  of  diffusion  may  be  somewhat  changed. 

Chemical  decomposition  may  be  even  effected  in  this  way,  one 
ingredient  of  the  compound  diffusing  more  rapidly  than  the  other. 


THE   THREE   STATES   OP   MATTER. 


387 


From  a  solution  of  bisulphate  of  potash  saturated  at  20°  C  ,  there 
were  diffused  in  fifty  days  31.8  parts  of  bisulphate  of  potash,  and 
12.8  parts  of  hydrated  sulphuric  acid.  From  a  solution  of  8 
parts  of  anhydrous  alum  in  100  parts  of  water  there  were  dif- 
fused in  eight  days,  at  17°. 9  C.,  5.3  parts  of  alum  and  2.2  parts  of 
sulphate  of  potash  ;  and  other  similar  examples  might  be  cited.* 

6.  The  diffusion  of  a  salt  into  the  solution  of  another  salt 
takes  place  with  nearly  the  same  velocity  as  into  pure  water,  at 
least  when  the  solutions  are  dilute.     Here,  as  in  all  experiments 
on  liquid  diffusion,  uniformity  of  action  takes  place  only  in  dilute 
solution.    As  the  solution  becomes  saturated,  the  cohesion  of  the 
particles  of  the  solid  appears  to  introduce  irregularities. 

7.  "  The  velocity  with  which  a  soluble  salt  diffuses  from  a 
stronger  into  a  weaker  solution,  is  proportional  to  the  difference 
of  concentration  between  two  contiguous  strata."     This  law  has 
been  experimentally  demonstrated  by  Frick  in  the  case  of  chlo- 
ride of  sodium,  but  it  cannot  as  yet  be  regarded  as  completely 
established.! 

(202.)  Osmose.  —  When  two  liquids  are  separated  by  a 
porous  diaphragm,  diffusion  may  still 
take  place,  although  the  phenomena 
are  modified  in  a  remarkable  manner 
by  the  presence  of  the  septum.  This 
is  best  illustrated  by  means  of  the 
apparatus  called  an  osmometer.  It 
may  be  constructed  in  various  ways, 
but  as  represented  in  Fig.  330  it  con- 
sists of  a  membranous  bag  or  bladder 
opening  into  a  glass  tube,  to  which  it 
is  fastened  hermetically.  The  bladder 
is  filled  with  a  concentrated  solution 
of  common  salt,  and  suspended  in  a 
jar  filled  with  pure  water.  Since  the 
animal  membrane  is  readily  penetrat- 
ed by  the  water,  it  is  evident  that 
the  water  on  the  one  side,  and  the 
salt  solution  on  the  other,  must  be  in 
direct  contact,  and  hence  a  diffusion  of  Fig'  33°- 


Graham's  Chemistry,  Vol.  II.  p.  614. 


t  Ibid.,  p.  610. 


388  CHEMICAL   PHYSICS. 

the  salt  must  take  place,  following  the  laws  of  liquid  diffusion 
enunciated  in  the  last  section.  We  should,  therefore,  expect 
that  the  salt  would  pass  out  into  the  water  of  the  jar,  as  we 
find  to  be  the  case ;  but  the  remarkable  fact  in  connection  with 
this  experiment  is,  that  a  volume  of  water  enters  the  bladder 
which  is  very  much  greater  than  could  be  introduced  by  simple 
liquid  diffusion,  amounting  in  some  cases  to  several  hundred 
times  that  of  the  salt  displaced,  the  liquid  slowly  rising  in  the 
glass  tube  of  the  osmometer  until  it  attains  a  very  considerable 
height.  The  flow  of  water  through  the  membrane  is  termed 
osmose,  and  the  unknown  power  which  produces  it,  osmotic 
force.  It  is  a  force  of  great  intensity,  capable  of  supporting  a 
column  of  water  several  metres  high.  The  first  important  phe- 
nomenon to  be  studied  in  this  connection  is  this  remarkable  flow 
of  water.  The  movement  of  the  salt  in  the  opposite  direction 
appears  to  follow  the  laws  of  liquid  diffusion,  and,  according  to 
Graham's  experiments,  is  not  influenced  by  the  presence  of  the 
membrane,  unless  it  is  quite  thick. 

We  have  supposed  that  the  bladder  in  this  experiment  con- 
tained a  solution  of  common  salt ;  but  we  may  use  in  its  place 
alcohol,  or  solutions  of  cane  sugar,  of  Glauber's  salt,  and  of 
many  other  saline  bodies,  with  precisely  the  same  result.  The 
conditions  of  osmose  appear  to  be,  that  the  liquids  are  capable  of 
mixing,  and  that  the  membrane  or  septum  which  separates  them 
has  a  greater  adhesion  for  one  liquid  than  for  the  other. 

When  the  osmose  takes  place  between  Water  and  solutions  of 
salts,  the  quantity  of  salt  which  passes  through  the  membrane 
into  the  water  is  always  replaced  by  a  definite  quantity  of  water, 
and  the  ratio  obtained  by  dividing  the  last  quantity  by  the  first 
has  been  termed  the  osmotic  equivalent  of  the  salt.  This  ratio 
varies  with  the  nature  of  the  salt,  and  also,  to  some  extent  cer- 
tainly, with  that  of  the  membrane.  It  moreover  increases  with 
the  temperature,  but  it  appears  to  be  independent  of  the  density 
of  the  solution.  The  osmotic  equivalent  for  Glauber's  salts,  for 
example,  when  the  pericardium  of  the  calf  is  used  as  the  septum, 
was  found  by  Hoffmann  *  to  be  5.1. 

The  action  of  the  septum  in  osmose  has  been  explained  in 
various  ways.  The  simplest  explanation  which  has  been  given 

*  Untersuchungen  tiber  das  endosmotische  Aequivalent  des  Glaubersalzes.  Giessen, 
1858. 


THE   THREE   STATES   OF   MATTER.  889 

is  based  on  the  unequal  adhesion  of  the  two  liquids  to  the  porous 
septum.  Let  us  suppose  that  the  septum  is  a  piece  of  the  blad- 
der of  an  ox,  and  that  on  one  side  it  is  in  contact  with  alcohol, 
and  on  the  other  with  water.  As  was  stated  (194)  the  mem- 
brane has  a  very  much  greater  attraction  for  water  than  for 
alcohol,  and  would  therefore  absorb  the  first  to  the  entire  exclu- 
sion of  the  second,  were  it  not  for  the  adhesion  between  the  two 
liquids.  In  consequence  of  this,  the  alcohol  is  slowly  diffused 
through  the  water  contained  in  the  membrane,  which  thus  be- 
comes saturated  with  greatly  diluted  alcohol.  Hence,  on  the 
side  of  the  membrane  towards  the  alcohol,  nearly  pure  water  is 
in  contact  with  strong  alcohol,  and  a  rapid  diffusion  of  the  first 
into  the  last  necessarily  results.  The  place  of  the  water  thus 
escaping  is  supplied  by  fresh  water,  and  a  current  of  water  is 
thus  established  flowing  in  towards  the  alcohol.  On  the  side  of 
the  membrane  towards  the  water,  we  have,  on  the  other  hand, 
very  dilute  alcohol  in  contact  with  water,  so  that,  although  dif- 
fusion takes  place,  it  is  very  much  less  rapid  than  that  in  the 
opposite  direction.  The  flow  of  the  water  is  then  the  result  of 
two  forces,  —  first,  the  excess  of  the  attraction  of  the  bladder 
for  water  over  its  attraction  for  alcohol,  and,  secondly,  the  diffu- 
sive force  between  the  two  liquids ;  while  the  flow  of  the  alcohol 
is  due  to  the  diffusive  force  alone,  and  must  therefore  be  less 
rapid. 

This  subject  of  osmotic  action  has  also  been  carefully  investigated 
by  Professor  Graham,  who  has  established  several  important  facts  in 
relation  to  it. 

The  most  remarkable  conclusion  is,  that  all  substances  may  be  divided 
into  two  classes,  which  he  names  crystalloids  and  colloids.  The  first  class 
are  capable  of  crystallizing,  and  as  a  general  rule  they  form  perfectly 
fluid  solutions,  which  have  a  decided  taste.  The  second  class,  on  the  other 
hand,  are  incapable  of  crystallizing,  and  give  insipid  viscid  solutions, 
which  readily  form  into  jelly.  Hence  the  name  colloid,  from  <eo'XX»;,  glue. 
Moreover,  while  crystalloid  bodies,  like  sugar  or  salt,  diffuse  with  com- 
parative rapidity,  the  colloids,  such  as  gum,  starch,  caramel,  gelatine,  and 
albumen,  are  characterized  by  a  remarkable  sluggishness  and  indisposi- 
tion to  diffusion.  This  fact  is  made  evident  by  the  following  table,  and 
it  will  be  noticed  that  sulphate  of  magnesia  and  cane-sugar,  which  are 
among  the  least  diffusible  of  crystalline  bodies,  diffuse  seven  times  as 
rapidly  as  albumen,  and  fourteen  times  as  rapidly  as  caramel,  both  well- 
marked  colloids. 

33* 


390  CHEMICAL  PHYSICS. 

Approximate  Times  of  Equal  Diffusion. 

Hydrochloric  Acid 1. 

Chloride  of  Sodium       ........         2.33 

Cane-Sugar      '. 7. 

Sulphate  of  Magnesia    .        * 7. 

Albumen  .         .       ;>  ,  "   >        .         .         .         .         .         .    "     .  49. 

Caramel     ,  ,-,'    ,.*•.,*, .98. 

Upon  this  marked  difference  of  qualities,  Graham  has  based  a  most 
valuable  method  of  separating  the  two  classes  of  bodies  from  each  other, 
which  he  terms  dialysis.  A  shallow  tray  is  prepared  by  stretching  parch- 
ment paper  (which  is  itself  an  insoluble  colloid)  over  one  side  of  a  gutta- 
percha  hoop,  and  holding  it  in  place  by  a  somewhat  larger  hoop  of  the 
same  material.  The  solution  to  be  dialysed  is  poured  into  this  tray,  which 
is  then  floated  on  pure  water  in  a  shallow  dish,  the  volume  of  the  water 
being  from  six  to  ten  times  greater  than  that  of  the  solution.  Under 
these  conditions,  the  crystalloid  will  diffuse  through  the  porous  septum 
into  the  water,  leaving  the  colloid  on  the  tray,  and  in  the  course  of  one 
or  two  days  the  separation  will  have  taken  place  more  or  less  completely. 

The  value  of  this  process,  both  in  chemistry  and  pharmacy,  can  be 
readily  understood.  In  examining  organic  mixtures  for  poisons,  it  affords 
a  ready  means  of  separating  the  mineral  acids  and  the  vegetable  alka- 
loids (all  crystalline  bodies)  from  the  vegetable  colloids,  with  which 
they  are  mixed,  and  which  would  obscure  their  chemical  reactions ;  and 
again  it  furnishes  an  equally  efficient  means  of  freeing  silicic  acid,  cara- 
mel, albumen,  and  other  colloid  bodies,  from  saline  impurities,  which  it  is 
very  difficult,  if  not  impossible,  to  remove  in  any  other  way.  It  is  not 
essential  for  the  success  of  this  process  that  the  solution  of  the  colloid 
should  remain  fluid,  for  even  after  the  solution  has  set  into  a  firm  jelly 
the  diffusion  will  continue  apparently  as  rapidly  as  before. 

The  best-known  colloid  bodies,  such  as  gum,  starch,  fruit-jelly,  and 
glue,  —  the  type  of  the  class,  —  are  substances  of  organic  origin,  and  this 
condition  of  matters  seems  to  be  especially  adapted  in  the  plan  of  crea- 
tion for  forming  the  tissues  of  living  beings ;  but  there  are  also  many 
inorganic  colloids,  and  one  at  least  which  plays  a  very  important  part  in 
the  mineral  kingdom.  The  soluble  form  of  silicic  acid  is  a  true  colloid. 
It  can  readily  be  obtained  by  pouring  a  solution  of  silicate  of  soda  into 
diluted  hydrochloric  acid,  the  acid  being  maintained  in  great  excess. 
When,  now,  the  resulting  liquid  is  placed  on  a  dialyser,  the  excess  of 
hydrochloric  acid  and  the  common  salt  formed  by  the  chemical  reaction, 
together  with  a  small  amount  of  silica,  diffuse  into  the  water  below,  leav- 
ing on  the  tray  a  solution  containing  the  great  mass  of  the  silica  in  a 
pure  condition. 


THE  THREE   STATES   OF  MATTER. 


391 


In  this  way  a  solution  can  readily  be  obtained  containing  10  or  12  per 
cent  of  silica.  Such  a  solution  gelatizes  spontaneously  in  a  few  hours 
even  at  the  ordinary  temperature,  and  immediately  when  heated.  The 
more  dilute  the  solution  the  longer  it  can  be  kept  without  change,  and  a 
solution  holding  only  one  per  cent  of  silica  is  practically  unalterable  by 
time.  In  a  like  manner  Professor  Graham  has  obtained  alumina,  sesqui- 
oxide  of  iron,  sesquioxide  of  chromium,  and  stannic,  meta-stannic,  titanic, 
tungstic,  and  molybdic  acids,  dissolved  in  water  in  a  coloidal  condition, 
and  presenting  properties  similar  to  those  of  silicic  acid  in  the  same  state. 
All  these  substances  usually  exist  in  the  crystalline  condition.  The  col- 
loid condition  is  an  abnormal  state,  and  in  all  colloids  there  is  usually  a 
tendency  to  approach  the  crystalloid  form.  The  water  of  crystallization 
in  a  crystalloid  is  represented  in  a  colloid  by  what  has  been  called  water 
of  gelatinization. 

Liquids  on  Gases. 

(203.)  Adhesion  of  Liquids  to  Gases. 
— The  adhesion  of  liquids  to  gases  is  ex- 
emplified by  the  familiar  fact,  that,  when 
liquids  are  poured  from  one  vessel  to  an- 
other, bubbles  of  air  are  carried  down  with 
the  descending  stream,  which  rise  and  break 
upon  the  surface  of  the  liquid.  The  adhe- 
sion of  water  to  air  is  a  force  of  considerable 
power,  and  is  applied  in  some  places  for 
producing  the  constant  blast  which  is  re- 
quired for  working  an  iron  forge.  In  Fig. 
331  is  represented  the  machine  which  is 
used  for  this  purpose  at  some  iron  forges 
in  Catalonia.  Water  is  discharged  from 
the  reservoir  A,  into  which  it  flows  from 

a  higher  level, 
into  the  tube 
J5,  through  a 
conical  orifice, 
a  a.  The  op- 
enings c  c  ad- 
mit air  to  the 
upper  part  of 

tne    tut)e    ^> 

Fig.  331. 


392  CHEMICAL   PHYSICS. 

which  is  carried  down  by  the  stream  of  water  into  the  reservoir  C, 
and  then  forced  through  the  tube  EF  G  and  the  tuyere  TU 
into  the  crucible  of  the  forge.  The  stream  of  water  is  broken 
on  a  projecting  ledge,  and  escapes  by  the  opening  Z>.  By  rais- 
ing or  lowering  the  stopper  g*,  the  quantity  of  water  which 
falls,  and  hence  also  the  intensity  of  the  blast,  can  easily  be 
regulated. 

An  aspirator  for  establishing  a  current  of  gas  through  various 
forms  of  chemical  apparatus,  founded  on  the  principle  of  this 
blast  machine,  has  been  described  by  M.  W.  Johnson.*  It  con- 
sists merely  of  a  tube  ten  or  twelve  inches  in  length,  attached  by 
means  of  an  india-rubber  connector  to  a  water-cock.  Near  the 
top  of  this  tube  there  is  a  lateral  tubulature,  which  is  connected 
by  an  india-rubber  hose  with  the  vessel  through  which  the  air  is 
to  be  drawn.  When  the  water-cock  is  partially  opened,  a  very 
uniform  and  abundant  current  of  gas  is  drawn  in  at  the  lateral 
opening,  and  its  velocity  can  be  regulated  by  varying  the  length 
of  the  tube. 

(204.)  Solution  of  Gases.  —  Another  effect  of  adhesion,  still 
more  important  in  its  chemical  relations  than  the  one  just  con- 
sidered, is  the  absorption  of  gases  by  water  and  other  liquids. 
Water  has  the  power  of  dissolving  all  gases,  although  in  very 
different  proportions,  varying  from  one  thousand  times  its  own 
volume,  in  the  case  of  ammonia,  to  only  about  one  fiftieth  of  its 
volume,  in  that  of  nitrogen. 

The  amount  of  gas  dissolved  by  a  liquid  on  which  it  exerts  no 
chemical  action  depends  upon,  — 

1st.  The  peculiar  nature  of  the  gas  and  the  absorbing  liquid. 

2d.  The  pressure  to  which  the  gas  is  exposed. 

3d.  The  temperature. 

The  volume  of  a  gas  (reduced  to  0°  and  to  76  c.  m.  pressure) 
which  is  absorbed  by  one  cubic  centimetre  of  a  liquid  under  the 
pressure  of  76  c.  m.  is  called  the  coefficient  of  absorption.  This 
coefficient  of  absorption  varies  with  the  temperature,  but  for  any 
given  temperature  it  is  a  constant  quantity  for  the  same  gas  and 
liquid.  The  coefficients  of  absorption  at  0°  of  a  few  of  the  best 
known  gases  are  given  in  the  following  table,  both  for  water  and 
for  alcohol :  — 

* 'Journal  of  the  Chemical  Society  of  London,  Vol.  IV.  p.  186. 


THE   THREE    STATES    OF   MATTER. 


393 


Name  of  Gas. 

Nitrogen,        .         . 
Hydrogen, 
Oxygen, 

Carbonic  Acid,  . 
Sulphide  of  Hydrogen, 
Sulphurous  Acid, 
Ammonia,     . 


Volume  in  HTml3  absorbed  by  one  c.  m.3  of 


Water. 

0.02035 
.  0.01930 

0.04114 
.  1.79670 

4.370GO 
.  C8.86100 
1049.GOOOO 


Alcohol. 

0.12634 

0.06925 

0.28397 

4.32950 

17.89100 

328.62000 


(205.)  Variation  of  the  Coefficient  of  Absorption  with  the 
Temperature.  —  In  a  solid,  the  force  which  the  solvent  power 
of  a  liquid  has  to  overcome  is  that  of  cohesion  ;  in  a  gas,  on 
the  other  hand,  it  is  that  of  repulsion ;  and  we  should  therefore 
naturally  expect,  contrary  to  what  is  true  of  solids,  that  the  sol- 
ubility of  gases  would  diminish  with  the  increase  of  the  tempera- 
ture. This  we  find  to  be  the  case,  and,  with  a  few  exceptions, 
the  solubility  of  a  gas  is  greater  the  lower  the  temperature.  As 
in  the  case  of  solids,  however,  the  law  of  the  variation  depends 
upon  the  nature  of  the  gas,  and  must  therefore  be  determined  for 
each  special  case.  In  Table  VII.  of  the  Appendix,  the  coefficients 
of  solubility  of  the  most  familiar  gases  are  given  for  different  tem- 
peratures within  the  limits  of  ordinary  observation.  By  compar- 
ing together  the  results  of  observation  at  different  temperatures, 
we  can  obtain,  as  in  the  case  of  the  solubility  of  solids,  interpo- 
lation formula  by  means  of  which  the  coefficients  may  be  cal- 
culated for  other  temperatures  within  certain  restricted  limits. 
Thus  in  the  case  of  the  absorption  of  nitrogen  by  water,  the 
results  of  five  experiments  were  as  given  in  the  following  table 
from  Bunsen's  Gasometry.* 


No.  of  the 
Experiment. 

Coefficient  from 
Formula. 

Difference. 

1 

4.0 

0.01843 

0.01837 

0.00006 

2 
3 
4 

6.2 
12.6 
17.7 

0.01751 
0.01520 

0.01  IP,«> 

0.01737 
0.01533 
0.0  1430 

—  0.00014 
+0.00013 
—0.00006 

5 

23.7 

0.01392 

0.01384 

—  0.00008 

By  combination  of  the  experiments  1,  2,  3  ;  2,  3,  4  ;  3,  4,  5,  we 
obtain  the  interpolation  formula 


*  Gasometry,  by  Robert  Bunsen.    Translated  by  Roscoe.     London,     1857. 


394  CHEMICAL   PHYSICS. 

e  =  0.020346  —  0.00053887*  +  0.000011156*%         [131.] 

by  means  of  which  the  numbers  of  Table  VII.  may  be  calcu- 
lated. For  the  interpolation  formulae  by  which  the  coefficients 
of  absorption  of  other  gases  may  be  calculated,  as  well  in  alcohol 
as  in  water,  we  must  refer  the  student  to  the  excellent  work 
of  Professor  Bunsen  already  cited,  from  which  Table  VII.  has 
been  taken. 

To  the  general  law  that  the  solubility  of  a  gas  diminishes 
with  the  increase  of  the  temperature,  there  are  several  excep- 
tions. Thus,  the  coefficient  of  absorption  of  oxygen  in  alcohol  is 
constant  at  0.28397  for  temperatures  between  0°  and  24°,  and 
the  same  is  true  also  for  hydrogen  in  water.  So  also  one  vol- 
ume of  water  at  5°  absorbs  less  chlorine  gas  than  at  8° ;  but  here, 
as  in  similar  cases,  the  apparent  exception  to  the  law  is  caused 
by  the  intervention  of  chemical  affinity.  Chlorine  forms  at  0° 
a  definite  crystalline  compound  with  water,  and  the  solubility 
of  this  solid  increases  with  the  temperature  up  to  10°.  Above 
this  temperature  the  crystalline  hydrate  cannot  exist,  the  chlo- 
rine dissolves  as  a  gas,  and  its  solubility  follows  the  general 
law,  diminishing  with  the  temperature. 

Although  the  solubility  of  a  gas  increases  as  the  tempera- 
ture falls,  yet  at  the  moment  the  liquid  freezes,  the  absorbed 
gas  is  almost  entirely  set  free.  During  the  freezing  of  water 
the  air  dissolved  separates  from  it,  forming  bubbles  in  the  ice. 
So  also  the  oxygen  which  is  absorbed  in  large  quantity  by  melted 
silver  is  evolved  when  it  solidifies.  But  when  at  the  freezing 
point  the  dissolved  gas  forms  a  definite  compound  with  the 
water,  it  sometimes  happens  that  no  gas  is  evolved  when  the 
water  freezes,  as  is  the  case  with  the  solution  of  chlorine  just 
mentioned. 

(206.)  Variation  of  the  Solubility  of  a  Gas  with  the  Pres- 
sure.—  This  variation  follows  a  very  simple  law.  The  quan- 
tity of  gas  *  absorbed  by  a  liquid  varies  directly  as  the  pressure 
which  the  gas  exerts  upon  it.  If  now,  instead  of  considering 
the  quantity  of  gas  absorbed,  we  consider  the  volume  absorbed 
under  any  given  pressure,  it  follows,  from  Mariotte's  law,  that 
this  volume  must  be  the  same  in  all  cases.  Thus,  for  example,  at 
0°  one  cubic  centimetre  of  water  absorbs  1.797  cTm.3  of  carbonic 

*  By  the  term  quantity  of  a  gas  is  always  to  be  understood  the  number  of  cubic  cen- 
timetres measured  at  0°  C.  and  under  a  pressure  measured  by  76  c.  m.  of  mercury. 


THE   THREE   STATES   OF  MATTER. 


895 


acid  gas,  whatever  may  be  its  pressure.  If  the  pressure  is  76  c.  m., 
the  quantity  of  gas  absorbed  measures,  at  the  standard  tempera- 
ture and  pressure,  exactly  1.797  c.  m.3.  If  now  the  pressure  is 
doubled,  the  volume  of  gas  absorbed  is  the  same  as  before,  but 
the  quantity  (measured  at  0°  C.  and  76  c.  m.)  will  be  found  equal 
to  twice  1.797  or  3.594  c.  m.3,  and  the  same  is  true  for  all  pres- 
sures within  the  limits  at  which  Mariotte's  law  holds  good. 
(165.)  It  is  true  that  the  law  has  not  been  demonstrated  ex- 
perimentally except  in  a  few  cases  and  within  very  restricted 
limits,  but  it  is  highly  probable  that  it  is  as  constant  as  that  of 
Mariotte.  Representing  by  V0  and  V0'  the  quantities  of  a  given 
gas  absorbed  by  a  given  volume  of  liquid  corresponding  to  the 
pressures  H0  and  //0',  we  have  for  the  mathematical  expression  of 
this  fundamental  law  of  gasometry  the  proportion 


V. :  V,'  =  B. :  HJ. 


[132.] 


The  principles  of  this  section  are  illustrated  by  the  apparatus 
represented  in  Figs.  332  and  333,  used  for  saturating  water  with 
carbonic  acid  gas  under 
pressure  (soda-water).  It 
is  made  of  earthenware ; 
and  the  two  chambers  A 
and  B9  as  shown  in  the 
section,  are  connected  to- 
gether by  the  fine  tube 
a  b.  Through  the  neck  of 
the  apparatus  at  w,  water  is 
introduced  into  the  upper 
chamber,  B,  which  is  then 
closed  by  a  screw  plug. 
Through  this  plug  passes  a 


Fig.  332. 


Fig.  333. 


tube,  p  t,  closed  by  a  valve 
stopcock,  by  means  of  which  the  water  may  be  drawn  off  when 
saturated  with  gas.  Through  a  tubulature  at  0,  which  can  also 
be  closed  by  a  screw  plug,  the  materials  for  making  carbonic 
acid  gas  (bicarbonate  of  soda,  tartaric  acid,  and  water)  are  in- 
troduced into  the  lower  chamber,  A.  The  gas,  as  it  is  evolved, 
escapes  through  the  tube  b  a  into  the  upper  part  of  the  chamber 
B,  where  it  comes  in  contact  with  the  surface  of  the  water,  and 
is  in  part  dissolved,  while  the  rest  exerts  a  pressure  upon  it 


896  CHEMICAL  PHYSICS. 

amounting  to  several  atmospheres.  On  opening  the  stopcock, 
the  water  charged  with  gas  is  driven  out  with  force,  and  the 
amount  of  gas  dissolved  is  found  to  be  exactly  proportional  to 
the  pressure  which  it  exerted  on  the  surface  of  the  water. 

When  the  water  thus  surcharged  with  gas  is  drawn  out  into  a 
glass  tumbler,  the  excess  of  gas  escapes  with  effervescence.  If 
the  process  is  closely  examined,  it  will  be  noticed  that  the  bubbles 
of  gas  rise  from  the  sides  and  bottom  of  the  tumbler,  and  if,  while 
the  water  is  still  saturated,  we  drop  into  it  a  solid  body  with  a 
rough  surface,  a  piece  of  bread,  for  example,  there  will  ensue  a 
brisk  effervescence  around  the  body.  The  cause  of  this  phenom- 
enon is  thus  explained.  The  gas,  as  we  have  assumed,  is  held 
in  solution  by  the  adhesion  of  the  liquid  particles.  In  the  midst 
of  the  water  the  particles  of  carbonic  acid  are  surrounded  on  all 
sides  by  particles  of  liquid,  but  immediately  in  contact  with  the 
solid  they  are  only  attracted  on  one  side  by  the  liquid,  since  on 
the  other  they  are  in  contact  with  the  solid  surface.  It  is  evident 
that  the  adhesive  force,  and  hence  also  the  solvent  power,  must  be 
less  in  the  last  case  than  in  the  first,  so  that  the  particles  of  gas 
in  contact  with  the  solid  surfaces  will  be  the  first  to  assume 
the  aeriform  condition.  These  particles  uniting  together  form  a 
small  bubble  of  gas,  which,  as  it  rises  through  the  solution,  con- 
stantly enlarges,  and  acquires  a  considerable  size  before  it  breaks 
on  the  surface.  The  bubble  increases  in  size  as  it  ascends,  be- 
cause, as  is  evident,  it  must  have  the  same  effect  as  a  solid  body 
on  all  the  particles  of  the  solution  with  which  it  comes  in  contact, 
diminishing  the  adhesive  force  between  the  water  and  gas. 

If  water  saturated  with  carbonic  acid  is  placed  under  a  glass 
bell  resting  on  the  plate  of  an  air-pump,  the  carbonic  acid  will 
escape  from  the  solution,  and  collect  in  the  bell,  until  the  quantity 
remaining  in  solution  corresponds  to  the  pressure  exerted  by 
the  carbonic  acid  which  has  escaped.  The  presence  of  air  in 
the  bell  does  not  in  any  way  affect  the  final  result,  and  precisely 
the  same  quantity  of  carbonic  acid,  and  no  more,  would  rise  into 
the  bell  if  the  air  were  completely  removed.  It  is  true,  how- 
ever, that,  if  the  bell  were  exhausted,  this  quantity  would  escape 
instantaneously,  while,  if  it  is  filled  with  air,  the  equilibrium  is 
only  attained  after  a  considerable  time.  The  same  is  true  if  the 
bell  is  filled  with  other  gases  than  air.  Let  us  now  suppose  that, 
after  the  equilibrium  has  been  attained,  a  portion  of  the  mixture 


THE  THREE   STATES   OF  MATTER.  397 

of  carbonic  acid  and  air  is  removed  by  the  pump.  The  pressure 
which  the  carbonic  acid  exerts  on  the  solution  will  thus  be  di- 
minished, and  more  gas  will  escape  from  the  solution,  until  the 
equilibrium  between  the  gas  dissolved  and  the  pressure  of  gas  in 
the  bell  is  again  restored.  It  is  evident  that  the  whole  gas  can- 
not be  removed  from  a  solution  by  the  air-pump,  since  we  can 
never  remove  the  whole  of  the  gas  from  the  surface  of  the  liquid, 
and  cannot  therefore  entirely  remove  the  pressure  which  the  gas 
escaping  from  the  solution  exerts.  This  object,  however,  can 
be  readily  attained  by  placing  at  the  side  of  the  glass  holding  the 
solution  another  glass,  containing  some  chemical  reagent  which 
has  the  power  of  absorbing  the  gas.  Thus,  if  we  place  under 
the  same  bell  containing  a  solution  of  carbonic  acid  a  concen- 
trated solution  of  caustic  potash,  this  reagent  will  keep  the  bell 
free  from  carbonic  acid,  and  reduce  the  pressure  it  exerts  to 
nothing,  so  that  the  gas  will  continue  to  escape  from  the  solution 
until  the  whole  is  removed.  If  at  the  same  time  we  exhaust  the 
air  with  the  pump,  we  shall  greatly  hasten  the  process,  although 
the  final  result  is  not  affected  by  the  presence  of  the  air,  or  any 
other  chemically  inactive  gas. 

The  amount  of  carbonic  acid  present  in  the  atmosphere  is  so 
small,  that  it  exerts  no  appreciable  pressure  ;  so  that,  if  a  solu- 
tion of  this  gas  is  exposed  to  the  atmosphere,  the  whole  of  the  gas 
should  according  to  the  law  escape.  This  we  find  to  be  the  case, 
although,  on  account  of  the  slow  diffusion  of  carbonic  acid  into 
air,  it  requires  a  long  time  before  the  whole  has  disappeared. 
The  same  must,  of  course,  also  be  true  of  solutions  of  all  gases 
with  the  exception  of  those  composing  the  atmosphere. 

The  most  available  means  of  driving  out  a  gas  from  a  solution 
is  boiling.  The  high  temperature  diminishes  the  coefficient  of 
absorption,  and  moreover  the  escaping  vapor  carries  away  with 
it  the  gas  from  the  surface  of  the  liquid,  so  that  the  pressure 
which  the  gas  exerts  on  this  surface  is  constantly  diminishing, 
and  with  it  also  the  amount  of  the  gas  which  the  liquid  can  hold 
in  solution.  On  this  same  principle,  protoxide  of  nitrogen  can 
be  entirely  removed  from  water  by  passing  through  it  a  current 
of  air. 

There  are  a  few  gases,  such  as  chlorohydric  acid,  which  have 
so  strong  an  affinity  for  water  that  they  cannot  be  removed  by 
boiling,  since,  after  the  solution  is  reduced  to  a  certain  degree 
34 


398  CHEMICAL  PHYSICS. 

of  concentration,  the  liquid  and  gas  evaporate  together  as  a 
whole. 

(207.)  As  a  general  rule,  the  solubility  of  a  gas  is  diminished 
by  the  presence  of  other  substances  in  the  solution.  Tims,  for 
example,  water  containing  sulphuric  acid  or  any  salt  will  absorb, 
in  most  cases,  less  gas  than  when  pure.  As  a  necessary  conse- 
quence, the  gas  which  water  holds  in  solution  can  in  great  meas- 
ure be  driven  out  by  the  addition  of  oil  of  vitriol,  or  by  dissolving 
in  it  some  salt.  So  also  melted  silver,  which  absorbs  from  the 
atmosphere  a  large  volume  of  oxygen,  disengages  with  efferves- 
cence the  whole  of  the  dissolved  gas,  on  the  addition  of  an  equal 
weight  of  melted  gold. 

Whenever,  on  the  other  hand,  as  is  sometimes  the  case,  the 
solubility  of  a  gas  is  increased  by  the  presence  of  salts  or  other 
substances  in  solution,  this  exception  to  the  general  rule  is  appar- 
ently caused  by  the  chemical  affinity  of  the  dissolved  substance. 
The  presence  of  phosphate  of  soda  increases  greatly  the  solubility 
of  carbonic  acid,  and  the  presence  of  sulphate  of  copper  and  sul- 
phate of  protoxide  of  iron,  the  solubility  of  oxide  of  carbon  and 
deutoxide  of  nitrogen,  respectively.  It  is  true  that  in  all  these 
cases  the  gas  can  be  driven  out  of  the  solution  by  boiling,  but 
nevertheless  it  is  probable  that  unstable  compounds  are  in  each 
case  formed ;  and  this  opinion  is  substantiated  in  the  last  case  by 
the  very  remarkable  change  of  color  which  the  solution  of  green 
vitriol  undergoes  by  absorbing  deutoxide  of  nitrogen  gas. 

The  principles  of  this  section,  it  should  be  noticed,  apply  only 
to  solid  and  liquid  bodies,  since  the  coefficient  of  absorption  of 
one  gas  is  not  apparently  influenced  by  the  presence  in  the  solu- 
tion of  another  gas  on  which  it  is  chemically  inactive.  This  last 
principle  will  be  considered  in  detail  in  section  (209). 

(208.)  Determination  of  the  Coefficient  of  Absorption. — As  has 
been  already  stated,  the  coefficient  of  absorption  is  the  volume  of 
gas  (measured  in  cubic  centimetres  at  0°  and  76  c.  m.)  absorbed 
by  one  cubic  centimetre  of  liquid.  Since  this  coefficient  varies  with 
the  temperature,  it  must  be  determined  for  each  temperature,  or 
we  may  determine  it  with  accuracy  for  several  temperatures  at 
suitable  intervals,  and  then  from  these  results  deduce  an  interpo- 
lation formula  by  which  we  may  calculate  the  coefficient  for  all 
intermediate  temperatures,  and  prepare  tables  like  Table  VII. 
of  the  Appendix.  It  is  only  then  necessary  to  inquire  how  the 


THE   THREE   STATES    OF   MATTER. 


399 


coefficient  is  determined  for  any  given  temperature,  t.    There  are, 
in  general,  two  methods  which  are  used  for  this  purpose. 

First  Method.  —  The  first  method  consists  in  passing  a  current 
of  the  gas  through  the  liquid  under  experiment,  until  the  last  is 


Fig.  334. 

saturated;  then,  having  carefully  observed  the  temperature  of 
the  solution,  transferring  with  proper  precautions  a  measured 
volume  to  a  glass  beaker,  and  determining  the  weight  of  the  dis- 
solved gas  by  some  process  of  chemical  analysis.  This  method 
will  be  better  understood  if  illustrated  by  an  example,  and  we 
will  select  for  the  purpose  the  determination  of  the  coefficient  of 
absorption  of  sulphide  of  hydrogen  in  alcohol,  which  was  made 
by  Drs.  Schonfeld  and  Carius,  with  the  apparatus  represented  in 
Fig.  334.* 

The  flask  a  a  is  closed  by  a  tight  cork,  through  which  four 
holes  have  been  bored.     Through  the  first  of  these  passes  a  ther- 

*  See  Bunsen's  Gasometry,  page  160. 


400  CHEMICAL  PHYSICS. 

mometer,  5;  through  the  second,  the  tube,  c,  conducting  the  gas; 
through  the  third,  a  short  tube,  d,  serving  as  a  vent  to  the  gas, 
and  ending  in  a  small  india-rubber  tube,  which  can  be  easily 
closed  by  a  glass  rod ;  lastly,  through  the  fourth  hole  passes  a 
siphon  tube,  e.  These  tubes  exactly  fit  the  holes  in  the  cork,  so 
that  if  the  tube  d  is  closed  while  the  current  of  gas  is  flowing 
into  the  flask  through  the  tube  c,  the  solution  will  be  forced  out 
through  this  siphon  tube,  e. 

In  making  the  determination,  the  sulphide  of  hydrogen  was 
generated  from  sulphide  of  iron  and  dilute  sulphuric  acid,  and, 
having  been  washed  with  water,  was  passed  through  alcohol  in 
the  flask,  which  had  been  previously  boiled  in  order  to  expel  all 
the  air  it  contained  in  solution.  The  alcohol  in  the  mean  time 
was  kept  at  a  constant  temperature  by  placing  the  flask  in  a  wa- 
ter-bath, and  this  temperature,  which  was  carefully  observed  by 
the  thermometer  &,  we  will  call  t°.  The  tube  d  was  also  left 
open,  so  that  the  sulphide  of  hydrogen  gas,  which  filled  the  iipper 
part  of  the  flask,  exerted  the  same  pressure  on  the  surface  of  the 
alcohol  as  that  indicated  by  the  barometer  at  the  time  of  the 
experiment.  We  will  represent  this  by  H.  At  the  end  of  two 
hours,  when  it  was  assumed  that  the  liquid  was  saturated  with 
the  gas,  the  india-rubber  connector  at  d  was  closed  by  a  glass 
rod,  and  the  solution,  as  it  was  forced  out  through  the  siphon  e, 
collected  in  a  measuring-glass.  The  tube  e  was  so  adjusted  as 
to  reach  to  the  bottom  of  the  measuring-glass,  and  after  the  glass 
was  full,  the  solution  was  permitted  to  overflow  the  mouth  for 
some  time,  and  until  the  upper  layers  of  the  liquid,  which  had 
been  exposed  to  the  air,  and  consequently  lost  a  portion  of  their 
gas,  had  been  replaced  by  the  saturated  solution  rising  from 
below.  The  glass  was  then  quickly  closed  by  its  stopper,  and  its 
contents  immediately  after  transferred  to  a  beaker  containing  a 
solution  of  chloride  of  copper.  The  volume  of  the  solution  used 
was,  of  course,  the  same  as  that  of  the  measuring-glass,  and  we 
will  represent  it  by  F.  Lastly,  the  sulphur  of  the  precipitated 
sulphide  of  copper  was  converted  into  sulphuric  acid  by  nitric 
acid,  and  weighed  in  the  usual  way  as  sulphate  of  baryta.  From 
the  weight  of  sulphate  of  baryta  the  weight  of  sulphide  of  hydro- 
gen contained  in  the  solution  was  easily  calculated.  Represent 
this  weight  by  W,  and  the  known  weight  of  one  cubic  centimetre 
of  sulphide  of  hydrogen  gas  at  0°  and  76  c.  m.  by  w  (Table  II.) , 


THE  THREE   STATES   OF   MATTER.  401 

and  we  have  all  the  data  for  calculating  the  coefficient  of  absorp- 
tion at  the  temperature  of  the  experiment. 

Y  =  volume  of  solution  saturated  with  H  S  at  t°  and  If  c.  m. 
W  =  weight  of  II  S  in  ditto,  at  t°  and  H  c.  m. 

Then  by  [132], 

W-ff-  =  weight  of  H  S  in  ditto  at  t°  and  76  c.m. 
Dividing  by  w,  we  get 

—  .  —  =  volume  of  H  S  (measured  at  0°  and  76  c.  m.)  dissolved  at 
t°  and  76  c.  m. 

It  was  assumed  in  this  determination  that  the  volume  of  alcohol 
underwent  no  change  by  absorbing  sulphide  of  hydrogen,  so  that 
V  represents  not  only  the  volume  of  the  solution,  but  also  the 
volume  of  the  alcohol  it  contained.  Hence,  V  cubic  centime- 

W    76 

tres  of  alcohol  at  t°  dissolve  —  .  -^.  cubic  centimetres  of  sulphide 

w     H 

of  hydrogen,  measured  at  0°  and  76  c.  m.     Consequently,  the 
coefficient  of  absorption,  or 


As  is  evident,  this  formula  is  not  only  applicable  to  the  particu- 
lar case  under  consideration,  but  may  also  be  used  in  all  similar 
cases,  in  which  the  volume  of  the  liquid  is  not  sensibly  altered 
by  dissolving  a  gas. 

If,  however,  we  seek  to  determine  the  solubility  of  sulphurous 
acid  gas  in  alcohol  by  the  same  method,  it  will  be  found  that  the 
assumption  made  in  the  last  example  is  no  longer  correct,  and 
that  it  is  essential  to  pay  regard  to  the  change  of  volume.  As 
for  the  rest,  the  determination  may  be  conducted  in  precisely 
the  same  manner,  only  the  weight,  IF,  of  sulphurous  acid  gas 
contained  in  a  measured  volume,  F,  of  the  solution,  must  be  de- 
termined by  some  special  method  of  chemical  analysis.  As  we 
cannot  conveniently  measure  the  volume  of  alcohol  before  the  ab- 
sorption corresponding  to  the  measured  volume,  F,  of  the  solution, 
we  determine  carefully  the  specific  gravity  of  the  alcohol  and 
of  the  solution,  and  thus  obtain  all  the  data  for  our  calculation. 
34* 


402  CHEMICAL  PHYSICS. 

V  =  volume  of  alcohol  saturated  with  S  O2  at  t°  and  H  c.  m. 

(Sp.  Gr.)         =•  specific  gravity  of  ditto. 

V.  (Sp.  Gr.)  =  weight  of  ditto.     See  [56]. 

W  =  weight  of  S  O2  dissolved  at  t°  and  He.  m.  in  F£"nT.3  of 

solution. 

.  V  .  (Sp.  Gr.)  —  W  =  weight  of  alcohol  in  Fc.  m.3  of  solution. 
(Sp.  Gr.y        =  specific  gravity  of  alcohol  before  absorption. 

Hence  by  [56], 

—  lA^CL—J/  -  =  volume  of  alcohol  in  Fc.m.3  of  saturated  solution. 
(bp.  Gr.y 

w  =  weight  of  one  cubic  centimetre  of  S  O2  gas  measured  at  0° 

and  76  c.  m. 

=  volume  of  S  O2  (measured  at  0°  and  76  c.  m.)  dissolved  in 
7fi 


FcTm-8  of  solution  at  t°  and  He,,  m. 


—  .  —  -  =  volume  of  ditto  dissolved  in  Fc.  m.8  of  solution  at  t°  and  76  c.m. 
w      H 

Hence  —  -/!£—>»  \r~  —  c.m.3  of  alcohol  dissolve,  at  t°  and  76 
(bp. 


c.  m.,    —  •  -jr  c7m.3  of  S  02  gas. 


Whence 


W     76  (Sp.Gr.)' 

"  w      H'   V7(Sp.Gr.)  — 


This  formula  may  be  used  in  all  similar  determinations  of  the 
coefficient  of  absorption,  where  the  volume  of  the  liquid  is  sensibly 
changed  by  the  absorption  of  the  gas.  When  there  is  no  change 


of  volume,  F  =     '    /£'  ^\T  —  ,  which,  substituted  in  [134], 
(Sp.Gr.)' 

reduces  it  to  [133]  . 

The  method  of  determining  the  coefficient  of  absorption  just 
described  is  the  best  whenever  the  gas  dissolves  in  large  quanti- 
ties in  the  liquid,  and  when  it  is  of  such  a  nature  that  the 
amount  in  solution  can  be  readily  determined  by  the  methods  of 
chemical  analysis.  In  the  practical  application  of  this  method, 
peculiar  precautions  are  required  in  each  special  case.  For  a 
description  of  these,  we  must  refer  the  student  to  the  work  of 
Professor  Bunsen,  already  noticed. 

Second  Method.  —  The  second  method  of  determining  the  co- 
efficient of  absorption  consists  in  shaking  up  in  a  graduated  glass 
tube  a  measured  volume  of  gas  with  a  measured  volume  of 


THE   THREE   STATES   OF   MATTER. 


403 


liquid,  and  carefully  observing  the  volume  of  gas  absorbed.  A 
very  elegant  apparatus  for  this  purpose,  called  an  absorption- 
metre,  is  described  and  figured  by  Bunsen  in  his  work  on  Gasom- 
etry,  and  a  diagram  illustrating  its  principle  is  given  here  in  Fig. 
335.  The  gas  is  collected  in  the  gradu- 
ated glass  tube  a  a  over  a  mercury  pneu- 
matic trough,  and  its  volume  carefully 
determined.  We  will  call  this  volume 
corrected  for  temperature,  F0.  At  the 
same  time,  we  observe  the  height  of  the 
barometer,  and  the  height  of  the  surface 
of  the  mercury  in  the  tube  above  the 
surface  of  the  mercury  in  the  pneumatic 
trough.  The  difference  of  these  heights 
gives  us  a  quantity,  H,  which  is  the  pres- 
sure to  which  the  gas  confined  in  the 
tube  is  exposed  (169).  Next,  a  volume 
of  liquid  from  which  all  the  air  has  been 
expelled  by  boiling  is  passed  up  into  the 
tube,  still  standing  over  the  mercury  Fig.  335. 

trough.  This  volume  is  also  carefully  observed,  and  we  will 
represent  it  by  V.  The  tube  is  now  closed  by  screwing  on 
to  the  iron  ring  c  c  (which  is  cemented  to  the  tube  a  short  dis- 
tance from  its  mouth)  the  iron  cap  bbdd.  The  surface  dd  is 
covered  with  a  piece  of  sheet  india-rubber,  which  is  pressed  by 
the  screw  against  the  mouth  of  the  tube,  and  hermetically  closes 
it.  The  tube  (filled  with  mercury,  gas,  and  the  liquid)  is  now 
transferred  to  the  glass  cylinder  gg.  This  cylinder  is  cemented 
to  a  base  A,  and  a  rectangular  projection/,  at  the  bottom  of  the 
iron  cap,  exactly  fits  a  corresponding  hole  in  the  upper  surface 
of  the  base.  The  cylinder  may  be  closed  by  an  iron  lid,  which 
turns  on  a  hinge  f ,  and  which  may  be  fastened  by  the  thumb- 
screw n.  To  the  under  surface  of  the  cover  a  piece  of  india- 
rubber,  m,  is  cemented,  which,  when  the  cover  is  closed,  presses 
against  the  top  of  the  glass  tube  and  keeps  it  in  place.  The 
graduated  tube  having  been  introduced  and  adjusted,  mercury  is 
poured  into  the  cylinder  until  it  covers  the  bottom  to  the  depth  of 
several  centimetres,  and  the  rest  of  the  cylinder  is  then  filled  with 
water.  The  cover  is  now  closed  and  fastened,  and  the  whole 
apparatus  violently  shaken  in  order  to  facilitate  the  solution  of 


404  CHEMICAL  PHYSICS. 

the  gas.  The  lid  is  next  opened,  and  by  turning  the  tube  the 
cap  is  unscrewed,  and  the  mouth  of  the  tube  opened  under  the 
mercury,  which  rises  to  take  the  place  of  the  gas  which  has  been 
absorbed.  By  turning  the  tube  in  the  reverse  direction  the 
mouth  is  now  closed,  and,  the  cover  having  been  shut  down  and 
fastened,  the  apparatus  is  again  shaken  ;  and  this  process  is 
repeated  until  no  further  absorption  of  gas  is  perceptible.  When 
the  absorption  is  completed,  the  volume  of  gas  remaining  in  the 
tube  is  carefully  observed.  This  volume  corrected  for  tempera- 
ture we  will  call  F'0.  The  pressure  H1,  to  which  the  gas  is 
exposed,  can  now  be  calculated  from  the  height  of  the  barometer, 
the  difference  of  level  of  the  mercury  in  the  tube  and  in  the  cyl- 
inder, and,  lastly,  the  heights  of  the  columns  of  water  in  the  two 
vessels.  These  quantities  having  been  carefully  observed,  we 
commence  the  calculation  by  finding  from  Table  XIX.  the  equiv- 
alents of  the  two  water  columns  in  centimetres  of  mercury. 
Eepresenting  these  values  by  h1  and  h",  the  difference  of  level 
of  the  mercury  by  A,  and  the  height  of  the  barometer  by  H,  we 
have  for  the  value  of  the  pressure  H1  =  H  —  h  -f-  Qi'  —  h"). 
A.  thermometer  placed  within  the  cylinder  gives  the  temperature 
of  the  water,  and  hence  the  temperature  at  which  the  coefficient 
is  determined.  We  have  now  determined  all  the  data  required 
for  calculating  the  coefficient. 

VQ  =  volume  of  gas  before  absorption,  at  0°  and  pressure  H  c.  m. 
F0  ^-  =  u  "  "  "  "  "  76  c.  m. 

F0'        =       "  "       after  «  "  "  S!  c.  m. 

F0'  H>  =       "  "  "  "  "  "  76  c.  m. 

76 

TT  J-f1 

VQ  —   —  VQ  —  =  reduced  volume  of  gas  absorbed  under  the  pressure  If. 

By  [132], 

V  ff 

-  °   -  —  F0'  =  reduced  volume  of  gas  absorbed  under  the  pressure  76 

c.  m.  by  Fc7~m.3  of  liquid. 


In  making  determinations  of  the  coefficient  of  absorption  by 
this  method,  it  is  necessary  to  correct  the  measured  tensions  of 


THE  THREE   STATES   OP   MATTER.  405 

gas  both  for  temperature  and  for  the  tension  of  vapor,  and  to 
reduce  the  measured  columns  of  mercury  to  0°  C.  The  method 
by  which  these  reductions  are  made  will  be  explained  in  the  next 
chapter,  and  examples  illustrating  the  whole  subject  will  be 
found  in  Bunsen's  work  on  Gasornetry,  already  noticed,  to  which 
we  must  refer  for  further  details. 

(209.)  Partial  Pressure.  —  If  we  conceive  of  three  masses  of 
different  gases,  occupying  the  volumes  vi9  v2,  v3,  and  each  exerting 
a  pressure  measured  by  jff,  and  then  suppose  that  the  diaphragms 
which  separate  them  are  removed,  the  three  gases  will  mix.  per- 
fectly together,  as  is  well  known,  until  each  is  equally  diffused 
through  the  whole  space  F,  which  equals  v{  +  ua  -\-  v3  ,  and 
the  mixture  will  then  exert  the  same  pressure  as  that  exerted  by 
each  gas  separately,  or  H.  It  is  evident,  then,  from  Mariotte's 
law  (163),  that  each  gas  of  this  mixture  must  exert,  by  itself, 
a  pressure  which  bears  the  same  relation  to  the  whole  pressure 
that  the  original  volume  of  this  gas  bears  to  its  expanded  vol- 
umes. It  is  easy,  then,  to  calculate  that  the  pressures  exerted  by 
the  three  gases  of  the  mixture  are  respectively 


i-^1-,       H,         ^-,       H,   and  —  ,-*       -  H.    [136.1 

Vl+Vz  +    »8  «>l  +  *>2    +  "3  V,  +  l>2  -f  V3  J 

These  pressures  are  called  partial  pressures,  in  distinction  from 
the  total  pressure,  which  is  equal  to  the  sum  of  these  partial 
pressures,  or 

H  +     _,  Va,—  H+       ,  v*  ,   -  H.    [137.] 


If  now  a  volume  of  liquid,  which  we  will  represent  by  FJ  ,  is 
exposed  to  this  gaseous  mixture,  it  will  absorb  of  each  gas  a 
quantity  which  is  exactly  proportional  to  the  partial  pressure 
which  this  gas  exerts.  In.  other  words,  the  law  of  (206)  holds 
true  in  regard  to  each  gas,  and  the  solubility  of  one  gas  is  not 
influenced  by  the  presence  of  the  rest. 

Representing  then  by  cl9  c2  ,  and  c3  the  coefficients  of  absorp- 
tion of  the  three  gases  respectively,  and  assuming  that  the  total 
volume  of  the  mixture  is  so  large,  or  so  frequently  renewed,  that 
the  partial  pressures  are  not  altered  by  the  absorption,  we  can 
easily  calculate  that  the  absolute  volume  of  each  gas  in  cubic 
centimetres  absorbed  by  the  given  volume,  FI,  of  the  liquid, 
will  be,  respectively, 


406  CHEMICAL  PHYSICS. 

r    V  Vl  —  r    V  V*  — 

c»  FI  t,1+(7j|_|_v,  •  76'  C*  Kl  Vl+vt  +  v,'  76' 

and  _  ^_          ^  [138.] 

-76- 


t 

The  sum  of  these  quantities,  or  the  total  volume  of  mixed  gases 
absorbed,  is 

" 


Dividing  each  of  the  quantities  [138]  by  this  sum,  we  shall  ob- 
tain the  composition  of  the  absorbed  gas,  or,  in  other  words,  the 
amount  of  each  gas  composing  one  volume  of  the  mixed  gases 
dissolved.  These  are 


Vl  +  CZ  VZ  -f- 


If  there  were  but  two  gases,  the  values  v3  ,  w3  ,  and  c3  must  evi- 
dently be  cancelled  in  all  the  above  equations  ;  and,  on  the  other 
hand,  the  formulae  may  readily  be  extended  to  any  number  of 
gases  by  introducing  additional  terms.  » 

The  solution  of  atmospheric  air  in  water  furnishes  a  good  illus- 
tration of  the  principles  of  this  section.  Let  it  be  required  to 
determine  the  absolute  volumes  of  oxygen  and  nitrogen  absorbed 
by  F!  volume  of  water  at  the  temperature  of  15°.  The  air  is  a 
mixture  of  oxygen  and  nitrogen,  exerting  on  the  water  a  variable 
pressure,  which  we  will  assume,  at  the  time  of  the  determination, 
is  76  c.  m.  ;  and  its  mean  composition  in  volume  is 

Oxygen,       .         .--    -.  -^      .         .         .     0.2096 
Nitrogen,     <.&  |     .  «•£$  W  •(•      .          0.7904         [141.] 

1.0000 

The  coefficients  of  absorption  at  15°  are,  by  Table  VII.  ,  of 
oxygen  0.02989,  and  of  nitrogen  0.01478.  The  absolute  vol- 
umes of  the  two  gases  absorbed  by  Fj  volume  of  water  are,  then, 
of  oxygen, 

0.02989  F,  X  0.2096  =  0.006265  Fl  ; 
and  of  nitrogen, 

0.01478  F!  X  0.7904  =  0.011682  Ft. 

The  composition  of  the  dissolved  gas  in  one  volume  is,  then, 
by  [140], 


THE   THREE   STATES   OF   MATTER.  401 

Oxygen,       ......     0.3491 

Nitrogen,         .....  0.6509          [142.] 

1.0000 

We  can  also,  evidently,  reverse  the  above  calculation,  and  from 
the  composition  of  the  dissolved  gas  calculate  the  composition  of 
the  gaseous  mixture  to  which  the  liquid  has  been  exposed.  Rep- 
resenting the  denominators  of  the  fractions  [140]  by  A,  we 
easily  obtain  the  values, 

Vi==^A,         vt  =  ^A,       and         v3  =  ^A,       [143.] 

<?l  C2  C3 

which  are  the  volumes  of  the  respective  gases  composing  V  c.  m.8 
of  the  mixture.  Dividing  each  of  these  quantities  by  the  sum 
of  the  whole,  we  obtain  the  composition  of  one  volume  of  the 
mixture.* 

ui  «a 

Wl    = 


Hi  -I-  —    -f    —  H    -L  ^t  -L  HI 

Cl  C-2  C3  ft  *fc  «l 

and  «s  [144.] 

3         L1  4.  "A  _i_  !f! 

Cl  C2  C3 

From  the  composition  of  the  mixture  of  oxygen  and  nitrogen 
dissolved  in  rain-water,  we  can  easily  calculate,  by  these  formulae, 
the  composition  of  the  air.  Evidently,  when  there  are  only  two 
gases,  the  third  value,  tv3  ,  and  the  last  term  of  the  denominators 
of  wl  and  w2  are  cancelled. 

All  the  above  formulae  are  based  upon  the  supposition,  that  the 
volume  of  the  gaseous  mixture  is  so  large  that  the  partial  pres- 
sures of  its  constituent  gases  are  not  essentially  changed  by 
the  absorption.  This  is  true  in  regard  to  the  atmosphere,  as 
already  stated  ;  but  when  we  experiment  upon  a  very  limited 
volume  of  a  gaseous  mixture,  as  in  the  absorption-tube  of  appa- 
ratus (Fig.  335),  such  an  assumption  is  far  from  being  correct, 
and  we  must  then  pay  regard  to  the  change  of  composition  and 
of  pressure  in  the  gaseous  mixture.  In  order  to  make  the  case 
as  simple  as  possible,  let  us  take  a  mixture  of  only  two  gases,  and 
consider  the  changes  it  will  undergo  by  absorption  if  in  contact 

*  It  will  afford  the  student  assistance,  in  following  out  the  course  of  reasoning  in  this 
section,  to  remember  that,  in  the  notation  adopted,  v\  -f  vt  +  vs  =  FcTm?  of  the  mixed 
gases  before  solution,  u\  -f-  «z  -f  U3  =  1  c.m.3  of  the  mixed  gases  in  solution,  and 
wi  -f  M?S  -f  it's  =  1  <^m.3  of  the  mixed  gases  before  solution. 


408  CHEMICAL   PHYSICS. 

with  a  volume  of  liquid,  adopting  for  the  purpose  the  following 
notation,  and  assuming  that  the  volumes  of  all  the  gases  entering 
into  the  calculation  are  measured  at  0°. 

F       =  volume  of  mixed  gases  before  absorption,  measured  at  pres- 

sure H. 

V      =  volume  of  mixed  gases  after  absorption,  measured  at  pressure  H'. 
Fx       =  volume  of  absorbing  liquid. 
*>i>  ^a  =  volumes  respectively  of  the  two  gases  in  the  unit  volume  of  the 

mixed  gases  before  absorption,  so  that  vl  -|-  vz  =  1  cTnT.3. 
MU  u^  =  volumes  respectively  of  the  two  gases  in  the  unit  volume  of  the 
mixed  gases  remaining  unabsorbed,  so  that  u^  -\-  u.2  =  1  c.  m.3. 
clt  c2  =  coefficients  of  absorption  of  the  two  gases  respectively. 

It  is  now  evident  that  the  volume  V  of  the  mixed  gases  con- 
tains Vi  Fc7nT.3  of  the  first  gas  measured  under  the  pressure  H. 
Under  a  pressure  of  76  c.  m.  this  same  volume  would  measure, 

by  [98]  ,  vl  V  =  -  c.m.3  By  the  absorption,  this  quantity  of  gas 
is  divided  into  two  parts  :  first,  a  quantity,  x,,  ,  which  remains  un- 
dissolved  ;  second,  a  quantity,  x2  ,  which  dissolves  in  the  liquid  ; 

rr 

so  that  we  have  xl  +  ^  =  v\  V  ^  .     The  value  of  xz  may  now 

readily  be  determined  by  the  laws  of  absorption,  since  we  know 
the  coefficient  of  absorption  c1?  and  can  easily  calculate  the  par- 
tial pressure  which  the  gas  exerts  on  the  liquid  after  the  absorp- 
tion. The  quantity  x^  of  gas,  if  measured  at  the  pressure  JEZ"', 

7fi 

would  equal  x±  -^  ;  and  since  the  whole  volume  of  mixed  gases 
remaining  unabsorbed,  or  F',  exerts  a  pressure  H'  ,  the  partial 
pressure  of  the  portion  of  this  volume  xv  ~yt  must  be  -—  76. 
At  the  pressure  of  76  c.  m.,  we  know  that  FJ  c7m.s  of  liquid  ab- 
sorbs Ci  FI  c.m.3  of  the  gas.  Hence,  under  the  pressure  of 
Y,  76  c.  m.,  the  same  volume  of  liquid  will  absorb  Cl  '  Xl  cTm:3 

of  gas.  This  is  the  value  of  xz  ;  and  substituting  it  above, 
we  obtain 


or  .1= 


By  a  similar  course  of  reasoning,  we  should  obtain,  for  the  vol- 
ume of  the  second  gas  remaining  unabsorbed,  the  value 


THE   THREE   STATES   OP  MATTER.  409 

_V,  VH 

76 

If,  for  the  sake  of  abbreviation,  we  put  AY  =  vi  V  H  and  A2  = 
v.z  V  H,  also  B^  =  ( 1  -f  ^-W)   and  &==  f  1  +  — xr/1)  >  we  sna^ 

have   a;i  =  _,  '     and  ?/i  =  ?r«-^-  and  from  these  we  can  easily 
76  ^i  76  i?2 

calculate  the  composition  of  the  unit  of  volume  of  the  unab- 
sorbed  gas,  which  we  shall  find  to  be 


and  .   ,,  [146.] 


(210.)  Analysis  of  a  Mixture  of  two  Gases  by  the  Absorption 
Meter.  —  It  is  evident,  from  the  computations  of  the  last  section, 
that  we  can  even  determine  the  unknown  composition  of  a  gase- 
ous mixture  from  the  change  of  volume  it  undergoes  by  absorp- 
tion in  a  known  volume  of  liquid.  This  leads  us  to  a  method  of 
gas  analysis,  which,  under  certain  circumstances,  admits  of  great 
accuracy,  and  enables  us  to  solve  problems  which  cannot  be  re- 
solved by  the  ordinary  methods  of  chemical  investigation.  Let 
us  suppose,  then,  that  we  have  given  the  following  data,  all 
reduced  to  0°  C.,  as  before. 

V     =.  the  original  volume  of  the  gaseous  mixture,  measured  under  the 

pressure  H. 
V    =  the  volume  of  the  mixture  after  absorption,  measured  under  the 

pressure  H1. 

Vi      =  the  volume  of  absorbing  liquid. 

Cj,  c3  =  the  coefficients  of  absorption  of  the   two   gases   composing   the 
mixture. 

It  is  required,  from  these  data,  to  determine  the  relative  pro- 
portions of  the  two  gases  in  the  original  mixture.  Let  us  repre- 
sent, then,  by  the  unknown  quantities  x  and  y  the  volumes  of 
the  two  constituent  gases  measured  under  the  pressure  1  ;  by  #' 
and  #',  the  volumes  of  these  gases  after  absorption  measured 
under  the  same  pressure. 

It  follows  directly  from  the  law  of  Mariotte,  that  the  volume 

x',  if  measured  under  the  pressure  H',  would  be  -^  ;  and  since 
35 


410  CHEMICAL  PHYSICS, 

this  volume,  after  the  absorption,  is  expanded  through  the  whole 
volume  F',  it  is  evident  that  the  partial  pressure  it  then  exerts  on 

X1 

the  absorbing  liquid  is  as  much  less  than  H'  as  -yr,  is  less  than 

x1 
V,  and  must  therefore  be  equal  to  ^.      The  volume   of  the 

first  gas  which  would  be  absorbed  by  Ft  HTm?  of  liquid  iinder 
the  pressure  of  76  c.  m.  and  at  0°  (when  measured  at  0°  and 
76  c.  m.)  is  clVi.  As  after  the  absorption  the  pressure  exerted 
by  the  first  gas  on  the  liquid  is  -^  >  the  volume  which  is  actu- 

ally  absorbed  (measured   at   0°   and   76   c.  m.)  is,  by   [132], 

c  V  x' 

~*firv*~'     ^  ^s  vo^ume  *s  measured  under  the  pressure  1  c.  m., 

it  will  become  c^  Fj  -™.     Hence  we  have 

d  Vl  —  =  the  volume  of  first  gas  absorbed  measured  under  the  pressure  1. 

Hence,  also, 


or  *'=-  [147.1 


From  this  value  of  x'  we  can  easily  calculate  the  partial  pres- 
sure which  the  unabsorbed  portion  of  the  first  gas  exerts  011  the 
absorbing  liquid.  If  measured  under  the  pressure  H',  the  vol- 
ume [147]  becomes 


and  the  partial  pressure  it  exerts  is  as  much  less  than  H'  as 
this  volume  is  less  than  V.  A  simple  proportion  gives  us,  for 
the  value  of  this  pressure,  T//  '  —  ^  .  In  like  manner,  by  a 

V    -f-  c{   K! 

precisely  similar  course  of  reasoning,  we  shall  obtain,  for  the  par- 
tial pressure  exerted  by  the  unabsorbed  portion  of  the  second  gas, 
-yrv_  —  y.  Now,  since  it  is  these  two  pressures  which  make  up 
the  observed  total  pressure  .H"',  we  have 


Returning  now  to  the  condition  of  the  gas  before  absorption, 
it  is  evident  that  the  volume  of  the  first  gas,  which  measures  x 


THE  THREE  STATES   OF  MATTER.  411 

under  the  pressure  1,  would  measure  -^  under  the  pressure  H. 
Hence  the  partial  pressure  which  this  gas  exerted  before  the 
absorption  was  as  much  less  than  H  as  the  volume  -^  is  less  than 
F,  and  must  therefore  have  been  -y .  In  like  manner,  we  find 
that  the  partial  pressure  exerted  by  the  second  gas  was  -y- ;  so 
that  we  also  have 

tf=£+f.  [149.] 

It  will  be  noticed  that  equation  [149]  may  be  derived  directly 
from  [148],  by  making  c{  and  c2  equal  to  zero,  which  would  be 
the  case  where  there  was  no  absorption.  These  equations  may 
also  be  written  in  the  forms 


'/      I       /  17  / 


i       x    '    y 

''    V~H  "     V~H' 
If  for  the  sake  of  abbreviation  we  put 

W=  VH, 

A  =  (  V  +  Cl  Fj)  #', 

B  =  (V'  +  c,  Fl)  ^T', 

the  equations  become 

^  ==  ~~T  ~\r  jii        an(i        1  ==  rif  "f~  w-- 

By  combining  the  two,  we  easily  obtain 

x_          W—B     A^m 

or,  calculating  the  percentage  composition, 

x  W—B     A  v  A—W    B 


.-.,., 


As  an  example  of  this  method  of  analysis,  we  will  take  the 
data  obtained  in  an  experiment  with  the  absorption-meter  on  a 
mixture  of  carbonic  acid  gas  and  hydrogen,  as  given  by  Bunsen. 


412 


CHEMICAL   PHYSICS. 


Volume.            Pressure.             Temp. 

c.m.                     o 

Gas  before  absorption, 

180.94         53.68         15.4 

Gas  after  absorption, 

122.01         68.09           5.5 

Volume  of  water, 

;VV-.-^V       .         356.7 

u              « 

356.1 

356.4 

Hence  we  obtain 

H  =        53.6800, 

F  =    171.290, 

H1  =        68.0900, 

F'=    119.610, 

c{   =          1.4199, 

Vl  =    356.400, 

c2   =          0.0193, 

W  =  9194.847, 

A  =42591.3250, 

B    =8612.568. 

Volume  at  GO. 

171.29 
119.61 


And  by  substituting  these  values  in  [151] ,  we  get  the  following 
percentage  composition :  — 


Hydrogen,     . 
Carbonic  Acid,  . 


By  Absorption. 

.  0.9206 
0.0794 
1.0000 


By  Eudiometer. 

0.9246 
0.0754 


1.0000 


And  it  will  be  noticed  how  closely  these  results  agree  with  those 
obtained  by  chemical  analysis  with  the  eudiometer,  which  are 
given  at  the  side  for  comparison. 

By  substituting  the  numerical  values  in  [146] ,  it  will  be  found 
that  the  percentage  composition  of  the  gas  remaining  unab- 
sorbed  is, 


Hydrogen, 
Carbonic  acid, 


0.9829 
0.0171 
1.0000 


The  same  method  of  gas  analysis  may  be  extended  to  mixtures 
of  three  or  more  gases  ;  but  when  the  number  of  gases  exceeds 
two,  the  formulae  become  quite  complex,  and  the  results  less 
accurate. 

Gases  on  Gases. 

(211.)  Effusion. — It  has  been  found  by  Professor  Graham,* 
that  the  velocities  with  which  different  gases,  when  under  pressure, 
flow  through  a  minute  aperture  in  a  metallic  plate,  are  closely 


*  Philosophical  Transactions,  1846,  p.  574. 


THE  THREE  STATES  OF  MATTER.  413 

related  to  their  specific  gravities ;  and  to  these  phenomena  has  been 
given  the  name  of  effusion.  In  his  experiments,  the  gases  were 
made  to  flow  through  an  aperture  in  a  very  thin  metallic  plate, 
not  more  than  one  three-hundredth  of  an  inch  in  diameter,  into 
a  bell-glass  on  the  plate  of  an  air-pump,  which  was  kept  vacuous 
by  continued  exhaustion.  The  velocity  of  the  flow  was  found 
to  increase  with  the  degree  of  exhaustion,  (that  is,  with  the  pres- 
sure,) until  it  amounted  to  about  one  third  of  an  atmosphere  ; 
but  higher  degrees  of  exhaustion  were  not  found  to  produce  a 
corresponding  increase  of  velocity ;  and  when  the  vacuum  was 
nearly  perfect,  a  difference  of  one  inch  in  the  height  of  the  mer- 
cury column  of  the  pump-gauge  scarcely  affected  the  rate  at 
which  the  gas  entered  the  bell.  Through  an  aperture  in  a  thin 
plate,  such  as  described,  sixty  cubic  inches  of  dry  air  were  found 
to  enter  the  vacuous  or  nearly  vacuous  receiver  in  one  thousand 
seconds,  and  in  successive  experiments  the  time  of  passage  did 
not  vary  more  than  one  or  two  seconds.  The  times  required  for 
equal  volumes  of  different  gases  to  flow  through  this  aperture 
were  found  to  be  very  nearly  proportional  to  the  square  roots  of 
their  specific  gravities.  Thus,  the  time  required  for  sixty  cubic 
inches  of  oxygen  to  flow  through  the  aperture  was  observed  to  be 
1,051.9, 1,051.9,  1,050.6,  1,050.2  seconds,  in  four  different  ex- 
periments. The  mean  of  these  numbers  is  1,051.1,  which  bears 
almost  precisely  the  same  relation  to  1,000,  the  time  occupied 
by  the  same  volume  of  air,  as  1.0515,  the  square  root  of  the  spe- 
cific gravity  of  oxygen,  bears  to  1,  the  square  root  of  the  specific 
gravity  of  air. 

Since  the  times  occupied  by  equal  volumes  of  different  gases 
in  flowing  through  a  fine  aperture  are  proportional  to  the  square 
roots  of  their  specific  gravities,  it  follows  that  the  velocity  of 
the  flow  must  be  inversely  proportional  to  the  square  roots  of  the 
specific  gravities,  or  directly  proportional  to  the  reciprocals  of 
these  quantities.  Representing,  then,  by  T  and  T',  the  number 
of  seconds  required  by  equal  volumes  of  two  gases  in  flowing 
into  a  vacuum,  we  have 

T  :  T'  =  t/(sp.  Gr.)  :  */(*•  <*••)'•  [1520 

Also  representing  by  t)  and  t)'  the  velocity  of  the  flow,  (that  is, 
the  volume  of  gas  entering  the  vacuum  in  one  second,)  we  have, 
since  T :  T'  =  \)'  :  fo, 

85* 


414 


CHEMICAL   PHYSICS. 


:  1)'  = 


.  Gr.y 


=.  [153.1 

M  L        J 


If  we  assume  that  the  velocity  of  air  is  unity,  it  follows  from 
[153] ,  that  the  velocity  of  any  other  gas,  as  compared  with  air, 
must  be  the  reciprocal  of  the  square  root  of  its  specific  gravity, 
if  the  principle  just  enunciated  is  correct.  That  this  is  really 
the  case  is  shown  by  the  following  table,  taken  from  •  Miller's 
Chemical  Physics.  Jn  the  last  column  of  this  table,  headed 
"  Rate  of  Effusion,"  the  velocities  of  different  gases  compared 
with  air  as  unity  are  given,  as  deduced  from  the  experiments  of 
Professor  Graham ;  and  it  will  be  noticed  that  they  very  closely 
coincide  with  the  reciprocals  of  the  square  roots  of  the  specific 
gravities  given  in  the  fourth  column.  The  coincidence  is  almost 
absolute  in  the  case  of  those  gases  whose  specific  gravities  vary 
but  slightly  from  that  of  the  air.  With  very  light  or  very  heavy 
gases  the  deviation  is  much  greater  ;  but  this  can  be  shown 
to  be  occasioned  by  the  tubularity  of  the  aperture,  arising  from 
the  unavoidable  thickness  of  the  metallic  plate. 

Effusion  of  Gases. 


1 

Velocity  of 

Rate  of 

Gas. 

Sp.  Gr. 

<v/Sp.  Gr. 

•v/Sp.  Gr. 

Diffusion. 

Effusion. 

Hydrogen, 

0.06926 

0.2632 

3.7994 

3.8300 

3.6130 

Marsh  Gas, 

0.55900 

0.7476 

.3375 

1.3440 

1.3220 

Steam,   .... 

0.62350 

0.7896 

.2664 

Carbonic  Oxide, 

0.96780 

0.9837 

.0165 

1.0149 

1.0123 

Nitrogen, 

0.97130 

0.9856 

.0147 

1.0143 

1.0164 

Olefiant  Gas,      . 

0.97800 

0.9889 

.0112 

1.0191 

1.0128 

Binoxide  of  Nitrogen,    . 

.03900 

1.0196 

0.9808 

Oxygen,      . 

.10560 

1.0515 

0.9510 

0.9487 

0.9500 

Sulphuretted  Hydrogen, 

.19120 

1.0914 

0.9162 

0.9500 

Protoxide  of  Nitrogen, 

.52700 

1.2357 

0.8092 

0.8200 

0.8340 

Carbonic  Acid, 

.52901 

1.2365 

0.8087 

0.8120 

0.8210 

Sulphurous  Acid, 

2.24700 

1.4991 

0.6671 

0.6800 

(212.)  Application  of  the  Law  of  Effusion.  —  The  law  of  effu- 
sion, which  was  verified  experimentally  by  Graham  in  the  case 
of  gases,  is  true  generally  of  the  flow  of  all  fluids,  under  pres- 
sure, through  an  aperture  in  a  very  thin  plate.  It  has  been 
applied  by  Bunsen*  in  a  process  of  determining  the  specific 


Bunsen's  Gasometry,  p.  121. 


THE   THREE   STATES   OF   MATTER. 


415 


gravity  of  gases,  which  is  exceedingly  simple,  and  of  especial  value 
where  only  a  small  quantity  of  the  gas  can  be  obtained.  The 
process  consists  in  observing  carefully  the  times  required  by  the 
same  volumes  of  any  given  gas  and  air  in  flowing  through  a  fine 
aperture  in  a  thin  plate  when  under  the  same  pressure.  Repre- 
senting these  times  by  T  and  T',  we  have,  from  [152]  , 

(Sp.Gr.*)  :  (Sp.Gr.y  =  T2  :  T'2; 

since  air  is  the  standard  of  specific  gravity,  (Sp.  Gr.y  =  1  ;  and 
we  easily  obtain 

(^.Gr.)=.  [154.] 


The  apparatus  used  by  Bunsen  in  these  deter- 
minations is  represented  in  Fig.  336.  It  consists 
of  a  glass  bell,  a  a,  holding  about  seventy  cubic  cen- 
timetres, and  closed  above  by  the  glass  stopcock  c. 
To  the  neck  of  the  bell,  at  e?,  there  is  adjusted,  by 
grinding  with  emery,  the  short  tube  e,  and  to  the 
top  of  this  tube  there  is  cemented  a  small  piece  of 
platinum-foil,  in  which  a  very  fine  hole  has  been 
perforated.  In  order  that  the  plate  should  be  as 
thin,  and  the  hole  as  fine,  as  possible,  the  platinum- 
foil  is  first  pierced  with  a  very  fine  cambric  needle, 
and  then  hammered  out  with  a  polished  hammer 
on  a  polished  anvil,  until  the  hole  is  no  longer 
perceptible  to  the  naked  eye,  and  can  only  be  seen 
when  the  plate  is  held  between  the  eye  and  a 
bright  light.  The  edges  of  the  plate  are  next  cut 
away,  so  as  to  leave  a  small  round  disk,  having 
the  hole  in  its  centre.  The  diameter  of  this  disk 
should  be  a  little  less  than  that  of  the  top  of  the 
tube,  to  which  it  can  easily  be  cemented  with  a 
blowpipe.  Within  the  bell,  when  in  use,  is  placed 
the  glass  float,  b  b,  made  of  thin  glass,  in  order 
that  it  may  be  as  light  as  possible.  At  the  top  of 
this  float  there  is  a  small  knob  of  black  glass,  /3, 
surmounted  by  a  thread  of  white  glass  ;  and  at 
the  points  /3,  and  j32  two  black  glass  threads  are 
melted  around  'the  stem  of  the  float,  which  serve 
as  index-marks. 


416  CHEMICAL  PHYSICS. 

In  using  this  instrument,  the  glass  bell,  filled  with  the  gas 
whose  specific  gravity  is  to  be  determined,  is  depressed  in  a 
mercury  trough  until  the  index-mark  ^,  on  its  side,  is  on  a 
level  with  the  surface  of  the  mercury.  This  index-mark  is  so 
placed  that,  when  the  bell,  previously  filled  with  gas,  is  de- 
pressed as  just  described,  the  float  will  be  below  the  surface  of 
the  mercury  in  the  trough.  The  bell  is  now  fastened  securely  in 
this  position,  and  the  telescope  of  a  cathetometer  so  adjusted  that 
its  axis  shall  graze  the  surface  of  the  mercury  in  the  trough,  one 
side  of  which,  being  made  of  glass,  enables  the  observer,  looking 
through  the  telescope,  to  see  the  bell  distinctly.  The  apparatus 
being  thus  arranged,  the  observer  opens  the  stopcock  c,  and  then 
closely  watches  the  tube  through  the  telescope.  After  some  time, 
the  white  thread  of  the  float  rises  into  the  field,  and  forewarns 
the  observer  that  the  black  knob  will  soon  appear.  The  moment 
this  is  seen,  he  commences  his  observation,  and  notes  the  exact 
number  of  seconds  before  the  index-mark  ft*  appears  in  the  field 
of  his  telescope,  of  the  approach  of  which  he  is  forewarned  by 
previously  seeing  the  mark  |3,. 

From  the  construction  of  the  instrument,  it  is  evident  that  the 
time  thus  observed  is  the  time  required  for  the  flow,  through  the 
fine  hole  in  the  plate  e,  of  a  given  volume  of  gas,  under  a  given, 
although  varying,  pressure  ;  and,  moreover,  that  this  volume  and 
pressure  must  be  the  same  in  all  experiments  with  the  same 
instrument.  Hence  the  squares  of  the  times,  in  the  case  of  dif- 
ferent gases,  must  be  proportional  to  their  specific  gravities  ;  so 
that,  having  once  for  all  determined  the  time  required  by  air,  we 
can  easily,  by  means  of  [154] ,  calculate  the  specific  gravity  of 
any  given  gas  from  a  single  observation  of  the  time  of  its  effusion. 
It  is  always  best,  however,  to  repeat  the  observation  several  times, 
and  take  the  mean  of  the  results. 

The  following  table  will  give  an  idea  of  the  degree  of  accuracy 
which  can  be  attained  by  this  process.  Column  I.  gives  the 
mean  specific  gravities  calculated  from  several  effusion  experi- 
ments on  each  gas,  and  Column  II.  the  specific  gravities  of  the 
same  gases  calculated  from  their  chemical  equivalents. 

The  agreement  between  the  calculated  and  the  observed  re- 
sults is  very  satisfactory ;  so  that,  although  this  process  is  not 
comparable  in  accuracy  with  the  direct  method  of  determining 
specific  gravities  hereafter  to  be  described,  it  is  nevertheless,  on 


THE   THREE   STATES   OF   MATTER. 


417 


account  of  its  great  simplicity,  recommended  by  Bunsen  for 
in  the  arts  when  only  approximate  results  are  required. 


use 


Gases. 

I. 

n. 

Differences. 

Air,         
Carbonic  Acid,    .... 
1  vol.  C  O  +  1  vol.  C  O2,      . 

1.000 
1.535 
1.203 
1  118 

1.000 
1.520 
1.244 
1  106 

+0.015 
—0.041 
+0  Ol9 

1  vol.  0  +  2  vol.  H,       . 
Hydrogen,  

0.414 
0.079 

0.415 
0.069 

—0.001 
+0.010 

(213.)  Transpiration.  —  The  flow  of  gases  under  pressure 
through  long  capillary  tubes  presents  a  class  of  phenomena  en- 
tirely different  from  those  of  effusion,  and  has  been  termed  by 
Graham  Transpiration.  With  a  tube  of  a  given  diameter,  Gra- 
ham found  that  the  shorter  the  tube,  the  more  nearly  the  rate  of 
transpiration  approximates  to  the  rate  of  effusion  ;  while,  on  the 
other  hand,  as  the  tube  was  lengthened,  he  observed  a  deviation 
from  the  effusion  rate,  which  was  very  rapid  with  the  first  increase 
of  length,  but  became  gradually  less,  and  reached  a  maximum 
when  a  certain  length  had  been  attained.  It  was  therefore  neces- 
sary, in  order  to  eliminate  the  effects  of  effusion  from  experiments 
on  transpiration,  to  employ  a  considerable  length  of  tube  ;  and 
when  this  precaution  was  observed,  uniform  results  were  obtained. 
The  length  required  in  any  case  was  found  to  vary  with  the 
diameter  of  the  tube,  and  also,  to  a  certain  extent,  with  the  na- 
ture of  the  gas.  The  most  important  conclusions  which  have 
been  deduced  from  the  researches  hitherto  made  on  transpira- 
tion are  as  follows :  — 

First.  The  velocity  of  transpiration  of  a  given  gas  through  a 
given  capillary  tube  increases  directly  with  the  pressure.  For 
example,  a  litre  of  air  of  double  the  density  of  the  atmosphere, 
and  therefore  exerting  twice  the  pressure,  will  pass  through  a 
capillary  tube  into  a  vacuum  in  one  half  of  the  time  required  by 
the  same  volume  of  air  of  its  natural  density.  This  is  a  very 
remarkable  fact,  and  it  shows  that  the  process  of  transpiration 
differs  very  greatly  in  character  from  effusion. 

Secondly.  With  tubes  of  the  same,  diameter,  the  velocity  of 
transpiration  of  a  given  gas  is  inversely  as  the  length  of  the 
tube.  For  example,  if  one  hundred  cubic  centimetres  of  air  will 
pass  through  a  capillary  tube  two  metres  long  in  ten  minutes,  a 


418 


CHEMICAL  PHYSICS. 


tube  of  the  same  diameter  four  metres  long  would  allow  the 
passage  of  only  fifty  cubic  centimetres  in  the  same  time. 

Thirdly.  The  velocity  of  transpiration  of  equal  volumes,  cceteris 
paribus,  diminishes  as  the  temperature  rises. 

Fourthly.  The  velocity  of  transpiration  was  found  to  be  the 
same,  whether  the  tubes  were  of  copper  or  of  glass,  or  even  when 
a  porous  mass  of  stucco  was  used. 

Fifthly.  The  velocity  of  transpiration  varies  with  different 
gases,  and  appears  to  be  a  constitutional  property  of  an  aeriform 
substance,  like  the  density  or  the  specific  heat,  not  depending,  as 
is  the  case  with  effusion,  on  the  specific  gravity. 

Of  all  gases  which  have  been  tried,  oxygen  has  the  slowest  rate  of 
transpiration ;  and  hence  it  may  be  conveniently  taken  as  a  stand- 
ard of  comparison  for  the  other  gases.  In  the  first  column  of  the 
following  table,  the  times  of  transpiration  of  equal  volumes  of  the 
best-known  gases  are  given,  as  compared  with  that  of  oxygen  ; 
and  in  the  second  column,  the  corresponding  velocities  of  trans- 
piration, which  are  the  reciprocals  of  the  first  quantities.  In  each 
case  the  gas  was  transpired  through  the  same  tube,  and  under 
precisely  the  same  circumstances  of  temperature  and  pressure. 

Transpirdbility  of  Gases. 


Oases. 

Times  for 
Transpiration  of 
equal  Volumes. 

Velocity  of 
Transpiration. 

1.0000 

1.0000 

Air,        .  •    &Bii:  v      ..;••  *ir-!tu-.j/«r 

0.9030 

.1074 

0.8768 

.1410 

-<  Binoxide  of  Nitrogen, 
(  Carbonic  Oxide,    ..... 

f  Protoxide  of  Nitrogen,      /  .  :  :  W  <  ,  I  q  > 

0.8764 
0.8737 
0.7493 
0  73fi^ 

.1410 
.1440 

.3340 
qaiA 

n  73  no 

"ftOrt 

ORfifid. 

"SOftO 

0  fj.^nn 

ROQA 

Sulphuretted  Hydrogen,    .      '^  v  ...'<  rr.uifl 
Light  Carburetted  Hydrogen,         .       »  .  ,.  • 

0.6195 
0.5510 
o  T!  is 

.6140 
.8150 
9350 

Cyanogen,     .        .        .        .        .        , 

0.5060 
0  5051 

.9760 
.9800 

0  4370 

2.2880 

Some  very  simple  relations  in  the  transpirability  of  different 
gases  may  be  discovered  by  examining  the  above  table.     Thus, 


THE   THREE   STATES  OF   MATTER. 


419 


equal  weights  of  oxygen,  nitrogen,  air,  and  carbonic  oxide  are 
transpired  in  equal  times  ;  the  velocities  of  nitrogen,  binoxide  of 
nitrogen,  and  carbonic  oxide,  are  equal ;  the  velocity  of  hydro- 
gen is  double  that  of  the  three  just  mentioned ;  the  velocities 
of  chlorine  and  of  oxygen  are  as  three  to  two.  Many  other 
similar  cases  might  be  cited  ;  but  these  relations  seem  to  be 
merely  accidental,  and  have  not  as  yet  been  connected  with  the 
other  properties  of  the  substances.  "  Professor  Graham  consid- 
ers, at  present,  that  it  is  most  probable  that  the  rate  of  transpi- 
ration is  the  resultant  of  a  kind  of  elasticity  depending  upon  the 
absolute  quantity  of  heat,  latent  as  well  as  sensible,  which  differ- 
ent gases  contain  under  the  same  volume,  and  therefore  that  it 
will  be  found  to  be  connected  more  immediately  with  the  specific 
heat  than  with  any  other  property  of  gases."* 

Lastly.  The  velocity  of  transpiration  of  a  mixture  of  equal 
volumes  of  two  gases  is  not  always  the  mean  of  the  velocities  of 
the  two  gases  when  separate.  For  example,  the  velocity  of  a 
mixture  of  equal  volumes  of  oxygen  and  hydrogen  is  1.110,  in- 
stead of  1.383,  which  would  be  the  mean  velocity  of  the  two 
gases. 

(214.)  Diffusion.  — The  tendency  of  gases  to  mix  with  each 
other  is  so  strong,  that  it  will  overcome  the 
greatest  differences  of  specific  gravity;  and, 
contrary  to  what  a  superficial  consideration 
would  lead  us  to  expect,  the  more  widely 
two  gases  differ  in  specific  gravity,  the  more 
rapid  is  the  process  of  intermixture.  This 
process  is  termed  diffusion,  and  may  be 
illustrated  by  means  of  the  apparatus  rep- 
resented in  Fig.  337,  consisting  simply  of 
two  bottles,  A  and  H,  connected  together 
by  a  long  glass  tube.  If  we  fill  the  upper 
bottle  with  hydrogen  and  the  lower  bottle 
with  chlorine,  we  shall  find,  in  the  course 
of  a  few  hours,  that  the  two  gases  have  been 
perfectly  mixed  together,  although  the  ra- 
tio of  their  specific  gravities  is  three  times 
as  great  as  the  ratio  of  the  specific  grav- 
ity of  mercury  to  that  of  water.  The  Fig.337. 

*  Miller's  Elements  of  Chemistry,  Part  I.  p.  86. 


420 


CHEMICAL  PHYSICS. 


chlorine,  although  thirty-six  times  heavier  than  hydrogen,  will 
be  found  to  have  made  its  way  into  the  upper  bottle,  as  may 
be  seen  by  its  green  color,  while  the  hydrogen  will  have  passed 
downwards  into  the  lower  one ;  and  when  once  mixed,  the  two 
gases  will  never  separate,  however  long  they  may  remain  at 
rest. 

What  has  been  shown  to  be  true  of  hydrogen  and  chlorine  is 
equally  true  of  all  other  gases  and  vapors,  which  do  not  act  chem- 
ically on  each  other.  The  only  differences  observed  with  differ- 
ent substances  are  the  times  required  to  effect  a  perfect  mixture ; 
but  when  once  made,  this  mixture,  in  all  cases,  continues  uni- 
form and  permanent.  This  subject  may  be  still  further  illus- 
trated by  filling  two  tall,  narrow  glass  bells  of  equal  diameters 
over  a  pneumatic  trough,  the  one  half  full  of  hydrogen,  and  the 
other  half  full  of  air,  so  that  the  water  shall  stand  at  the  same 
level  in  both.  If,  now,  we  pass  up  a  few  drops  of  ether  into  each 
jar,  the  same  quantity  of  ether  will  evaporate  in  both,  and  cause, 
ultimately,  the  same  depression  of  the  water-level ;  but  the  ex- 
pansion of  the  hydrogen  will  take  place  much  the  soonest, 
because,  being  fourteen  and  a  half  times  lighter  than  air,  the 
heavy  ether  vapor  will  mix  with  it  more  rapidly. 

The  law  which  governs  the  rapidity  of  gaseous  diffusion  was 
discovered  by  Graham,  by  means  of  the  apparatus  represented 

in  Fig.  338,  and  called  by  him 
a  diffusion,  tube.  It  consists  of 
a  glass  tube  thirty  or  forty  cen- 
timetres in  length,  one  end  of 
which  is  closed  by  a  plug  of 
plaster  of  Paris,  which  should 
be  as  thin  as  is  consistent  with 
strength.  This  tube  serves  as  a 
bell  for  holding  the  gas  under 
experiment  over  the  water  con- 
tained in  a  tall  glass  jar;  and 
it  may  be  easily  filled  without 
wetting  the  porous  diaphragm, 
by  means  of  a  glass  siphon-tube, 
as  represented  in  the  figure.  While  filling  the  tube,  the  top  is 
closed  by  means  of  a  glass  plate,  which  has  previously  been  care- 
fully ground  with  emery  on  to  the  upper  edge  above  the  plaster 


Fig.  338. 


THE   THREE   STATES   OP   MATTER.  421 

diaphragm.  The  tube,  when  filled  with  gas,  should  be  so  sup- 
ported that  the  water  may  be  on  the  same  level  within  and 
without  the  tube.  If  then  the  glass  covering-plate  is  removed, 
the  gas  will  be  found  to  mix  with  the  air  through  the  thin 
plaster  diaphragm,  the  gas  passing  out  into  the  atmosphere,  and 
the  air,  on  the  other  hand,  entering  the  tube.  The  relative  ve- 
locity of  the  two  currents  will  be  found  to  depend  on  the  relative 
density  of  the  gas  as  compared  with  air.  If  the  gas  is  lighter 
than  air,  the  outer  current  will  be  the  most  rapid,  and  the  water 
column  will  rise  in  the  tube  to  supply  the  vacuum  thus  formed  ; 
while,  on  the  other  hand,  if  the  gas  is  heavier  than  air,  the 
inward  current  will  be  the  most  rapid,  and  the  water  column  will 
be  depressed.  If  the  gas  is  hydrogen,  which  is  fourteen  and  a 
half  times  lighter  than  air,  the  outer  current  will  be  so  much  the 
most  rapid,  that  in  the  course  of  a  few  minutes  the  water  column, 
under  favorable  circumstances,  will  rise  to  over  one  half  the 
height  of  the  tube.  In  all  cases,  after  a  certain  time,  varying 
with  the  specific  gravity  of  the  gas  and  the  thickness  of  the  dia- 
phragm, the  gas  in  the  tube  will  have  been  replaced  entirely  by 
a  volume  of  air,  which  will  be  greater  or  less  than  the  original 
volume  of  gas,  according  as  the  velocity  of  diffusion  of  the  air  is 
greater  or  less  than  that  of  the  gas.  By  comparing,  then,  the 
original  volume  of  the  gas  with  the  volume  of  the  air  remaining 
in  the  tube  at  the  close  of  the  experiment,  we  shall  have  at  once 
the  relative  velocity  of  diffusion  of  the  two  gases.  In  making 
experiments  for  the  purpose  of  determining  the  velocity  of  diffu- 
sion, it  is  evidently  essential  to  maintain  the  water  at  the  same 
level,  both  within  and  without  the  tube,  since  otherwise  the  effects 
of  diffusion  would  be  modified  by  the  hydrostatic  pressure. 

As  an  illustration  of  the  method  of  determining  the  velocity  of 
diffusion,  let  us  suppose  that  the  tube  was  filled  with  100  ^Tm!3  of 
hydrogen  gas,  and  that  at  the  end  of  the  experiment,  during 
which  the  surface  of  the  water  within  and  without  the  tube  was 
carefully  maintained  at  the  same  level,  there  remained  in  the 
tube  26.1  c^m.3  of  air.  It  is  evident,  then,  that  during  the  time 
100  (Tin.3  of  hydrogen  escaped  from  the  tube  through  the  porous 
diaphragm,  26.1  ^n.3  of  air  entered.  Hence,  the  velocity  of 
the  diffusion  of  hydrogen  is  3.83  times  (equal  to  100  -f-  26.1) 
more  rapid  than  that  of  air.  In  the  same  way,  all  the  numbers 
in  the  column  of  the  following  table  headed  "  Velocity  of  Difiri- 
36 


422 


CHEMICAL   PHYSICS. 


sion  "  were  found.  They  in  each  case  indicate  the  velocity  of 
iiffusion  as  compared  with  air  ;  and  it  will  be  noticed  that  they 
•\ery  nearly  coincide  with  the  velocity  of  effusion. 

Diffusion  of  Gases. 


1 

Velocity  of 

Rate  of 

Gas. 

Sp.  Gr. 

VSp.  Gr. 

-ySpTGrT 

Diffusion. 

Effusion. 

Hydrogen, 

0.06926 

0.2632 

3.7994 

3.8300 

3.6130 

Marsh  Gas, 

0.55900 

0.7476 

.3375 

1.3440 

1.3220 

0  62350 

0.7896 

.2664 

Carbonic  Oxide, 

0.96780 

0.9837 

.0165 

1.0149 

1.0123 

Nitrogen, 

0.97130 

0.9856 

.0147 

1.0143 

1.0164 

Olefiant  Gas,      . 

0.97800 

0.9889 

1.0112 

1.0191 

1.0128 

Binoxide  of  Nitrogen,    . 

1.03900 

.0196 

0.9808 

Oxygen, 

1.10560 

.0515 

0.9510 

0.9487 

0.9500 

Sulphuretted  Hydrogen, 

1.19120 

.0914 

0.9162 

0.9500 

Protoxide  of  Nitrogen, 

1.52700 

.2357 

0.8092 

0.8200 

0.8340 

Carbonic  Acid, 

1.52901 

.2365 

0.8087 

0.8120 

0.8210 

Sulphurous  Acid, 

2.24700 

.4991 

0.6671 

0.6800 

It  appears,  then,  that  the  velocity  of  diffusion  of  a  gas  is  the 
same  as  the  velocity  of  effusion,  and  hence,  like  the  latter,  is 
inversely  proportional  to  the  square  root  of  its  specific  gravity. 
In  other  words,  gases  expand  into  each  other  according  to  the  same 
law  which  they  obey  in  expanding  freely  into  a  vacuum.  This  fact 
has  been  thought  to  support  the  theory  of  Dr.  Dalton,  that  gases 
are  inelastic  towards  each  other,  one  gas  offering  no  more  per- 
manent resistance  to  the  expansion  of  another  gas  than  would 
be  presented  by  a  vacuum.  Thus,  in  the  experiment  with  the 
two  bottles  (Fig.  337),  Dalton  supposed  that  the  hydrogen  ex- 
panded through  the  space  occupied  by  the  chlorine  just  as  if  the 
space  were  entirely  empty ;  and  he  explained  why  the  expan- 
sion was  not  instantaneous  by  the  supposition  that  the  particles 
of  chlorine  offer  the  same  sort  of  resistance  to  the  motion  of 
hydrogen  as  is  offered  by  the  stones  on  the  bed  of  a  brook  to 
the  running  of  water.  There  can  be  no  question  that  the  ulti- 
mate result  of  diffusion  is  always  in  conformity  with  Dalton's 
theory  ;  and  although  we  may  hesitate  to  assume  that  gases  are 
in  all  respects  vacua  to  each  other,  yet  this  theory  is  at  pres- 
ent the  most  convenient  mode  of  expressing  the  phenomena  of 
diffusion. 

If,  instead  of  using  a  homogeneous  gas,  we  introduce  a  mixture 


THE   THREE   STATES   OP   MATTER. 


423 


of  two  or  more  gases  into  the  diffusion-tube,  each  gas  will  be 
found  to  preserve  its  own  rate  of  diffusion.  Thus,  if  the  mixture 
consists  of  hydrogen  and  carbonic  acid,  the  hydrogen  will  escape 
from  the  tube  much  more  rapidly  than  the  carbonic  acid,  and  a 
partial  mechanical  separation  of  the  two  gases  may  thus  be 
effected. 

It  is  not  essential  that  the  top  of  the  diffusion-tube  should  be 
closed  with  plaster  of  Paris.  Any  dry  porous  substance,  such  as 
charcoal,  wood,  unglazed  earthen-ware,  or  dried  bladder,  may  be 
substituted  for  the  stucco ;  but  few  of  them  answer  so  well.*  The 
diaphragm  is  best  prepared  by  casting  a  very  thin  disk  of  plaster 
on  a  glass  plate,  and,  after  it  is  thoroughly  dried,  cutting  it  to 
the  required  size  with  a  sharp  knife,  and  cementing  the  edges 
with  sealing-wax  to  the  inner  rim  of  the  tube. 

The  ascent  of  a  column  of  water  in  the  tube,  when  hydrogen 
is  diffused,  forms  a  very  striking  experiment.  This  may  read- 
ily be  shown  to  an  audience  with  a  Gra- 
ham's diffusion-tube  about  a  metre  in  height 
and  four  or  five  centimetres  in  diameter, 
resting  the  bottom  in  a  pan  of  colored 
water.  The  tube  can  easily  be  filled  with 
hydrogen  by  displacement,  and  the  gas  re- 
tained in  its  place  by  covering  the  top  with 
a  ground-glass  plate,  which  should  be  re- 
moved at  the  time  of  the  experiment.  The 
same  principle  can  be  even  more  strikingly 
illustrated  by  means  of  an  apparatus  de- 
scribed by  Professor  Silliman,  Jr.,  and 
represented  in  Fig.  389.  It  is  made  by 
cementing  the  open  mouth  of  a  porous 
earthen-ware  cell  (such  as  are  used  in  a 
galvanic  battery)  to  the  mouth  of  a  glass 
funnel,  and  then  lengthening  the  spout  by 
attaching  to  it  a  long  glass  tube  of  the 
same  diameter.  When  in  use,  the  appa- 
ratus is  supported  as  represented  in  the  rig.  339. 
figure,  so  that  the  end  of  the  tube  shall  dip 
into  a  glass  filled  with  colored  water.  If,  now,  we  hold  over  the 


*  Later  experiments  have  shown  that  the  best  material  is  compressed  plumbago. 
A  film  of  collodion  on  paper  also  gives  excellent  results. 


424  CHEMICAL  PHYSICS. 

porous  cell  a  bell-glass  filled  with  hydrogen,  there  will  he  an 
immediate  rush  of  air  from  the  tube  through  the  water,  because 
the  hydrogen  diffuses  into  the  cell  nearly  four  times  as  rapidly  as 
the  air  passes  out ;  but  upon  removing  the  bell  of  hydrogen  the 
conditions  are  reversed,  —  the  hydrogen,  which  the  cell  now  con- 
tains, diffuses  into  the  atmosphere,  and  the  colored  water  imme- 
diately rises  into  the  tube. 

As  all  gases  are  expanded  by  heat,  and  therefore  rendered 
specifically  lighter,  it  follows  that  the  absolute  velocity  of  diffu- 
sion of  any  gas  (measured  by  volume)  increases  with  an  increase 
of  temperature ;  but  since  an  elevation  of  temperature  does  not 
increase  the  rate  of  diffusion  as  rapidly  as  it  does  the  volume  of 
a  gas,  it  is  also  true  that  the  same  weight  of  any  gas  will  be  dif- 
fused more  rapidly  at  a  low  than  at  a  high  temperature.  It  will 
hereafter  be  shown  that  heat  expands  all  gases  equally,  so  that 
their  relative  densities  are  preserved,  however  great  the  change  of 
temperature.  Hence  the  relative  velocities  of  diffusion,  which 
are  given  in  the  table  on  p.  422,  are  the  same  for  all  tempera- 
tures, provided,  of  course,  the  gases  be  heated  equally. 

This  diffusive  power  of  gases  is  of  the  greatest  importance  in 
preserving  the  purity  of  our  atmosphere.  As  it  is,  the  noxious 
carbonic  acid  from  our  lungs,  the  deleterious  fumes  from  our 
factories,  and  the  miasmatic  emanations  from  the  marshes,  are 
rapidly  spread  through  the  atmosphere  and  rendered  harmless  by 
extreme  dilution,  until  they  can  be  removed  by  the  beneficent 
means  appointed  for  this  end.  Moreover,  the  more  they  differ 
in  density  from  the  air,  and  the  more,  therefore,  they  would  tend 
to  separate  from  it,  the  stronger  is  the  force  by  which  they  are 
compelled  to  mix.  Were  it  not  for  this  provision  in  the  consti- 
tution of  gases,  these  injurious  substances  would  remain  where 
they  were  formed,  and  might  produce  the  most  disastrous  conse- 
quences. If  we  consider,  also,  the  oxygen  and  nitrogen  of  which 
the  atmosphere  essentially  consists,  they  differ  in  density  in  the 
proportions  of  1105  to  971 ;  but  yet  they  are  so  perfectly  mixed, 
that  the  most  accurate  chemical  analysis  has  been  able  to  detect 
no  difference  between  the  air  brought  from  the  top  of  Mont 
Blanc  and  that  from  the  deepest  mine  of  Cornwall.  Were  the 
force  of  diffusion  much  less  than  it  is,  these  two  gases  would  sep- 
arate partially,  and  the  atmosphere  be  unfitted  for  many  of  its 
important  functions. 


THE  THREE   STATES   OP  MATTER.  425 

Bunsen,*  who  has  more  recently  studied  the  phenomena  of 
gaseous  diffusion,  has  obtained  results  which  do  not  coincide  with 
the  simple  law  discovered  by  Graham,  and  enunciated  above. 
The  discrepancy  between  the  results  of  these  two  eminent  observ- 
ers probably  arises  from  the  great  thickness  of  the  plaster  dia- 
phragm in  the  apparatus  used  by  Bunsen  ;  in  consequence  of 
which  the  phenomena  of  diffusion  were  modified  by  those  of 
transpiration.  Compare  (213).  The  same  must  be  true,  to  a 
certain  extent,  of  the  diffusion-tube  of  Graham  ;  and  the  experi- 
mental results  will  probably  approach  the  law  in  proportion  as 
the  thickness  of  the  diaphragm  is  diminished,  actually  coinciding 
with  it  only  when  the  diaphragm  is  entirely  removed  and  the 
gases  expand  freely  into  each  other. 

(215.)  Passage  of  Gases  through  Membranes.  —  If  a  bladder 
half  filled  with  air,  and  having  its  mouth  tied,  is  passed  up  into 
a  bell-glass  of  carbonic  acid  standing  over  water,  it  will  become, 
in  the  course  of  twenty-four  hours,  fully  distended,  and  may  even 
burst,  owing  to  the  passage  of  carbonic  acid  gas  through  the 
pores  of  the  bladder.  This  is  not,  however,  a  simple  phenom- 
enon of  diffusion,  since  the  carbonic  acid  enters  the  bladder  as  a 
liquid  dissolved  in  the  water  permeating  the  substance  of  the 
membrane,  and  evaporates  from  the  inner  surface  of  the  bladder 
like  any  other  volatile  liquid.  A  similar  transfer  takes  place 
with  a  jar  of  gas  standing  on  the  shelf  of  a  pneumatic  trough. 
The  water  dissolves,  to  a  slight  extent,  the  gases  of  the  atmos- 
phere, which  subsequently  evaporate  into  the  jar,  while  at  the 
same  time  the  gas  in  the  jar  slowly  passes  out,  in  a  similar  way, 
into  the  atmosphere.  For  this  reason,  gases  confined  over  water 
cannot  be  kept  pure  for  any  length  of  time.  Analogous  phenom- 
ena have  been  observed  with  membranes  of  india-rubber,  a  sub- 
stance which  has  the  power  of  absorbing  many  gases  to  a  remark- 
able extent,  especially  those  which  are  more  easily  liquefied.  It 
is  probable  that  the  gases  are  always  liquefied  in  the  india-rubber, 
and  pass  through  it  in  this  condition,  evaporating  subsequently 
on  the  interior  surface  of  the  membrane.  A  similar  absorption 
must  take  place,  to  a  greater  or  less  extent,  with  any  diaphragm ; 
even  with  plaster  of  Paris  it  is  appreciable,  and  slightly  modifies 
the  experimental  results  of  diffusion. 


Bunsen's  Gasometry,  p.  198. 

36* 


CHAPTER    1Y. 

HEAT. 

(215  bis.)  Theory  of  Heat.  —  All  natural  substances  are,  in 
certain  conditions,  capable  of  producing  on  our  bodies  peculiar 
sensations,  which  we  designate  by  the  words  heat  and  cold.  These 
sensations  may  result  from  direct  contact  with  the  substance,  as 
when  we  touch  a  heated  stove ;  or  they  may  be  produced  at  a 
great  distance  from  it,  as  when  we  are  warmed  by  the  radiation 
from  burning  fuel  or  by  the  rays  of  the  sun. 

To  the  cause  of  these  effects  we  give  the  name  of  heat;  but 
according  to  the  most  generally  received  theory  heat  is  not  a  dis- 
tinct agent,  but  merely  an  affection  of  matter,  and  the  phenomena 
of  heat  are  thought  to  be  caused  by  the  motion  of  the  molecules 
of  which  all  matter  must  be  supposed  to  consist.  Not  only  are 
the  molecules  of  all  bodies  assumed  to  be  in  rapid  motion  among 
themselves,  but  the  motion  of  the  molecules  is  supposed  to  obey 
the  same  laws  as  the  motion  of  large  masses  of  matter.  More- 
over, the  molecules  are  assumed  to  be  perfectly  elastic,  so  that 
motion  may  be  transferred  from  one  molecule  to  another,  as  from 
one  billiard-ball  to  another.  Again,  when  a  moving  body  is 
suddenly  arrested,  it  is  supposed  that  the  motion  of  the  body  is 
distributed  among  the  surrounding  atoms  ;  and  on  the  other  hand 
it  is  inferred  that  moving  atoms  may  transfer  their  motion  to 
masses  of  matter,  and  the  atoms  of  steam,  it  is  thought,  thus 
impart  motion  to  the  piston  of  the  steam-engine. 

According,  then,  to  this  view,  a  heated  body  differs  from  a  cold 
body  only  in  the  fact  that  its  molecules  are  moving  more  rapidly 
within  its  mass.  The  moving  power  of  the  individual  molecules 
represents  what  we  call  the  temperature,  and  this  is  the  measure 
of  the  force  with  which  they  would  impress  the  nerves  of  feeling. 
The  higher  the  temperature,  the  greater  is  the  moving  power,  and 
for  the  same  temperature  the  molecules  of  all  bodies  are  assumed 
to  have  the  same  moving  power.  The  zero  of  absolute  cold  would 
be  the  temperature  at  which  the  molecules  are  at  rest,  but  such  a 


HEAT.  427 

point  has  never  been  reached,  even  if  it  is  a  possible  condition  of 
matter.  While  the  moving  power  of  the  individual  molecules 
represents  the  temperature  of  a  body,  the  total  moving  power  of 
all  the  molecules  represents  the  amount  of  heat  which  it  contains. 
Quantity  of  heat,  then,  is  simply  quantity  of  motion ;  and,  as  we 
shall  hereafter  see,  the  quantity  of  motion  corresponding  to  each 
heat  unit  is  capable  of  exact  measurement. 

The  transfer  of  heat  from  one  body  to  another  is  simply  the 
transfer  of  motion  from  the  molecules  of  the  one  body  to  the 
molecules  of  the  other.  This  transfer  may  result  either  from 
the  direct  collision  of  the  molecules,  as  when  one  ivory  ball 
strikes  another,  or  it  may  be  effected  through  the  intervention 
of  the  ether  atoms  by  which  the  molecules  of  all  bodies  are 
assumed  to  be  surrounded,  the  line  of  ether  atoms  along  which 
the  motion  may  be  supposed  to  be  transmitted,  as  along  a  line  of 
ivory  balls,  representing  the  rays  of  heat.  Such  is  thought  to  be 
the  difference  between  the  conduction  and  the  radiation  of  heat ; 
although  it  may  be  that  motion  cannot  pass  even  from  molecule 
to  molecule  except  through  the  contiguous  atoms  of  ether. 

The  difference  between  the  three  states  of  aggregation  of  mat- 
ter, according  to  the  theory  we  are  considering,  depends  upon 
the  relative  freedom  of  motion  of  the  material  molecules.  In  a 
gas  this  motion  is  wholly  unrestrained,  and  the  tension  of  the  gas 
is  supposed  to  be  due  to  the  collision  of  the  atoms  against  the 
walls  of  the  containing  vessel.  If  the  walls  are  unyielding,  the 
atoms  recoil  without  losing  any  moving  power,  as  any  elastic  ball 
would  rebound  from  a  fixed  obstacle  (109).  When,  however, 
the  walls  yield  to  the  atomic  blows,  then  the  atoms  lose  a  portion 
of  their  moving  power,  and  a  lower  temperature  is  the  result.  In 
both  solids  and  liquids  the  motion  is  supposed  to  be  more  or  less 
circumscribed  by  the  molecular  forces,  just  as  the  force  of  gravita- 
tion restrains  the  motion  of  the  planets  and  keeps  each  in  a  fixed 
orbit.  In  the  solid  the  motion  is  more  circumscribed  than  in 
the  liquid,  but  in  regard  to  the  mode  of  motion  in  eitiier  case 
there  is  no  uniformity  of  opinion.  As  the  temperature  of  a  body 
increases,  the  moving  power  of  its  molecules  may  become  great 
enough  to  overcome  the  molecular  forces,  and  then  the  molecules, 
freed  from  the  restraint  which  bound  them,  will  move  among  each 
other  with  more  or  less  freedom,  the  solid  changing  first  into  a 
liquid  and  afterwards  into  a  gas.  Since,  however,  the  molecular 


428  CHEMICAL  PHYSICS. 

forces  can  only  be  overcome  by  the  expenditure  of  moving  power, 
such  a  change  must  be  attended  with  the  absorption  of  heat ;  and 
when,  on  the  other  hand,  in  consequence  of  the  reduction  of  tem- 
perature, and  consequently  of  the  moving  power  of  the  molecules, 
these  are  brought  again  under  the  influence  of  the  molecular 
forces,  an  equivalent  amount  of  heat  is  set  free ;  just  as  a  stone, 
which,  thrown  from  the  earth,  falls  again  to  the  ground,  acquires, 
while  falling,  the  same  momentum  which  it  lost  while  rising. 

It  will  hereafter  appear  that  the  change  of  state  of  aggregation 
is  always  accompanied  by  such  an  absorption  or  evolution  of  heat 
as  the  theory  predicts.  Moreover,  it  will  also  appear  that  the 
arrest  of  motion  is  always  attended  with  the  evolution  of  heat, 
and  that  the  amount  of  heat  evolved  is  the  exact  equivalent  of  the 
moving  power  which  has  disappeared ;  as  must  necessarily  be  the 
case,  if,  as  the  theory  assumes,  the  moving  power  is  transferred  to 
the  neighboring  molecules  at  the  moment  of  collision,  and  their 
motion  manifests  itself  in  the  phenomena  of  heat. 

According  to  the  modern  theory  of  chemistry,  equal  volumes 
of  all  substances  in  the  state  of  gas  contain  precisely  the  same 
number  of  molecules,  or,  what  amounts  to  the  same  thing,  the 
molecules  of  all  bodies  in  the  state  of  gas  occupy  exactly  equal 
volumes.  Hence  it  follows  that  the  weights  of  the  molecules  of 
any  two  substances  must  be  to  each  other  in  the  same  proportion 
as  the  specific  gravities  of  these  substances  when  in  the  state  of 
gas,  or 

m:mt  =  Sp.  Gr.  :  Sp.  Gr.' 

If,  then,  we  assume  that  the  hydrogen  molecule  shall  be  the  unit 
in  our  system  of  molecular  weights,  we  can  easily  calculate  the 
molecular  weights  of  all  other  bodies  as  compared  with  that  of 
hydrogen.  The  molecular  weights  thus  obtained  are  either  the 
same  numbers  as  those  which  express  in  chemistry  the  combining 
proportions  of  the  different  elements,  or  else  they  are  some  simple 
multiple  of  these  numbers. 

If,  now,  we  represent  by  V  and  V,  the  velocities  with  which  the 
molecules  of  any  two  substances  in  the  state  of  gas  are  moving  at 
any  given  temperature,  for  example,  0°  Centigrade,  then,  since, 
according  to  our  theory,  the  moving  power  of  any  two  such  mole- 
cules must  be  the  same  at  the  same  temperature,  we  shall  have 


HEAT.  429 

and  from  this  we  can  readily  deduce  the  proportion 


V:  V,  = 

that  is,  the  velocities  of  the  motion  of  the  molecules  of  any  two 
substances  in  the  state  of  gas  are  inversely  proportional  to  the 
square  roots  of  the  weights  of  these  molecules,  or  to  the  square 
roots  of  the  specific  gravities  of  the  gases.  The  diffusion  of  gases 
(214)  is  evidently  a  necessary  result  of  molecular  motion,  and 
the  relative  velocity  of  diffusion  must  be  the  same  as  the  relative 
velocity  of  the  molecular  motion,  and  hence  must  be  inversely 
proportional  to  the  square  roots  of  the  specific  gravities  of  the 
different  gases.  This  is  the  simple  law  already  enunciated  on 
page  422. 

According  to  the  theory  here  adopted,  the  value  \  m  F2,  which 
represents  both  the  moving  power  of  a  given  molecule  and  the 
temperature  of  the  body  of  which  the  molecule  is  a  part,  repre- 
sents also  the  quantity  of  heat  which  that  molecule  contains. 
Hence,  as  all  molecules  at  the  same  temperature  have  the  same 
moving  power,  they  must  have  also  the  same  quantity  of  heat. 
It  must,  therefore,  require  the  same  quantity  of  heat  to  raise  the 
temperature  of  a  single  molecule  of  any  substance  the  same  num- 
ber of  degrees.  And  if  this  is  true  of  single  moleculeSj  it  must  be 
true  of  equal  numbers  of  such  molecules,  or,  in  other  words,  of 
weights  of  different  substances  which  bear  to  each  other  the  same 
relation  as  the  weights  of  their  respective  molecules.  If,  then, 
the  weights  of  two  substances,  M  and  M',  are  to  each  other  in  the 
same  proportion  as  the  weights  of  the  molecules  of  these  sub- 
stances, m  and  m',  then  the  same  quantity  of  heat  will  raise  the 
temperature  of  the  unequal  weights  M  and  M1  the  same  number 
of  degrees.  Or,  if  we  represent  by  S  and  S'  the  quantities  of  heat 
which  are  required  to  raise  the  temperature  of  one  kilogramme 
of  each  of  two  substances  one  degree,  and  by  m  and  m'  the  relative 

weights  of  their  respective  molecules,  then  -  and  -;  will  represent 

the  relative  number  of  molecules  of  each  substance  in  one  kilo- 
gramme ;  and  since  the  quantity  of  heat  required  must  be  pro- 
portional to  the  number  of  molecules,  we  shall  have 

—  :—.  =  $  :#,  or  m  &  =  m'  #. 
m    m' 

The  quantities  S  and  &  are  called  the  specific  heats  of  the 


430  CHEMICAL  PHYSICS. 

substances ;  and  hence,  according  to  the  theory,  the  products 
obtained  by  multiplying  together  the  specific  heats  of  different 
substances  and  their  molecular  weights  (or  combining  propor- 
tions) should  be  equal.  In  the  case  of  the  chemical  elements 
this  is  very  nearly  true ;  and  it  would  probably  be  found  precisely 
true  for  all  substances,  could  the  comparison  always  be  made 
under  precisely  the  same  conditions,  and  when  the  substances 
were  in  the  state  of  gas. 

Again,  since  equal  volumes  of  different  gases  always  contain 
the  same  number  of  molecules,  our  theory  would  lead  us  to 
anticipate  that  equal  quantities  of  heat  would  raise  the  tem- 
perature of  the  same  volume  of  any  gas  to  an  equal  extent.  This 
also  we  find  to  be  true  of  the  permanent  gases  ;  and  although  in 
the  case  of  the  vapors  the  deviations  from  this  law  are  apparently 
very  great,  yet  such  deviations  are  probably  owing,  in  part  at 
least,  to  the  imperfect  aeriform  condition  of  these  bodies,  and  also 
perhaps  to  the  mechanical  condition  of  the  molecules  themselves, 
of  which  our  th&ory  has  as  yet  taken  no  account. 

Of  the  various  theories  which  have  been  proposed  to  explain 
the  phenomena  of  heat,  the  one  here  stated  is  the  simplest  and 
the  most  intelligible,  predicting,  as  well  as  could  be  expected,  the 
general  order  of  the  phenomena.  It  must  be  admitted,  however, 
that,  as  here  stated,  this  theory  is  open  to  grave  objections,  and, 
like  all  theories  in  science,  it  should  be  regarded  as  a  provisional 
expedient,  and  not  as  an  established  principle.  That  the  phe- 
nomena of  heat  have  a  purely  mechanical  cause  is  most  probable, 
but  the  mode  or  the  seat  of  the  motion  which  causes  them  is 
wholly  a  matter  of  conjecture.  We  shall  discuss  the  phenomena 
of  heat  in  this  chapter  as  far  as  is  possible  independently  of  any 
theory,  using  for  the  purpose  the  ordinary  language  of  science. 
It  must  be  remembered,  however,  that  much  of  this  language  is 
based  on  the  old  theory,  now  rapidly  passing  away,  which  re- 
garded heat  as  a  material,  although  an  imponderable  agent.  No 
difficulty,  however,  will  arise,  if  it  is  remembered  that  quan- 
tity of  heat  means  simply  quantity  of  motion,  and  that  all  terms 
relating  to  quantity  are  as  strictly  applicable  to  motion  as  they 
are  to  matter. 

(216.)  The  Action  of  Heat  on  Matter.  —  The  mechanical  effects 
of  heat  on  matter  may  be  all  explained  by  assuming  that  heat 
acts  as  a  repulsive  force  between  the  particles,  and  therefore 


HEAT.  431 

opposes  the  attractive  force  of  cohesion.  The  first  effect  of  heat 
on  matter,  in  either  of  its  three  states,  is  to  expand  it.  This 
may  be  illustrated  by  a  great  variety  of  familiar  facts  and  experi- 
ments. A  ball  of  metal,  which  exactly  fits  a  ring  when  cold, 
will  not  pass  through  it  when  heated.  The  parts  of  a  wheel  are 
.bound  together  by  the  contraction  of  the  tire,  which  is  put  on 
while  hot.  Clocks  go  slower  in  summer  than  in  winter,  because 
the.  pendulum  is  lengthened  by  the  heat. 

Different  substances  expand  unequally  for  the  same  increase  of 
temperature.  We  estimate  the  expansion  either  by  measuring  the 
increase  of  length  or  the  increase  of  bulk.  The  first  is  called  the 
linear  expansion,  the  second  the  cubic  expansion.  In  the  case  of 
solids  we  generally  measure  solely  the  linear  expansion,  while 
in  the  case  of  liquids  and  gases  we  as  generally  measure  solely 
the  cubic  expansion.  The  one,  however,  can  easily  be  calculated 
from  the  other,  since  the  cubic  expansion  is  about  three  times  as 
great  as  the  linear  expansion.  The  following  table  will  give 
an  idea  of  the  amount  of  expansion  in  different  substances, 
and  will  show  that  gases  expand  very  much  more  than  liquids, 
and  liquids  very  much  more  than  solids. 

Between  the  Freezing  and  Boiling  Points  of  Water  : 

A  rod  of  zinc  increases  in  length   7J7,  that  is,  323  c.  m.  become  324. 

«        lead         «  »           siT,       «        351     «          «        352. 

"        tin           «  «          tfa,      «        516     «          «        517. 

«         silver       «  «  li       ?Jf,       «        524     "          «        525. 

"         glass  (crown)  "         TI>JJ,       "      1142     "          «      1143. 


Alcohol    increases    in    volume      £,        that  is,      9  £~irT.8    become    10. 
Water  "  «  fa  "          23     "  «          24. 

Mercury        «  «  .fa  «          55     «  «          56. 

Air  and  the  permanent  gases  expand  ££,  that  is,  30  £~nT.8  become  41. 

Before,  however,  we  study  the  phenomena  of  expansion  in 
detail,  it  is  important  to  examine  the  various  means  by  which  the 
effects  of  expansion  are  used  as  a  measure  of  temperature. 


432  CHEMICAL  PHYSICS. 


THERMOMETERS. 

(217.)  Mercurial  Thermometer.  —  It  is  obvious  that  we  might 
use,  as  the  measure  of  temperature,  the  effect  caused  by  heat  in 
expanding  either  solids,  liquids,  or  gases,  and  thermometers 
have  been  constructed  of  each  of  these  three  forms  of  matter. 
The  expansion  of  solids,  however,  is  so  small,  and  that  of  gases 
so  difficult  to  measure,  that  their  indications  are  not  available  for 
the  ordinary  purposes  for  which  a  thermometer  is  required  ; 
while  liquids,  on  the  other  hand,  having  an  intermediate  degree 
of  expansibility,  and  their  changes  of  volume  being  readily  meas- 
ured, are  well  suited  for  thermometrical  uses.  Of  the  various 
liquids  which  might  be  employed,  mercury  is  much  the  best,  not 
only  on  account  of  the  great  range  of  temperature  between  its 
freezing  and  boiling  points,  but  also  because  its  increase  of  vol- 
ume is  very  nearly  proportional  to  the  increase  of  temperature. 

In  order  to  make  a  mercury  thermometer,  a  capillary  glass  tube 
is  first  selected,  whose  bore  is  of  the  same  calibre  throughout,  so 
that  equal  lengths  of  the  tube  will  contain  equal  volumes  of 
mercury.  The  uniformity  of  the  bore  is  readily  tested  by  intro- 
ducing into  the  tube  a  small  amount  of  mercury,  and  moving 
this  short  column  gradually  from  one  end  to  the  other,  measuring 
its  length  in  each  successive  position.  This  should,  of  course,  be 
the  same  in  every  case  ;  and  if  not,  the  tube  must  be  rejected. 

The  glass  tube  having  been  selected,  and  cut  off  to  the  required 
length,  a  bulb  is  blown  upon  the  end  by  the  usual  method  of 
glass-blowing,  using,  however,  an  india-rubber  bag  instead  of  the 
mouth,  in  order  to  avoid  moisture.  The  size  of  the  bulb  is  varied 
according  to  the  degree  of  sensibility  required  in  the  instrument ; 
but  it  is  always  made  large  in  comparison  with  the  tube,  so  that 
a  slight  expansion  of  the  enclosed  liquid  will  cause  it  to  fill  a 
considerable  length  of  the  bore.  The  form  of  the  bulb  may  be 
either  spherical  or  cylindrical.  The  first  is  most  easily  made ; 
but  the  last,  from  exposing  a  greater  surface,  is  more  readily 
affected  by  changes  of  temperature.  To  facilitate  the  introduc- 
tion of  the  mercury,  a  cup  is  sometimes  cemented  to  the  open 
end  of  the  tube,  although  a  paper  funnel  fastened  with  twine  will 
answer  every  purpose. 

The  tube  thus  prepared  is  now  easily  filled  with  mercury. 
Holding  the  tube  in  a  vertical  position,  we  pour  mercury  into  the 


HEAT. 


433 


'cup,  and  heat  the  bulb  with  a  lamp  in  order  to  expel  a  portion  of 
the  air.  On  removing  the  lamp  the  glass  soon  cools,  and  the 
mercury  is  forced  in  by  the  pressure  of 
the  atmosphere,  partially  filling  the 
bulb.  We  now  again  apply  the  lamp, 
as  represented  in  Fig.  340,  until  the 
mercury  boils ;  and  continue  the  boil- 
ing for  several  minutes,  in  order  that 
the  mercury  vapor  may  drive  out  all 
the  air  and  moisture.  The  lamp  is  then 
again  removed,  when  the  mercury, 
pressed  in  by  the  atmosphere,  descends 
and  fills  completely  the  whole  appara- 
tus. The  cup  is  then  emptied  of  the 
excess  of  mercury,  and  the  tube  just 
below  it  drawn  out  to  a  narrow  neck 
in  the  flame  of  a  blowpipe,  when  the. 
cup  may  be  broken  off. 

As  the  tube  is  now  filled  with  mer- 
cury, a  greater  or  less  portion  of  it 
must  be  removed,  depending  on  the 
range  to  be  given  to  the  instrument. 
This  is  accomplished  by  heating  the 
bulb  to  the  highest  temperature  which 

the  thermometer  is  expected  to  measure,  when  the  excess  of 
mercury  is  expelled  through  the  minute  aperture  left  in  the  neck 
of  the  tube.  The  source  of  heat  is  now  withdrawn ;  and  the 
moment  the  column  of  mercury  begins  to  descend,  the  flame  of  a 
blowpipe  directed  against  the  end  of  the  stem  hermetically  seals 
the  tube.  It  remains  then  only  to  graduate  the  instrument. 

(218.)  Graduation  of  the  Thermometer.  —  If  the  bore  is  uni- 
form, it  is  evident  that  the  rise  of  the  mercury  in  the  tube  will 
be  proportional  to  the  expansion,  so  that  we  have  in  the  ther- 
mometer an  instrument  with  which  we  can  measure  any  change 
of  volume  of  the  included  liquid ;  and  if  we  assume  that  the 
expansion  is  proportional  to  the  increase  of  temperature,  it  is 
evident  that  it  will  also  serve  as  a  very  delicate  measure  of  tem- 
perature. 

The  thermometer  is  always  graduated  by  means  of  two  fixed 
temperatures,  —  those  of  melting  ice  and  of  boiling  water.     The 
37 


io. 


434 


CHEMICAL  PHYSICS. 


bulb  and  the  portion  of  the  tube  filled  with  mercury  are  first  sur- 
rounded by  pulverized  ice,  and  the  point  to  which  the  mercury  falls 
is  marked  with  a  file  on  the  stem  (Fig. 
341) .  The  thermometer  is  next  immersed 
in  steam  escaping  freely  into  the  atmos- 
phere, and  the  point  to  which  the  mercury 
rises  marked  as  before.  The  temperature 
of  free  steam  is  always  approximatively 
the  same  as  that  of  boiling  water,  and  even 
more  constant,  not  being  affected  by  many 
circumstances,  such  as  the  nature  of  the 
vessel  and  the  presence  of  impurities,  which 
may  change  slightly  the  boiling-point. 

The  apparatus  represented  in  Figs.  342 
and  343,  invented  by  Regnault,  is  admi- 
rably adapted  for  fixing  the  boiling-point. 
Its  construction  is  sufficiently  evident 
from  the  drawing,  and  does  not,  there- 
fore, require  description.  The  steam  ris- 
ing from  the  boiling  water  circulates  in  the  direction  of  the 
arrows,  escaping  by  the  tube  D ;  and  the  object  of  the  double 
envelope  is  merely  to  prevent  the  steam  from  condensing  in  the 
inner  cylinder  A. 


Fig.  341. 


Fig.  342. 


Fig.  343. 


HEAT.  435 

Since  the  temperature  of  boiling  water  and  of  the  steam  escap- 
ing from  it  varies  with  the  atmospheric  pressure,  it  is  evidently 
essential  to  pay  regard  to  this  circumstance  in  graduating  the 
thermometer.  The  fixed  point  adopted  for  the  graduation  is  the 
temperature  at  which  water  boils  under  a  pressure  of  76  c.  m. ; 
and  if  the  barometer,  at  the  time  of  graduation,  indicates  a  dif- 
ferent pressure,  it  is  necessary  to  make  a  correction  accordingly. 
This  correction  is  easily  calculated,  since  Wollaston  determined 
that  the  boiling-point  of  water  increases  one  Centigrade  degree 
for  every  increase  of  pressure  measured  by  2.7  c.  m.  of  mercury 
column.  In  determining  the  boiling-point  with  Regnault's  ap- 
paratus, it  is  necessary  to  guard  against  any  accidental  variation 
of  pressure  in  the  interior ;  and  for  this  reason,  it  is  furnished 
with  the  manometer-tube  m. 

The  two  fixed  points  having  been  marked  on  the  tube,  the 
distance  between  them  is  next  divided  into  equal  parts,  called 
degrees.  Two  different  scales  are  used  in  this  country.  In  the 
Centigrade  scale,  which  is  the  one  most  generally  used  for  scien- 
tific purposes,  the  distance  is  divided  into  one  hundred  degrees, 
which  are  numbered  from  the  freezing-point  of  water.  These 
divisions  are  continued  of  the  same  size  both  above  100°  and 
below  0°,  the  last  being  distinguished  by  a  minus  sign  ;  thus, 
— 10°  stands  for  ten  degrees  below  zero.  In  the  Fahrenheit  scale, 
which  is  used  almost  exclusively  in  common  life,  the  distance 
is  divided  into  one  hundred  and  eighty  degrees,  which  are  num- 
bered from  a  point  thirty-two  degrees  below  the  freezing-point  of 
water ;  so  that  on  this  scale  the  freezing-point  of  water  is  at 
32°,  and  the  boiling-point  at  32°  +  180°  =  212°. 

The  Fahrenheit  scale  originated  with  an  instrument-maker  of 
Dantzic,  from  whom  it  is  named,  and  appears  to  have  been  based 
on  some  theoretical  views  in  regard  to  the  expansion  of  mercury 
which  have  long  since  been  forgotten.  It  is  supposed  that  the 
zero  was  chosen  as  marking  the  greatest  cold  which  had  been 
observed  at  Dantzic,  and  which  Fahrenheit  regarded  as  the  great- 
est possible.  We  are  now,  however,  able  to  reduce  the  tempera- 
ture of  bodies  at  least  one  hundred  and  fifty  degrees  below  the 
zero  of  Fahrenheit,  so  that  this  zero  is  far  from  marking  the 
greatest  possible  cold ;  moreover,  since  cold  is  merely  the  absence 
of  heat,  and  since  we  cannot  remove  all  the  heat  from  matter, 
we  can  never  expect  to  reach  the  absolute  •  zero.  Indeed,  the 


436  CHEMICAL   PHYSICS. 

whole  thermometric  scale  is  to  be  regarded  as  purely  arbitrary, 
and  may  be  compared  to  a  chain,  extending  indefinitely  both  up- 
wards and  downwards.  We  select  some  point  on  the  chain,  and 
begin  to  count  the  degrees  from  that.  We  fix  the  length  of  our 
degrees  by  selecting  a  second  point,  at  a  convenient  distance 
above  the  first,  and  dividing  the  intervening  length  into  an  arbi- 
trary number  of  equal  parts.  Thus  all  is  arbitrary ;  and  there 
is  no  peculiar  virtue  in  the  two  points  which  have  been  chosen, 
other  than  that  they  can  be  easily  determined  with  accuracy,  and 
include  between  them  the  range  of  temperature  with  which  we 
are  usually  most  concerned. 

The  Centigrade  scale  has  been  adopted  in  this  work,  not  only 
because  it  has  a  decimal  subdivision,  but  also  because  it  is  the  one 
most  generally  adopted  in  the  scientific  works  both  of  this  coun- 
try and  of  Europe.  At  the  end  of  the  book  there  will  be  found 
a  table  by  which  the  degrees  of  the  Centigrade  scale  may  be  con- 
verted into  those  of  the  Fahrenheit.  This  reduction  can  easily 
be  made  mentally,  since  100°  C.  =  180°  F.,  or  5°  C.  ?=  9°  P.; 
hence  F.°  =  |  C.°  +  32.  The  32  is  added,  because  the  zero  of 
Fahrenheit  is  32  Fahrenheit  degrees  below  the  zero  of  the  Centi- 
grade. An  easy  rule  for  mental  calculation  is,  Double  the  number 
of  Centigrade  degrees,  subtract  one  tenth  of  the  whole,  and  add 
thirty-two.  When  the  Centigrade  degrees  are  below  zero,  they 
are  marked  with  a  minus  sign  ;  and  this  sign  must  be  regarded 
in  using  the  above  rule. 

Besides  the  two  just  mentioned,  the  scale  of  Reaumur  is  also 
used  in  some  countries  of  Europe.  On  this  scale  the  distance 
between  the  freezing  and  boiling  points  of  water  is  divided  into 
eighty  equal  parts,  but  the  zero  is  the  same  as  on  the  Centigrade. 
It  is,  however,  never  used  in  this  country,  and  is  seldom  referred 
to  in  scientific  works. 

In  all  thermometers,  after  the  length  of  a  degree  has  been 
ascertained  by  dividing  the  distance  between  the  freezing  and 
boiling  points  of  water  into  equal  parts,  the  divisions  are  con- 
tinued of  the  same  size  beyond  the  two  fixed  points  on  either 
side.  This  method  of  graduation  occasions  a  defect  in  the 
instrument  which  must  now  be  noticed. 

(219.)  Defects  of  the  Mercury  Thermometer.  —  It  will  be 
obvious,  from  a  moment's  reflection,  that  we  do  not  observe  in  a 
thermometer-tube  the  absolute  expansion  of  mercury,  but  only 


HEAT.  437 

the  relative  expansion  as  compared  with  that  of  the  glass  bulb. 
Did  the  glass  expand  as  much  as  the  mercury,  the  column  of 
liquid  would  evidently  remain  stationary  at  all  temperatures. 
If  it  expanded  more  than  the  mercury,  an  increase  of  tempera- 
ture would  cause  the  column  to  fall.  In  fact,  the  expansion  of 
mercury  is  seven  times  greater  than  that  of  glass  ;  so  that  its 
apparent  expansion,  when  enclosed  in  a  glass  vessel,  is  about  one 
seventh  less  than  the  absolute  expansion.  The  rise  of  the  column 
of  mercury  in  a  thermometer-tube  is,  then,  a  mixed  effect  of  the 
expansion  of  the  enclosed  mercury  and  of  the  glass  envelope. 

It  is  further  evident,  that  the  whole  value  of  the  thermometer, 
as  a  measure  of  temperature,  rests  upon  the  assumption  that  the 
expansion  of  a  given  quantity  of  mercury  is  exactly  proportional 
to  the  amount  of  heat  which  enters  it.  If,  for  example,  a  given 
amount  of  heat,  entering  the  mercury  of  a  thermometer,  causes 
it  to  expand  0.001  of  its  volume,  and  consequently  to  rise  in 
the  stem  one  centimetre,  it  is  assumed  that  twice,  three  times, 
etc.  as  much  heat  will  cause  it  to  expand  0.002,  0.003,  etc.  of 
its  volume,  and  to  rise  in  the  stem  2,  3,  etc.  centimetres.  This 
assumption  is  not,  however,  absolutely  correct,  for  the  rate  of 
expansion  of  mercury  gradually  increases  with  the  tempera- 
ture; so  that,  in  the  example  just  cited,  twice  as  much  heat  will 
cause  the  mercury  to  expand  a  little  more  than  0.002,  and  three 
times  as  much  heat  a  little  more  than  0.003  of  its  original  vol- 
ume. Or,  to  take  another  illustration,  let  us  suppose  that  a 
certain  amount  of  heat,  entering  the  mercury  of  a  thermometer, 
causes  the  column  to  rise  in  the  stem  one  centimetre,  which  we 
may  suppose,  in  a  given  case,  to  be  the  length  of  one  Centigrade 
degree  ;  and  let  us  also  suppose  that  exactly  equal  amounts  of 
heat  enter  the  same  thermometer  during  successive  intervals  of 
time.  If  the  rate  of  expansion  of  mercury  were  uniform,  each 
addition  of  heat  would  cause  the  mercury  to  rise  exactly  one 
centimetre  ;  BO  thatj  if  the  stem  were  divided  into  centimetres, 
each  of  these  would  indicate  the  same  accession  of  heat.  As  it 
is,  however,  the  addition  of  the  second  quantity  of  heat  causes 
the  mercury  to  rise  a  little  more  than  a  centimetre,  the  addition 
of  the  third  quantity  causes  a  rise  still  greater  than  before,  and 
so  on.  Hence,  in  order  that  the  degrees  of  the  thermometer 
may  indicate  equal  accessions  of  heat,  they  should  slowly  in- 
crease in  length  from  zero  up*  In  the  case  of  mercury,  the  rate 
37* 


488 


CHEMICAL   PHYSICS. 


18 


Fig.  344. 


of  expansion  changes  so  slowly,  that  the  increase 
in  the  length  of  the  degrees  would  not  be  per- 
ceptible to  the  eye  within  the  usual  range  of  the 
scale  ;  but  if  the  thermometer  is  filled  with 
water,  whose  rate  of  expansion  increases  very 
rapidly,  the  effect  becomes  very  evident.  The 
water  thermometer,  represented  in  Fig.  344,  is 
so  graduated  that  each  division  on  the  scale 
corresponds  to  an  equal  amount  of  heat ;  and  it 
will  be  noticed  that  the  degrees  near  the  top  of 
the  scale  are  several  times  longer  than  those 
near  the  zero  point.  This,  then,  is  an  exagger- 
ated representation  of  the  way  in  which  a  mer- 
cury thermometer  should  be  graduated,  in  order 
to  be  perfectly  accurate ;  the  length  of  the  de- 
grees should  slowly  increase  from  the  zero  point 
up.  In  practice,  however,  as  has  been  described, 
they  are  made  of  the  same  length.  The  error, 
thus  caused,  is  not  important  between  the  two 
fixed  points ;  since,  by  dividing  the  given  dis- 
tance into  equal  parts,  we  obtain  a  mean  length 
for  the  degree,  which,  although  too  long  for  the 
degrees  near  the  freezing-point,  and  too  short 
for  the  degrees  near  the  boiling-point,  is  exact 
for  the  intermediate  degrees,  and  very  nearly 
correct  for  all.  But  above  the  boiling-point  the 
same  is  not  the  case  ;  for  while  the  degrees 
marked  on  the  scale  have  the  same  length  as 
those  below,  the  true  length  of  the  degree  is 
constantly  increasing,  until  the  difference  be- 
comes very  considerable.  Hence  a  thermometer 
above  the  boiling-point  always  indicates  too  high 
a  temperature  ;  and,  for  the  same  reason,  below 
the  freezing-point  indicates  too  low  a  temperature. 
The  value  of  the  mercury  thermometer  as  an 
accurate  instrument  would  not  be  materially  im- 
paired by  the  facts  stated  above,  since  it  would 
always  be  possible  to  estimate  the  amount  of 
deviation  in  any  case,  and  apply  the  correction 
to  the  observed  results.  Unfortunately,  however, 


HEAT. 


439 


its  indications  are  also  affected  by  the  unequal  expansion  of  the 
glass  envelope.  It  so  happens  that  the  rate  of  expansion  of  glass 
increases  quite  as  rapidly  as  that  of  mercury  ;  so  that  the  error 
induced  by  the  increased  rate  of  expansion  of  mercury  is  in  part 
corrected,  indeed  sometimes  over-corrected,  by  the  increasing 
capacity  of  the  glass  bulb.  Unfortunately,  the  rate  of  expansion 
differs  very  considerably  in  different  kinds  of  glass,  and  even  in 
the  sairie  glass  under  different  circumstances  ;  so  much  so,  that 
two  thermometers,  even  when  constructed  with  the  greatest  care, 
seldom  agree  for  temperatures  very  much  above  or  below  the 
fixed  points.  It  is  thus  evident,  that,  while  the  expansion  of 
the  glass  tends  to  correct  the  error  which  would  be  caused  by 
the  unequal  expansion  of  mercury,  it  nevertheless  renders  the 
indications  of  the  thermometer  uncertain  to  a  slight  extent,  and 
sufficiently  to  deprive  the  instrument  of  that  accuracy  which  is 
desirable  in  a  scientific  investigation. 

The  facts  stated  in  this  section  are  illustrated  by  the  following 
table,  from  the  well-known  memoir  of  Regnault  *  on  this  subject. 

Comparison  of  Different   Thermometers. 


Air  Thermometer. 
True  Tempera- 
ture. 

Thermometer 
without  Glass. 

Thermometer, 
i'lint-glaaa. 

Thermometer, 

Crown-glass. 

Coefficient  of  Expan- 
sion of  Mercury. 

0 

0 

O 

0 

o 
0 

o 
0 

0.000  1790 

50.00 

49.65 

50.20 

0.000  1815 

100.00 

100.00 

100.00 

100.00 

0.000  1830 

120.00 

120.33 

120.12 

119.95 

0.000  1850 

140.00 

140.78 

140.29 

139.85 

0.000  1861 

160.00 

161.33 

160.52 

159.74 

0.000  1871 

180.00 

182.00 

180.80 

179.63 

0.000  1881 

200.00 

202.78 

201.25 

199.70 

0.000  1891 

220.00 

223.67 

221.82 

219.80 

0.000  1901 

240.00 

244.67 

242.55 

239.90 

0.000  1911 

246.30 

246.30 

260.00 

265.78 

263.44 

260.20 

0.000  1921 

280.00 

287.00 

284.48 

280.52 

0.000  1931 

300.00 

308.34 

305.72 

301.08 

0.000  1941 

320.00 

329.79 

327.25 

321.80 

0.000  1951 

340.00 

351.34 

319.30 

343.00 

0.000  1962 

Column  1  gives  the  temperatures  of  the  air  thermometer  taken 
as  the  standard,  which  may  be  regarded  as  very  close  approxima- 


*  Me'moires  de  1'Institut,  Tom.  XXI.  pp.  239,  328. 


440  CHEMICAL  PHYSICS. 

tions  to  the  true  temperature.  Column  2  gives  the  corresponding 
temperatures  which  would  be  indicated  by  a  mercury  thermome- 
ter, graduated  in  the  usual  way,  if  the  glass  did  not  expand  at  all ; 
showing  the  error  which  would  be  caused  by  the  varying  rate  of 
expansion  of  the  mercury  alone.  Column  3  gives  the  correspond- 
ing temperatures  indicated  by  a  mercury  thermometer  made  of 
flint-glass  (cristal  de  Choissy-le-Roi) ,  showing  that  this  error  is 
in  part  corrected  by  the  unequal  expansion  of  the  glass  bulb. 
Column  4  gives  the  corresponding  temperatures  indicated  by  a 
thermometer  of  crown-glass  (verre  ordinaire  de  Paris),  showing 
that  the  indications  of  thermometers  made  with  different  varieties 
of  glass  do  not  necessarily  accord.  Finally,  column  5,  giving  the 
coefficients  of  expansion  of  mercury  at  each  temperature  (250), 
is  added,  in  order  to  show  how  rapidly  the  rate  of  expansion  in- 
creases with  the  temperature. 

It  will  be  noticed  that  the  thermometers  agree  perfectly  at  the 
two  fixed  points  to  which  they  are  graduated.  Moreover,  be- 
tween these  two  points  the  differences  are  comparatively  small, 
since  from  the  very  method  of  graduation  the  errors  are  distrib- 
uted ;  but  above  100°  the  differences  between  the  indications  of 
the  mercury  thermometers  and  the  true  temperatures  are  contin- 
ually increasing.  The  variations  from  the  true  temperature  in 
the  case  of  the  theoretical  thermometer  without  glass  are  very 
large.  In  the  flint-glass  thermometer  the  differences  are  less, 
because  the  varying  rate  of  expansion  of  mercury  is  partially 
corrected  by  that  of  the  glass.  In  the  case  of  the  crown-glass 
thermometer,  there  is  a  singular  anomaly.  This,  on  account  of 
the  remarkable  law  of  expansion  which  crown-glass  obeys,  keeps 
nearly  in  accord  with  the  air  thermometer  up  to  246°. 80,  at 
which  point  it  coincides  with  it ;  but  above  this  point,  at  which 
they  separate,  the  differences  between  the  two  rapidly  increase. 
It  will  also  be  noticed,  that  the  differences  between  the  temper- 
atures indicated  by  the  thermometers  of  flint  and  crown  glass 
are  quite  large  ;  and  it  is  evident  that  the  last  are  greatly  to  be 
preferred  in  all  scientific  investigations.  Smaller  differences 
have  been  observed  between  thermometers  made  of  varieties  of 
crown-glass  ;  but  they  are  not  of  practical  importance  when 
neither  of  the  varieties  contains  lead. 

The  facts  just  stated  will  be  rendered  clearer  by  Fig.  345, 
which  is  a  geometrical  construction  of  the  results  given  in  the 


HEAT.  441 

table  on  page  439.  The  figures  on  the  horizontal  line,  or  axis  of 
abscissas,  stand  for  the  temperatures  of  an  air  thermometer; 
those  on  the  vertical  line,  or  axis  of  ordinates,  for  the  differences 


Fig  345. 

between  the  indications  of  this  thermometer  and  of  different 
mercury  thermometers.  The  curve  On  am  shows  the  varia- 
tions from  the  true  temperature  of  the  theoretical  thermometer 
without  glass  ;  and  the  curves  Onac,  On  av,  Ona  s,  Onao, 
the  variations  of  thermometers  made  with  flint-glass  of  Choissy- 
le-Roi,  green  glass,  Swedish  glass,  and  "verre  ordinaire  de 
Paris,"  respectively.  The  anomaly  in  the  case  of  the  thermom- 
eter made  with  the  common  Paris  glass  is  beautifully  illustrated 
by  the  last  curve. 

(220.)  Change  of  the  Zero  Point.  —  Mercury  thermometers, 
even  when  constructed  with  the  greatest  care,  are  liable  to  error 
from  another  cause,  which  cannot  be  so  easily  explained  as  the 
one  just  considered.  The  zero-point  of  the  thermometer  fre- 
quently rises  on  the  scale,  the  displacement  amounting  at  times 
even  to  two  degrees.  By  this  is  meant,  that  when  the  thermom- 
eter is  surrounded  by  melting  ice,  as  in  Fig.  341,  the  mercury 
will  not  sink  to  the  original  zero,  but  only  to  a  point  possibly 
even  two  degrees  above  it.  According  to  Despretz,  this  change 
may  continue  for  an  indefinite  period  ;  and  it  is  therefore  impor- 
tant to  verify  the  position  of  the  zero-point  of  a  thermometer 
before  using  it  in  an  observation  where  great  accuracy  is  required. 
If  the  point  has  been  displaced,  the  amount  of  the  displacement 
must  be  subtracted  from  the  observed  temperatures. 

Besides  this  slow  rising  of  the  zero-point,  sudden  variations  in 
its  position  have  been  noticed  after  the  thermometer  has  been  ex- 
posed to  a  higher  temperature.  These  variations  are  sometimes 
permanent,  and  at  other  times  merely  transient,  the  zero-point 


442  CHEMICAL  PHYSICS. 

returning  to  its  original  position  after  the  instrument  has  been 
cooled  for  some  time.  All  these  facts  tend  to  show,  that  determi- 
nations of  temperature  with  a  mercury  thermometer  are  liable 
to  sources  of  error  which  cannot  always  be  guarded  against ;  and 
it  is  therefore  best,  when  great  accuracy  is  required,  to  substitute 
for  the  mercury  thermometer  the  air  thermometer  of  Regnault, 
which  will  be  described  in  a  future  section. 

(221.)  Standard  Thermometers.  —  The  causes  of  error  in  the 
mercurial  thermometer  already  noticed  arise  from  the  very  na- 
ture of  the  materials,  and  are  inseparably  connected  even  with 
such  instruments  as  have  been  constructed  with  all  the  refine- 
ments of  modern  science.  Ordinary  thermometers  are  liable  to 
errors  of  construction  of  a  far  greater  magnitude.  It  is  evident, 
from  the  theory  of  the  instrument,  that  unless  the  bore  of  the 
tube  has  the  same  calibre  throughout,  equal  increments  in  the 
volume  of  the  mercury  will  not  cause  an  equal  rise  of  the  column 
in  all  its  parts ;  and  the  indications  of  the  instrument,  graduated 
in  the  usual  way,  will  be  more  or  less  erroneous.  Now  it  is 
seldom,  and  probably  never,  the  case,  that  a  thermometer-tube 
has  an  absolutely  uniform  bore.  Hence,  in  making  a  standard 
instrument,  it  is  essential  that  the  tube  should  be  calibrated 
throughout,  and  the  size  of  the  degrees  proportioned  to  the  vary- 
ing diameter  of  the  tube.  This  is  done  by  introducing  a  short 
column  of  mercury  into  the  tube,  gradually  moving  it  from  one 
end  to  the  other  by  means  of  a  small  elastic  bag  tied  to  the  open 
mouth,  and  dividing  the  tube  into  lengths  equal  to  the  lengths  of 
the  mercury-column.  This  length  is  taken  so  short  that  the 
diameter  of  the  tube  may  be  assumed,  without  appreciable  error, 
not  to  vary  throughout  the  short  distance ;  and  when  the  tube  is 
graduated,  each  of  these  lengths  is  divided  into  the  same  number 
of  equal  parts. 

Regnault,  who  has  very  greatly  improved  the  methods  of  grad- 
uating standard  thermometers,  uses  for  the  purpose  a  dividing 
engine,  similar  to  the  one  represented  in  Fig.  346,  which  is  con- 
structed by  M.  Duboscq,  of  Paris.  It  consists  of  the  iron  frame 
A  Q,  in  which  is  mounted  the  long  steel  screw  H.  This  screw 
is  confined  at  its  two  ends  by  brass  collars,  in  which  it  turns 
freely.  On  the  top  of  the  iron  frame  moves  the  carriage  B,  to 
which  the  tube  to  be  divided  is  fastened.  Motion  is  communi- 
cated to  this  carriage  by  the  screw  /I,  which  plays  through  a 


HEAT.  443 

socket  fastened  to  the  under  side,  and  therefore  invisible  in  the 
drawing.  By  turning  the  screw,  the  carriage  &,  and  the  tube 
fastened  upon  it,  are  moved  forward  under  the  graver,  a,  which 


Fig.  346. 

is  attached  to  a  very  ingenious  apparatus  for  regulating  the 
lengths  of  the  division-lines,  making  every  fifth  and  tenth  line 
longer  than  the  rest.  This  dividing  apparatus  is  supported  on 
the  upright  piece  of  iron,  P,  which  is  itself  firmly  fastened  to  the 
frame  of  the  engine. 

The  whole  value  of  the  apparatus  depends  on  the  long  screw, 
which  is  made  with  great  care,  and  its  threads  so  adjusted  that 
one  revolution  moves  forward  the  carriage  exactly  one  milli- 
metre. Motion  is  communicated  to  the  screw  by  the  handle  M, 
acting  through  the  cogs  m  and  n  on  the  broad  wheel  opr,  and 
this,  in  its  turn,  on  a  ratchet-wheel  fastened  to  the  head  of  the 
screw,  and  moving  within  the  first.  The  wheel  o  p  r  can  revolve 
in  one  direction  independently  of  the  ratchet-wheel  and  the 
screw;  but  when  turned  in  the  opposite  direction,  a  small  detent, 
fastened  to  the  inner  surface  of  its  rim,  catches  in  the  teeth,  and 
moves  the  ratchet-wheel  and  screw  with  it.  The  rim  of  the 
wheel  opr  is  divided  on  both  sides  into  degrees,  and  by  means 
of  a  set  of  stops  its  motion  can  be  limited  to  any  number  of  rev- 


444  CHEMICAL  PHYSICS. 

olutions,  or  to  any  fraction  of  a  revolution.  Let  us  suppose  that 
the  stops  are  so  adjusted  that  the  wheel  opr  can  turn  through 
two  revolutions  and  -^V  Starting,  then,  from  the  first  stop,  and 
turning  the  handle  M  until  the  motion  is  arrested  by  the  second 
stop,  the  screw  H  will  be  revolved  twice  and  T5/0-.  Consequently, 
the  carriage  B  will  be  moved  forward  2.54  millimetres.  On 
now  turning  the  handle  M  in  the  opposite  direction,  the  wheel 
op  r  will  be  turned  back  to  its  first  position,  without  moving  the 
screw,  and  then,  on  reversing  the  motion,  the  carriage  will  be 
moved  forward  2.54  m.  m.,  as  before,  and  so  on  indefinitely.  If 
at  each  advance  we  make  a  mark  with  the  graver,  a,  it  is  evident 
that  our  tube  will  be  divided  into  lengths  of  2.54  in.  m.,  or  into 
any  other  lengths  for  which  we  may  choose  to  adjust  the  stops. 

This  engine  may  also  be  used  for  measuring  the  length  of  di- 
visions already  made ;  only  for  this  purpose  a  small  microscope, 
furnished  with  cross-wires,  should  be  attached  to  the  upright,  P, 
at  the  side  of  the  graver.  The  microscope  having  been  adjusted 
so  that  the  cross-wire  is  just  over  the  first  mark  on  the  tube,  and 
the  stops  which  limit  the  motion  of  the  wheel  op  r  having  been 
removed,  the  handle  M  is  turned  until  the  cross-wire  is  exactly 
over  the  second  mark,  the  observer  carefully  noting  the  number 
of  revolutions  and  fraction  of  a  revolution  required,  by  means  of 
an  index  provided  for  the  purpose.  Let  Us  suppose  10.75  revo- 
lutions are  required  ;  then,  evidently,  the  length  of  the  division 
is  10.75  millimetres. 

In  using  the  dividing  engine  for  calibrating  a  thermometer,  the 
tube  is  adjusted  on  the  carriage  B  so  that  its  axis  shall  be  per- 
fectly parallel  to  the  axis  of  the  long  screw  H.  A  short  column 
of  mercury  having  been  previously  introduced  into  one  end,  the 
length  of  this  column  is  carefully  measured  as  just  described, 
and  the  position  of  its  two  extremities  marked  with  a  fine  hair- 
pencil  on  the  tube.  Adjusting  the  cross-wire  of  the  microscope 
to  the  head  of  the  mercury-column,  this  is  next  pushed  forward 
in  the  tube  through  exactly  its  own  length.  The  length  is 
again  measured,  and  the  position  of  the  head  of  the  mercury- 
column  having  been  marked  as  before,  the  same  process  is  re- 
peated until  the  tube  is  divided  into  lengths  of  equal  capacity, 
and  their  value  known.  Each  of  these  lengths  is  next  to  be 
divided  into  the  same  number  of  equal  parts,  and  any  convenient 
number  is  selected,  which  shall  give  to  the  degrees  as  nearly  as 


HEAT.  445 

possible  the  size  required.  In  order  to  illustrate  the  method,  let 
us  suppose  that  the  lengths  between  the  pencil-marks  are  respect- 
ively as  follows :  — 

18.45  in.  m.,     18.39  m.m.,     18.32  m.m.,     18.24  m.m.,     18.15  m.m., 

and  that  it  is  decided  to  divide  each  length  into  thirty  degrees. 
The  lengths  of  the  degrees  in  the  different  divisions  will  then  be, 
respectively, 

O.Glom.m.,     0.613  m.m.,     O.Gllm.m.,     O.GOSm.m.,     O.G05m.m. 

This  calculation  having  been  made,  the  tube  is  covered  with  a 
varnish  such  as  is  used  in  etching,  and  the  stops  on  the  wheel 
op  r  (Fig.  346)  so  adjusted  as  to  limit  its  motion  to  0.615  of  one 
revolution.  The  point  of  the  graver  is  also  adjusted  to  the  first 
pencil-mark,  and  a  cut  made  through  the  varnish,  exposing  the 
glass.  The  handle  M  is  now  turned  until  its  motion  is  arrested 
by  the  stop,  and  another  cut  made.  The  motion  of  the  handle 
having  been  reversed,  the  same  process  is  repeated  thirty  times, 
when  the  point  of  the  graver  will  have  reached  the  sqcond  pencil- 
mark,  and  thirty  degrees,  each  0.615  m.  m.  in  length,  are  marked 
on  the  tube.  The  adjustment  of  the  stop  must  now  be  changed, 
so  as  to  limit  the  motion  of  the  wheel  to  0.613  of  a  revolution, 
and  thirty  more  divisions  made ;  and  so  on  until  the  graduation 
is  completed,  when  the  tube  is  removed  from  the  engine,  and  the 
figures  which  serve  to  number  the  divisions  are  marked  in  with 
the  hand.  It  only  remains,  now,  to  expose  the  tube  to  the  vapor 
of  fluohydric  acid,  which  corrodes  the  glass  wherever  the  graver 
has  exposed  its  surface,  and  subsequently  to  verify  the  work  by 
passing  another  column  of  mercury  through  the  tube.  This 
should  cover  the  same  number  of  divisions  in  any  position,  and 
will  do  so  if  the  graduation  has  been  carefully  performed. 

The  stem  of  the  thermometer  thus  adjusted,  a  bulb  is  blown 
upon  the  end,  or,  what  is  better,  a  cylindrical  reservoir  previously 
prepared  is  cemented  to  it  with  a  blowpipe.  The  capacity  of  this 
reservoir  must  be  proportional  to  the  size  of  the  tube,  and  to  the 
range  of  temperature  which  the  thermometer  is  intended  to 
cover.  Let  us  suppose  that  it  is  required  that  N  divisions  of 
the  thermometer  should  correspond  to  100°  C.,  and  we  wish  to 
know  what  must  be  the  size  of  the  reservoir  for  a  given  graduated 
tube.  We  first  weigh  the  tube,  both  when  empty  and  when  con- 
38 


446  CHEMICAL  PHYSICS. 

taining  a  column  of  mercury  which  covers  an  observed  number  of 
divisions.  This  gives  us  the  weight  of  mercury,  10,  occupying  n 

divisions  of  the  tube.  From  this  we  obtain  N  —  ,  the  weight  of 
mercury  which  will  fill  N  divisions,  and  by  [56]  N  ,„  ~  y 

the  corresponding  volume.  But  this  volume  represents  the  ex- 
pansion which  the  mercury  in  the  reservoir  of  our  proposed  ther- 
mometer must  undergo  when  heated  from  0°  to  100°.  Now  we 
know  that  the  apparent  expansion  of  mercury,  under  these  cir- 
cumstances, is  ^  of  its  volume  at  0°.  Representing,  then,  by  V 
the  unknown  volume  of  the  reservoir,  we  shall  have 


and 


-  ,  ,,  -T-N- 

Go  n  (Sp.Gr.)  '  n  (Sp.Gr.) 

If  the  reservoir  is  spherical,  F=  J  ;r  Z>3,  from  which  we  can 
calculate  the  required  diameter  ;  and  if  it  is  cylindrical, 
F=  ^  ?t  D*  A,  from  which  we  can  approximative^  determine 
the  required  length,  7t,  when  the  diameter  is  known. 

The  tube  and  bulb  are  now  filled  with  perfectly  pure  mercury, 
and  the  fixed  points  marked  upon  it  in  the  usual  way,  when  the 
thermometer  is  finished  and  ready  for  use.  The  divisions  marked 
upon  a  thermometer  so  constructed  are  not,  of  course,  degrees  of 
either  of  the  three  scales  mentioned  in  (218)  ;  but  it  is  always 
easy  to  calculate  from  the  indications  of  this  arbitrary  scale  the 
corresponding  degrees  of  the  Centigrade  scale.  We  ascertain,  by 
observation,  the  number  of  divisions  on  the  thermometer  between 
the  freezing  and  boiling  points,  which  we  may  represent  by  JV, 
and  also  the  number  of  the  divisions  on  the  arbitrary  scale  corre- 
sponding to  the  freezing-point  (the  zero  of  the  Centigrade  scale). 
Represent  this  number  by  w,  the  degrees  of  the  Centigrade  scale 
by  C°,  and  those  of  the  arbitrary  scale  by  A°.  We  have,  then, 

N=  100°  C.,  and  C°  =  ™  (A°  —  n):     Suppose,  for  example, 

that  there  are  354  divisions  on  the  arbitrary  scale  between  the 
fixed  points,  and  that  the  freezing-point  is  at  the  132d  division 
from  the  bottom  of  the  scale  ;  and  let  it  be  required  to  determine 
to  what  temperature  the  230th  division  corresponds  in  Centi- 
grade degrees.  We  shall  have,  C°  =  $™  (230  —  132)  =  27.68. 
It  is  usual  to  prepare  a  table  for  each  thermometer  thus  con- 
structed, giving  the  temperature  in  Centigrade  degrees  corre- 
sponding to  every  division  of  the  tube. 


HEAT. 


447 


no 


The  scale  of  a  standard  thermometer  should  always  be  en- 
graved on  the  glass  stem,  as  in  Fig.  347  ;  since,  if  it  is  engraved 
on  a  strip  of  metal  or  ivory  fastened  to  the 
tube,  the  expansion  of  the  scale  introduces  new 
sources  of  error  into  the  instrument.  It  is  also 
essential  for  a  good  standard,  that  it  should  in- 
clude the  boiling  and  freezing  points  upon  its 
scale.  Where  a  large  range  is  required,  the 
great  length  which  this  involves  may  be  best 
avoided  by  making  several  thermometers  with 
continuous  scales,  and  enlarging  the  tube  of  each 
instrument  at  those  parts  which  are  covered  by 
the  scales  of  the  other  thermometers  of  the  set. 
A  thermometer  so  constructed  is  represented  in 
Fig.  848,  although  the  enlargement  is  very  greatly 
exaggerated.  It  is  possible  in  this  way  to  di- 
vide each  Centigrade  degree  into  twenty  parts, 
and  yet  include  both  of  the  fixed  points  on  tho 
scale. 

The  length  of  the  degrees  of  a  thermometer, 
and  hence  its  sensibility  to  small  differences  of 
temperature,  depends  upon  the  size  of  the  reser- 
voir as  compared  with  that  of  the  tube,  and  can 
be  increased  by  the  maker  at  pleasure.  No 
advantage,  however,  is  gained  by  increasing  the 
length  of  the  degrees  on  the  stem  beyond  a  lim- 
ited extent ;  since,  on  account  of  the  imperfec- 
tions of  the  instruments  noticed  in  the  last  section,  it  is  useless 
to  subdivide  the  Centigrade  degree  into  more  than  twenty  parts, 
and  only  the  most  carefully  constructed  standards  will  bear  as 
great  a  subdivision  as  this.  Even  when  the  scale  is  graduated  to 
twentieths,  it  is  possible  for  a  practised  eye  to  estimate  the  hun- 
dredth of  a  Centigrade  degree. 

It  is  evident  that  the  smaller  the  absolute  size  of  the  bulb,  the 
more  rapidly  a  thermometer  will  be  affected  by  changes  of  tem- 
perature ;  and  hence  it  is  always  best  to  make  the  bulb  as  small 
as  circumstances  will  permit,  and  also  to  give  to  it  a  long  cylin- 
drical shape,  which,  for  the  same  volume,  exposes  a  much  greater 
surface  for  the  entrance  of  heat  than  a  sphere. 

The  size  of  the  column  of  mercury  in  the  stem  of  a  thermom- 


Fig.  347.        Fig.  348. 


448  CHEMICAL  PHYSICS. 

eter  is  so  small,  as  compared  with  that  of  the  stem  itself,  that  it 
is  essential,  in  order  to  avoid  the  parallax  caused  by  the  thick- 
ness of  the  glass,  to  place  the  eye  in  reading  on  a  level  with  the 
surface  of  the  column.  The  scale  of  a  delicate  thermometer  is 
always  best  read  through  the  telescope  of  a  eathetometer  (Fig. 
260),  placed  at  a  sufficient  distance  to  prevent  the  heat  of  the 
body  from  affecting  the  instrument. 

(222.)  In  using  a  standard  thermometer,  it  is  important  to 
immerse  both  the  bulb  and  the  stem  in  the  medium  whose  tem- 
perature is  to  be  measured ;  for  if  the  stem  of  the  thermometer 
is  exposed  to  a  lower  temperature  than  the  bulb,  the  whole  of  the 
mercury  will  not  be  equally  expanded,  and  the  thermometer  will 
indicate  too  low  a  temperature.  Since  in  testing  the  tempera- 
ture of  a  small  quantity  of  liquid  this  complete  immersion  of  the 
thermometer  is  impossible,  it  is  necessary  in  such  cases  to  add  to 
the  observed  temperature  a  small  correction,  which  becomes  very 
important  when  the  temperature  of  the  medium  greatly  exceeds 
that  of  the  air. 

In  order  to  illustrate  the  method  of  calculating  the  correction, 
let  us  suppose  that  the  thermometer  is  used  for  testing  the  tem- 
perature of  an  oil-bath  ;  and  that,  while  the  bulb  and  a  portion 
of  the  stem  are  immersed,  the  greater  part  of  the  mercury- 
column  is  above  the  surface  of  the  liquid,  as  represented  in  Fig. 
401.  It  is  now  required  to  determine  how  much  higher  the  ther- 
mometer would  stand  if  the  whole  column  were  exposed  to  the 
same  temperature  as  the  bulb.  For  this  purpose,  we  will  repre- 
sent the  different  quantities  entering  into  the  calculations  as 
follows :  — 

x          =  the  unknown  temperature  of  the  bath. 

t°          =  the  temperature  indicated  by  the  thermometer. 

ti°  =  the  mean  temperature  of  the  mercury  in  the  stem,  ascertained 
by  placing  in  contact  with  it  the  bulb  of  a  small  thermome- 
ter at  about  mid-height  of  the  column. 

6  =  the  number  of  degrees  which  the  portion  of  the  mercury-column 

above  the  surface  of  the  bath  occupies  hi  the  thermometer- 
tube. 

t°—~tf=.  the  difference  of  temperature  between  the  bulb  and  the  stem 
approximatively. 

It  is  evident  that,  if  the  temperature  of  the  mercury  above 
the  surface  of  the  bath  were  increased  t°  — ti°9  the  thermometer 


HEAT.  449 

would  indicate  the  true  temperature  ;  so  that,  to  find  the  cor- 
rection required,  we  have  only  to  calculate  how  much  a  column 
of  mercury  measuring  6  degrees  on  the  scale  will  increase  in 
length  when  its  temperature  is  raised  t°  —  1°.  The  apparent 
expansion  in  glass  of  a  given  volume  of  mercury,  amounting  for 
each  degree  of  temperature  to  ^jVu?  will  amount  for  t°  —  t°  to 


jO  _   f  O 

1    of  the  whole.     Hence,  a  quantity  of  mercury  which  fills 

booU  ,o  _  .  o 

one  degree  of  a  thermometer-tube  will  fill  1  -|  —  '  degrees 
of  the  same  tube  after  its  temperature  has  risen  t°  —  1°  ;  and  in 
like  manner  a  quantity  of  mercury  which  fills  6  degrees  of  a 
thermometer-tube  will  fill,  after  the  same  rise  of  temperature, 

A   //O  _   j  0\ 

6  H  —  *oc          degrees.     In  other  words,  the  column  of  mer- 

Q    Sf    _    (  0\ 

cury  above  the  surface  of  the  bath  would  rise   -  A  l  -    de- 

boo'/ 

grees,  if  its  temperature  were  raised  to  that  of  the  bath.  This, 
then,  is  the  correction  required,  and  we  have,  in  any  case, 


Since  the  mean  temperature  of  the  mercury-column  can  never 
be  accurately  determined,  there  is  always  an  uncertainty  in  re- 
gard to  the  value  of  the  correction  ;  and  it  is  therefore  best,  when 
practicable,  to  avoid  the  necessity  of  any  by  immersing  the  whole 
stem  in  the  bath. 

(223.)  A  thermometer  indicates  temperature  by  either  receiv- 
ing or  imparting  heat  until  its  own  temperature  is  the  same  as 
that  of  the  body  tested.  It  is  therefore  evident  that,  unless  the 
temperature  of  the  body  is  maintained  constant  by  accessions  of 
heat  from  some  external  source,  a  thermometer  will  give  correct 
indications  only  when  its  own  mass  bears  a  very  inconsiderable 
proportion  to  that  of  the  body.  This  very  obvious  fact  must  be 
carefully  borne  in  mind  while  using  the  instrument  ;  and  when 
the  quantity  of  heat  which  the  thermometer  receives  or  imparts 
is  appreciable,  the  change  of  temperature  which  is  thus  caused 
in  the  body  must  be  calculated,  and  the  observations  corrected 
accordingly.  The  student  will  be  able  to  devise  methods  by 
which  the  correction  can  in  any  given  case  be  estimated,  after 
studying  the  sections  on  Specific  Heat. 

For  further  information  in  regard  to  the  construction  and  use  of 
38* 


450  CHEMICAL  PHYSICS. 

standard  thermometers,  we  would  refer  the  student  to  the  vol- 
ume of  memoirs  of  Regnault  already  noticed,  and  to  a  note  by 
J.  I.  Pierre,  published  in  the  Annales  de  C/iimie  et  de  Physique, 
3e  Serie,  Tom.  V.  p.  428. 

(224.)  House  Thermometers.  —  The  scales  of  ordinary  ther- 
mometers are  graduated  011  strips  of  wood,  metal,  or  ivory,  to 
which  the  tube  is  subsequently  attached  (Fig.  349). 
Such  thermometers  are  less  fragile  and  more  easily 
read  than  those  graduated  on  the  stem,  and  at  the 
same  time  are  sufficiently  accurate  for  determining 
the  temperature  of  a  bath  or  of  a  room,  and  for  most 
meteorological  observations.  They  are  not,  however, 
usually  graduated  from  the  two  fixed  points,  as  de- 
scribed in  (218),  but  by  comparison  with  a  standard 
thermometer.  For  this  purpose,  the  instrument  to  be 
graduated  and  the  standard  are  dipped  together  into 
a  bath  of  water.  Care  being  taken  to  maintain  the 
water  at  the  same  temperature  for  some  time,  the 
number  of  degrees  indicated  by  the  standard  is  then 
marked  on  the  stem  of  the  new  instrument  at  the 
level  of  the  mercury-column.  In  the  same  way,  by 
changing  the  temperature  of  the  bath,  several  other 
points  are  determined.  These  are  subsequently 
transferred  to  the  strip  on  which  the  scale  is  to  be 
engraved,  and  the  distance  between  them  divided 
into  the  number  of  degrees  required. 

It  has  been  found  almost  impossible  to  maintain 
a  liquid  bath  at  the  same  temperature  in  all  its  parts 
for  any  length  of  time,  when  this  temperature  con- 
siderably exceeds  that  of  the  air  ;  so  that  we  cannot 
be  certain  that  two  thermometers,  dipped  into  the 
bath  side  by  side,  have  been  exposed  to  exactly  the 
same  degree  of  heat.  The  method  of  graduation 
just  described  ought,  therefore,  never  to  be  used  for  an  instru- 
ment of  precision ;  but  it  is  sufficiently  accurate  for  common 
house  thermometers.  These  instruments,  when  well  made,  may 
be  relied  upon  to  within  a  Fahrenheit  degree  between  the  two 
fixed  points ;  but  beyond  these  points,  and  especially  below  the 
freezing-point,  they  are  frequently  very  erroneous.  Two  ther- 
mometers hanging  side  by  side,  which  have  been  made  by  the  best 


HEAT.  451 

makers  with  their  usual  care,  will  not  unfrequently  differ  several 
degrees  when  the  temperature  is  below  0°  F.,  —  a  fact  which 
accounts  for  the  great  discrepancies  in  the  observations  of  low 
temperatures. 

(225.)  Thermometers  filled  with  other  Liquids.  —  Mercury 
boils  at  360°  C.  and  freezes  at  — 40°,  and  the  range  of  a  mer- 
cury thermometer  is  necessarily  confined  within  these  limits  of 
temperature.  Moreover,  near  its  freezing-point  the  rate  of  ex- 
pansion of  mercury  becomes  very  irregular,  and  its  indications 
cannot  be  relied  upon  below  — 86°,  or  even  — 35°  C.  Degrees 
of  temperature  above  360°  are  measured  by  means  of  a  class  of 
instruments  called  pyrometers,  which  will  be  described  in  con- 
nection with  the  laws  of  expansion  of  solids  and  gases  ;  while 
for  temperatures  below  — 35°,  we  use  thermometers  filled  with 
alcohol,  or  other  liquids  which  do  not  freeze  even  at  these  great 
degrees  of  cold. 

There  is  no  other  liquid  which  can  be  compared  with  mercury 
in  its  fitness  for  filling  thermometers.  The  great  range  of  tem- 
perature between  its  freezing  and  boiling  points,  the  fact  that  it 
does  not  adhere  to  the  surface  of  glass,  and  that  it  can  readily 
be  obtained  perfectly  pure,  are  all  circumstances  which  pecu- 
liarly adapt  it  to  thermometric  purposes.  It  is  true,  as  we  have 
seen,  that  the  rate  of  its  expansion  increases  with  the  tempera- 
ture ;  still,  between  the  two  fixed  points  the  change  is  so  slight 
that  the  indications  of  the  thermometer  are  not  perceptibly  af- 
fected by  it.  This  is  not  true  of  thermometers  filled  with  any 
other  liquid.  Such  thermometers,  when  graduated  on  the  same 
principle  as  the  mercury  thermometer,  give  results  which  are 
entirely  at  variance  both  with  it  and  with  themselves.  For  ex- 
ample, Deluc  obtained  the  following  comparative  results  with 
thermometers  filled  with  mercury,  oil,  alcohol,  and  water.  The 
numbers  in  the  same  vertical  column  of  the  table  are  the  tem- 
peratures indicated  by  these  several  thermometers  when  immersed 
in  the  same  bath. 


o  o  o  o  o 


Mercury,  —12.5     —6.25         0  25.0  50.0  75.0  100 

Oil,  0  24.1  49.0  74.1  100 

Alcohol,  —9.6    —4.90         0  20.6  43.9  70.2  100 

Water,  0  5.1  25.6  57.2  100 


452  CHEMICAL  PHYSICS. 

Similar  results  were  also  obtained  by  M.  Pierre,  in  his  very 
extended  investigation  of  the  expansion  of  liquids,  during  which 
lie  compared  thermometers  containing  twelve  different  liquids 
with  the  mercury  thermometer.  As  is  shown  by  the  above  ta- 
ble, he  found  the  water  thermometer  the  most  defective.  Ther- 
mometers filled  with  alcohol  or  with  sulphide  of  carbon  gave 
less  erroneous  results  ;  but  of  all  the  liquids  he  examined,  com- 
mon ether,  chloride  of  ethyle,  and  bromide  of  ethyle,  were  least 
irregular  in  their  rate  of  expansion,  and  are  therefore  best 
adapted,  after  mercury,  for  filling  thermometers. 

Nevertheless,  alcohol  thermometers  are  generally  used  for 
measuring  very  low  temperatures.  They  are  graduated  by  com- 
parison with  standard  mercury  thermometers,  in  the  way  described 
in  the  last  section,  taking  care  to  have  a  large  number  of  points 
of  comparison,  which  should  be  as  near  together  as  possible.  But 
even  when  graduated  with  the  greatest  care,  such  thermometers 
do  not  give  indications  which  accord  with  each  other,  or  with  a 
mercury  thermometer.  Captain  Parry,  in  his  Arctic  voyages,  ob- 
served differences  of  10°  C.  between  alcohol  thermometers  of  the 
best  makers ;  and  similar  facts  were  noticed  both  by  Franklin  and 
by  Kane.  These  discrepancies  unquestionably  originated  in  part 
from  the  impurity  of  the  alcohol,  or  from  other  errors  of  con- 
struction ;  but  they  are  also,  to  a  certain  degree,  inherent  in  the 
thermometer  itself.  An  accurate  instrument  for  measuring  low 
temperatures  is  still  one  of  the  great  desiderata  of  science. 

(226.)  Maximum  and  Minimum  Thermometers.  —  It  is  fre- 
quently desirable  to  have  the  means  of  determining,  without  the 
aid  of  an  observer,  the  highest  or  lowest  temperature  which  has 
occurred  during  the  night,  or  any  other  interval  of  time ;  and 
for  this  purpose  a  great  variety  of  self-registering  thermometers 
have  been  invented.  One  of  the  simplest  is  that  of  Rutherford 
(Fig.  350).  This  consists  of  two  thermometers,  fastened  to  a 
plate  of  wood,  or  some  other  material.  The  tubes  of  the  ther- 
mometers are  bent  at,  right  angles  just  above  the  bulbs,  as  rep- 
resented in  the  figure,  and  the  instrument  when  in  use  is 
suspended  by  a  cord,  so  that  the  two  stems  shall  be  in  a  horizontal 
position.  The  upper  thermometer  is  filled  with  mercury,  and  in 
front  of  the  mercury-column  a  short  piece  of  iron  wire  is  placed 
in  the  tube  (seen  at  A),  which  is  pushed  forward  by  the  mercury 
and  left  at  the  highest  point  which  the  column  reaches,  thus  indi- 


HEAT. 


453 


eating  the  maximum  temperature.  The  lower  thermometer  is 
filled  with  alcohol,  and  the  tube  contains  a  small  enamel  cylinder 
(seen  at  jB),  surrounded  by  the  liquid.  As  the  alcohol  expands, 
it  readily  passes  by  the  enamel  cylinder ;  but  when  it  contracts, 


20  40 


40          30         20 


10  20          50 

40  0  40 


Fig.  350. 

the  cylinder  is  drawn  back  with  the  receding  column,  and  left  at 
the  lowest  point,  indicating  the  minimum  temperature  during  the 
same  period.  After  each  observation,  the  enamel  cylinder  is 
brought  to  the  end  of  the  alcohol-column  by  inclining  the  instru- 
ment ;  and  in  like  manner  the  iron  wire  is  restored  to  the  end 
of  the  mercury-column  by  means  of  a  magnet. 

The  iron  wire  in  the  tube  of  Rutherford's  maximum  thermom- 
eter is  liable  to  become  immersed  in  the  mercury,  if  the  instru- 
ment is  not  carefully  handled ;  and  when  this  accident  occurs,  it 
is  very  difficult  to  remedy  the  evil  without  refilling  the  tube. ' 
Negretti  and  Zambra  have  invented  a  maximum  thermometer 
which  is  not  open  to  the  same  objections.  Between  the  bend  d 


Fig.  351. 


and  the  bulb  (Fig.  351)  they  insert  into  the  tube  of  the  ther- 
mometer a  small  rod  of  glass,  a  Z>,  which  nearly  fills  the  bore. 
When  the  mercury  expands,  it  pushes  by  this  obstruction ;  but 
when  it  contracts,  the  column  breaks,  leaving  the  head  of  the 


454  CHEMICAL   PHYSICS. 

column  at  the  highest  point  it  had  attained.  On  turning  the 
thermometer,  so  that  its  stem  shall  have  a  vertical  position,  the 
mercury  readily  passes  back  to  the  bulb,  in  virtue  of  its  weight. 

Walferdin's  maximum  thermometer  is  represented  in  Fig.  352. 
It  is  made  like  an  ordinary  mercury  thermometer,  only  the  upper 
part  of  its  stem  is  surrounded  by  a  reservoir  containing 
mercury,  which  is  so  arranged  that,  when  the  instrument 
is  inverted,  the  end  of  its  tube  dips  under  the  mercury 
in  the  reservoir.  No  graduation  on  the  stem  is  neces- 
sary ;  but  before  the  instrument  is  to  be  used,  the  bulb 
must  be  heated  until  the  mercury  overflows  the  end  of  the 
tube.  It  is  then  inverted ;  when,  on  cooling,  the  mercury 
rises  from  the  reservoir  by  mechanical  adhesion,  com- 
pletely filling  the  stem.  If  the  thermometer  is  now 
replaced  in  position,  its  bulb  and  tube  being  full  of 
mercury,  it  is  evident  that,  as  the  temperature  rises,  the 
mercury  will  gradually  flow  over  from  the  tube  into  the 
reservoir ;  and  when  the  temperature  subsequently  falls, 
the  mercury,  contracting,  will  leave  an  empty  space  at 
the  top  of  the  tube.  The  highest  temperature  to  which 
the  instrument  has  been  exposed  is,  then,  that  at  which 
the  mercury  remaining  in  the  bulb  and  stem  just  fills 
them  both  completely  ;  and  this  can  be  ascertained  by 
comparison  with  a  standard  thermometer,  placing  both 
in  a  water-bath,  gradually  heating  it,  and  observing  the 
temperature  indicated  by  the  standard  when  the  mercu- 
rial column  reaches  the  top  of  the  stem. 

The  same  principle  has  been  applied  by  Walferdin  for 
measuring  very  small  differences  of  temperature.  The 
thermometer  for  this  purpose  may  be  constructed  in  pre- 
cisely the  same  way,  only  it  is  made  extremely  sensitive,  so  that 
an  expansion  corresponding  to  four  Centigrade  degrees  would 
raise  the  mercury-column  through  the  whole  length  of  the 
stem.  The  stem  is,  moreover,  very  carefully  graduated  into 
parts  of  equal  capacity,  each  division  corresponding  to  a  very 
small  fraction  of  a  degree.  To  show  how  this  thermometer  is 
used,  let  us  suppose  that  we  wish  to  observe  the  temperature  at 
which  water  boils  under  different  atmospheric  pressures,  where 
the  whole  possible  variation  is  between  101°  and  98°.  We  should, 
in  the  first  place,  expose  the  instrument  to  a  temperature  of  101°, 


HEAT.  455 

as  indicated  by  a  standard  thermometer,  and  wait  until  the  ex- 
cess of  mercury  had  overflowed  into  the  upper  reservoir.  On 
now  allowing  the  temperature  to  fall,  the  mercury-column 
will  rapidly  sink  in  the  tube,  and  at  97°  will  already  have 
receded  into  the  bulb.  The  thermometer  is  now  in  con- 
dition to  measure  with  great  accuracy  differences  of  tem- 
perature between  98°  and  101°  ;  and  in  like  manner  it 
may  be  adjusted  to  any  other  range  of  four  degrees.  If, 
for  example,  the  division  on  the  stem  correspond  to 
thousandths  of  a  Centigrade  degree,  and  we  observe  a 
difference  in  the  boiling-point  of  water  under  two  differ- 
ent pressures  equal  to  fifteen  of  these  divisions,  we  con- 
clude that  the  temperature  is  0.015  of  a  degree  higher 
in  one  case  than  in  the  other.  Since  the  quantity  of 
mercury  which  forms  the  thermometer  differs  with  the 
range  of  the  instrument,  it  is  evidently  necessary  to  de- 
termine the  value,  in  fractions  of  a  Centigrade  degree,  of 
one  of  its  divisions  after  each  adjustment.  The  form  of 
reservoir  represented  in  Fig.  352  is  difficult  to  make,  and 
there  is  generally  substituted  for  it  a  simple  enlargement 
of  the  upper  end  of  the  tube,  as  represented  in  Fig.  353. 
The  neck  of  the  bulb  B  is  strangled  at  (7,  so  that  a 
slight  tap  given  to  the  tube  while  the  instrument  is  cool- 
ing causes  the  column  to  break  at  that  point,  leaving  the  Fig.  353. 
excess  of  mercury  in  the  bulb. 

THERMOSCOPES. 

(227.)  Air  Thermometers.  —  The  name  thermoscope  (Oeppr}, 
oveo7reo>)  is  a  convenient  designation  for  a  class  of  instruments 
which  are  used  chiefly  for  detecting  slight  changes  of  temper- 
ature, and  not,  like  the  thermometer  (0e/>A«?,  /ierpoi/),  for  de- 
termining its  value  in  degrees.  In  a  large  number  of  thermo- 
scopes,  these  variations  are  indicated  by  the  change  in  volume 
of  confined  air,  which  not  only  expands  very  regularly  and 
quickly,  but  also  to  a  very  much  greater  degree  than  liquids,  for 
tliB  same  increase  of  temperature.  Such  instruments  are  fre- 
quently called  air  thermometers  ;  but  they  must  not  be  con- 
founded with  the  air  thermometer  of  Regnault,  which  gives  the 
most  accurate  measures  of  temperature  that  we  can  attain. 


456 


CHEMICAL  PHYSICS. 


The  air  thermometer  represented  in  Fig.  354  is  ascribed  to 
Sanctorius,  an  Italian  philosopher  of  the  seventeenth  century, 
and  is  supposed  by  some  to  have  been  the  first  instrument  used  for 
measuring  temperature.  It  consists  of  a  bulbed  tube,  whose  ex- 
tremity rests  in  an  open  vessel  containing  colored  water,  which 
also  partially  fills  the  tube.  When  the  bulb  is 
heated,  the  liquid  falls  in  the  tube,  and  rises 
when  the  bulb  is  cooled.  The  tube  is  generally 
fastened  to  an  upright  piece  of  wood,  on  which 
a  scale  of  equal  parts  is  painted.  In  another 
form  of  the  same  instrument  (Fig.  355),  the 
expansion  of  the  air  is  indicated  by  the  motion 
of  a  drop  of  colored  liquid  in  the  stem  at  A. 
These  instruments  are  evidently  affected  by 
the  varying  pressure  of  the  atmosphere,  and 
are  necessarily  imperfect. 

The  same  objection  does  not  apply  to  the  dif- 
ferential thermometer  of  Leslie,  used  by  him 
in  his  experiments  on  the  radiation  of  heat. 
This   consists  (Fig.  356)  of  two  bulbs   con- 
nected together  by  a  glass  tube  bent  twice  at  right  angles.     The 
bulbs  contain  air,  and  the  connecting  tube  is  half  filled  with  col- 
ored liquid,  which,  when  the  thermometer  is  at  rest,  stands  at  the 


Fig.  354.  Fig.  355. 


Fig.  356. 


Fig.  357. 


same  height  in  the  two  limbs  of  the  sipnon,  and  remains  in  this 
position  so  long  as  the  two  bulbs  are  equally  heated.  Any  dif- 
ference in  the  temperature  of  the  two  bulbs,  however,  is  at  once 
indicated,  as  represented  in  the  figure,  by  a  difference  of  level  in 


HEAT.  457 

the  two  liquid  columns,  and  can  be  measured  by  means  of  the 
scales  painted  on  the  wooden  frame  which  supports  the  tube. 
This  is  the  only  thermoscope,  of  its  class,  of  any  scientific  value. 
In  a  limited  number  of  cases  it  furnishes  an  instrument  of  great 
utility  and  delicacy,  and  its  indications  are  comparable  with  each 
other. 

Rumford's  differential  thermometer  (Fig.  357)  is  merely  a 
slight  variation  of  Leslie's,  the  difference  in  the  temperature  of 
the  two  bulbs  being  indicated  by  the  motion  of  a  drop  of  sul- 
phuric acid  along  the  horizontal  tube,  which  is  made  somewhat 
longer  than  in  Leslie's  instrument,  and  surmounted  by  a  scale  of 
equal  parts.  There  are  several  other  forms  of  air  thermometers, 
but  they  are  not  of  sufficient  importance  to  require  notice. 

(228.)  Thermo-multiplier.  —  But  of  all  instruments  for  detect- 
ing and  measuring  slight  differences  of  temperature,  by  far  the 
most  delicate  and  accurate  is  the  thermo-multiplier  of  Nobili  and 
Melloni.  The  principle  on  which  this  instrument  is  based  was 
discovered  by  Seebeck,  of  Berlin,  in  1822,  and  may  be  briefly 
stated  thus. 

If  two  metallic  bars,  of  different  crystalline  texture  and  unequal 
conducting  powers,  are  united  at  one  end  by  solder,  and  the  point 
of  junction  heated,  a  current  of  electricity  is  ex- 
cited, which  flows  from  the  point  of  junction  to- 
wards the  poorer  conductor.  Thus,  if  the  junction 
of  two  bars  of  bismuth  and  antimony  (Fig.  358) 
is  heated,  and  their  free  ends  are  connected  by 
wires,  the  current  flows  from  the  antimony  to  the 
bismuth  at  the  junction,  and  from  the  bismuth  to 
the  antimony  on  the  conducting-wire  connecting 
the  free  ends  of  the  bars.  If  cold,  instead  of  heat, 
is  applied  to  the  junction,  a  current  is  also  established,  but  in  the 
opposite  direction.  Similar  results  can  be  obtained  with  other 
metals,  which  may  fee  arranged  in  a  thermo-electric  series  in  the 
following  order  :  bismuth,  platinum,  lead,  tin,  copper  or  silver, 
zinc,  iron,  antimony.  The  most  powerful  combination  is  formed 
of  those  metals  which  are  most  distant  from  each  other  in  the 
list,*and  in  every  case,  when  the  junction  is  heated,  the  current 
flows  through  the  conducting-wire  from  those  which  stand  first 
to  those  which  stand  last. 

The  most  powerful  current  is  produced,  as  the  above  eeries 


458 


CHEMICAL  PHYSICS. 


shows,  by  the  combination  of  bismuth  and  antimony ;  but  a  single 
pair  of  bars,  even  of  these  metals,  produces  only  a  very  feeble 
effect.  The  force  of  the  electric  current  can,  however,  be  very 
greatly  increased  by  uniting  together  several  pairs  of  these  bars, 
as  represented  at  a  b,  Fig.  359,  and  connecting  together  the  free 
end  of  the  first  bismuth  bar  with  that  of  the  last  antimony  bar. 
Such  an  arrangement  is  called  a  thermo-electric  pile.  Since  the 


Fig.  359. 

force  of  the  current  is  not  found  to  depend  on  the  size  of  the  bars, 
they  may  be  made  very  small  ;  in  Melloni's  thermo-multiplier 
thirty  pairs  of  bismuth  and  antimony  bars  are  packed  away  in  the 
small  brass  case,  c  d,  Fig.  359,  not  more  than  two  or  three  centime- 
tres long.  The  soldered  ends  of  these  pairs,  called  the  faces  of 
the  pile,  are  seen  at  c  and  d;  and  the  two  cups,  o,  o',  called  the 
poles  of  the  pile,  are  directly  connected  with  the  free  ends  of  the 
two  terminal  bars.  Finally,  the  faces  of  the  pile  are  protected  from 
any  lateral  action  by  a  brass  cap,  t,  blackened  inside,  and  having 
a  movable  screen,  e,  in  front,  or  by  a  brass  cone  polished  on  its 
interior  surface,  which  serves  to  concentrate  the  rays  of  heat. 

When  the  two  faces  of  the  thermo-electric  pile  are  equally 
heated,  no  electrical  disturbance  results  ;  but  the  slightest  differ- 
ence of  temperature  causes  a  flow  of  electricity  through  the  wire 
connecting  the  two  poles.  The  direction  of  the  current  is  deter- 
mined by  the  relative  positions  of  the  bars,  always  following  the 
rule  stated  above.  The  force  of  this  current,  although  much 
greater  than  that  of  the  current  from  a  single  pair  of  bars,  is 
still  feeble,  and  can  only  be  detected  by  a  very  delicate  galva- 
nometer. This  instrument  will  be  described  in  detail  hereafter. 


HEAT.  459 

It  is  sufficient,  for  the  present,  to  state  that  it  is  an  application 
of  the  remarkable  facts  discovered  by  Oersted  in  1820.  This 
eminent  physicist  observed,  that,  if  a  conducting-wire  through 
which  an  electric  current  is  passing  is  placed  directly  over  and 
parallel  to  a  magnetic  needle 
(Fig.  361),  the  north  pole  of 
the  needle  is  deflected  to  the 
right  or  to  the  left,  according 
to  the  direction  of  the  current. 
If  the  conducting-wire  is  placed 
under  the  needle,  it  is  also 
deflected,  but  in  the  opposite 
direction.  Hence,  if  the  con- 
ducting-wire  is  formed  into  a  Fig.  301 
loop,  and  placed  around  the 

needle,  and  at  the  same  time  parallel  to  it,  in  such  a  manner  that 
the  current  may  flow  from  north  to  south  above  the  needle,  and 
from  south  to  north  below  it,  the  two  portions  of  the  wire  will 
conspire  to  deflect  the  needle,  and  the  effect  of  one  and  the  same 
current  will  be  doubled.  By  turning  the  wire  again  round  the 
needle,  the  effect  of  the  same  current  will  be  quadrupled,  and  by 
repeating  the  turns,  as  in  Fig.  362,  the  deflecting  force  may  be 
multiplied  to  a  very  great  extent ;  and  thus  the  deflections  of  a 
magnetic  needle  may  become  the  means  of  detecting  a  very  feeble 
electric  current.  The  galvanometer  represented  in  Fig.  360  is  a 
direct  application  of  this  principle.  The 
conducting-wire,  which  is  covered  with  silk, 
is  wound  round  the  ivory  frame  a  b  a  great 
number  of  times,  and  terminates  at  the  two 
ends,  n,  n'.  The  magnetic  needle  is  sus- 
pended, so  as  to  oscillate  freely  within  the  rig  302. 
ivory  frame,  by  means  of  a  single  strand  of 
raw  silk,/;  and  when  at  rest,  its  axis  is  parallel  to  the  turns  of 
the  conducting-wire.  Parallel  to  the  first  needle,  and  immovably 
connected  with  it,  is  a  second  needle,  /,  which  oscillates  just  above 
a  graduated  arc,  and  thus  indicates  the  amount  of  deflection. 
This  needle  also  serves  another  purpose.  Its  north  pole  is  placed 
directly  over  the  south  pole  of  the  first  needle,  and,  both  being 
of  equal  force,  the  action  of  the  earth's  magnetism  on  one  is  bal- 
anced by  its  action  on  the  other.  A  needle  so  arranged  is  termed 


460  CHEMICAL  PHYSICS. 

astatic,  and  will  remain  in  any  position  in  which  it  may  be  placed. 
Moreover,  the  action  of  an  electric  current  upon  it  is  not  influ- 
enced by  the  magnetism  of  the  earth.  The  graduated  disk  just 
referred  to  rests  on  the  ivory  frame,  and  is  made  of  copper,  which 
has  the  effect  of  deadening  the  oscillations  of  the  needle.  When 
in  use,  the  two  poles  of  the  thermo-electric  pile  (o,  o'7  Fig.  359) 
are  connected  with  the  ends  (n,  n',  Fig.  860)  of  the  conducting- 
wire,  which  is  wound  round  the  frame  of  the  galvanometer. 


Fig.  363. 

The  apparatus  is  so  delicate,  that  the  heat  of  the  hand,  placed 
several  feet  in  front  of  the  conical  cap  G,  will  be  at  once  percep- 
tible, by  deflecting  the  needle.  Moreover,  when  the  deflection  is 
not  greater  than  twenty  degrees,  the  angle  of  deviation  is  propor- 
tional to  the  difference  of  temperature  between  the  faces  of  the 
pile,  and  may  therefore  be  used  as  a  measure  of  the  intensity  of 
the  calorific  effect  produced  on  one  face  when  the  other  is  exposed 
to  a  constant  temperature.  Beyond  twenty  degrees,  the  angle 
of  deviation  is  no  longer  proportional  to  the  temperature  ;  but 
a  table  can  be  easily  constructed  for  each  instrument,  in  which, 
for  each  degree  of  deviation,  are  given  the  corresponding  differ- 
ences of  temperature  of  the  two  faces.  Melloni  does  not  extend 
these  tables  beyond  thirty-five  degrees,  because  the  slightest 
change  in  the  position  of  the  axis  of  suspension  of  the  needle 
would  cause  a  great  error  in  its  indications.  A  deflection  of 
thirty-five  degrees  corresponds  to  a  difference  of  from  six  to  eight 
degrees  in  the  temperature  of  the  two  faces  of  the  pile.  The 
instrument,  as  mounted  for  use,  with  its  various  screens  and 
appendages,  is  represented  in  Fig.  363. 


HEAT.  461 


PROBLEMS. 

Thermometers. 

272.  It  is  required  to  change  into  Fahrenheit  and  Reaumur  degrees  the 
following  temperatures  in  Centigrade  degrees :  — 

Temperature  of  maximum  density  of  water,  .  -f-  3°.87  C. 

Boiling-point  of  liquid  ammonia, —40 

"  "  sulphurous  acid, — 10 

alcohol, -f-75 

"  "  phosphorus, 290 

"  "  mercury, 360 

273.  It  is  required  to  change  into  Centigrade  and  Reaumur  degrees  the 
following  temperatures  in  Fahrenheit  degrees :  — 

Melting-point  of  mercury, —40°  F. 

"  "         bromine, —  4 

«        white  wax, +158 

"  "         sodium, 194 

"  "tin, 442.4 

"  "         antimony, 771.8 

Incipient  red  heat, 977 

Clear  cherry-red,  heat, 1,832 

Dazzling  white  heat, 9,732 

274.  How  many  degrees  Centigrade  and  Reaumur  are  n°  Fahrenheit  ? 

275.  How  many  degrees  Fahrenheit  and  Reaumur  are  n°  Centigrade  ? 

276.  At  what  temperatures  do  — x°  C.  equal  — x°  F.  ?  — x°  R.  equal 
_ x°  p.  ?  — x°  C.  equal  +x°  F.  ?  and  —  x°  R.  equal  +x°  F.  ? 

277.  The  boiling-point  was  marked  on  the  stem  of  a  mercurial  ther- 
mometer when  the  barometer  stood  at  74.65  c.  m. ;  the  distance  between 
this  point  and  the  freezing-point,  previously  determined,  was  found  to  be 
21.54  c.  m.     It  is  required  to  determine  the  position  of  the  true  boiling- 
point  on  the  stem  with  reference  to  the  first. 

278.  Solve  the  same  problem,  representing  the  height  of  the  barometer 
by  If,  and  the  distance  between  the  freezing-point  and  the  boiling-point 
by/. 

279.  In  order  that  a  mercurial  thermometer  may  measure  temperatures 
between  — 40°  and  +300°,  how  many  times  must  the  capacity  of  the  bulb 
be  greater  than  that  of  the  tube  ? 

280.  A  thermometer-tube  was  divided  into  1,500  parts  of  equal  ca- 
pacity, as  described  in  (221).     It  was  then  weighed,  first  when  empty, 
and  afterwards  when  containing  a  quantity  of  mercury  occupying  73  di- 
visions.    The  difference  of  these  weights  was  0.008  grammes.     It  is 
desired  that  the  distance  between  the  fixed  points  should  be  divided  into 
about  1,000  parts,  and  it  is  required  to  find  the  volume  of  the  reservoir 

39* 


462  CHEMICAL   PHYSICS. 

necessary  to  effect  this  object.  If  the  reservoir  is  spherical,  what  must 
be  its  diameter  ?  If  it  is  cylindrical,  what  must  be  its  length,  assuming 
that  its  diameter  is  0.52  c.  m.  ? 

281.  After  the  thermometer  of  the  last  problem  was  made,  it  was  found 
that  the  zero-point  corresponded  to  the  230th  division  from  the  bottom  of 
the  scale,  and  the  boiling-point  to  the  1,223d.     To  what  temperature  does 
the  765th  division  correspond  ?     Prepare  a  table  giving  the  temperature 
in  Centigrade  degrees  corresponding  to  every  tenth  division  on  the  tube. 

282.  A  thermometer  was  graduated  with  an  arbitrary  scale,  as  above ; 
the  zero-point  was  subsequently  found  to  coincide  with  the  56th  division, 
and  the  boiling-point  with  the   245th   division  of  this   scale,  when  the 
barometer  stood  at  74.25.     It  is  required  to  prepare  a  table,  giving  the 
temperature  in  Centigrade  degrees  corresponding  to  each  division  of  the 
scale. 

283.  The  temperature  of  an  oil-bath  was  observed  with  a  mercury- 
thermometer  graduated  to  Centigrade  degrees  to  be  260° ;  the  portion  of 
the  mercury-column  in  the  stem  not  immersed  occupied  190°,  and  the 
mean  temperature  of  this  column  was  94°.     Required  the  true  tempera- 
ture of  the  bath. 

284.  When  the  thermometer  of  problem  281  was  immersed  in  an  oil- 
bath,  the  mercury  rose  to  the  500th  division  of  the  scale  ;  the  portion  of 
the  mercury-column  in  the  stem  not  immersed  occupied  390  divisions,  and 
its  mean  temperature  was  8°.4.    Required  the  true  temperature  of  the  bath. 

285.  Reduce  the  following  temperatures,  observed  with  a  mercury- 
thermometer  made  of  crown-glass,  to  degrees  of  the  air-thermometer :  260°, 
180°,  230°,  200°,  300°,  and  320°. 

286.  The  coefficient  of  expansion  of  glass  for  one  Centigrade  degree 
is  0.0000088482.     How  great  is  it  for  one  Fahrenheit  degree?     How 
great  for  one  Reaumur  degree  ? 

287.  The  French  unit  of  heat  is  the  amount  of  heat  required  to  raise 
the  temperature  of  one  kilogramme  of  water  from  0°  C.  to  1°  C. ;  the 
English  unit  is  the  amount  of  heat  required  to  raise  the  temperature  of  one 
avoirdupois  pound  of  water  from  59°  F.  to  60°  F.     What  is  the  relation 
between  the  two  ?     (See  table,  p.  472.) 

288.  Convert  into  French  units  of  heat  7.843 ;  234.62 ;  and  52.796 
English  units. 

289.  Reduce  to  English  units  52.34 ;  1,964.72 ;   0.6845 ;  and  324.7 
French  units  of  heat. 

290.  Two  thermometers  are  made  of  the  same  glass ;  the  spherical 
bulb  of  the  first  has  an  interior  diameter  of  7.5  m.  m.,  and  its  tube  a  diam- 
eter of  0.25  m.  m. ;  the  bulb  of  the  second  has  a  diameter  of  6.2  m.  m., 
and  its  tube  a  diameter  of  0.15m.  m.     Required  the  relative  size  of  a 
degree  on  each. 


HEAT.  463 


SPECIFIC    HEAT. 

(229.)  Temperature.  —  The  amount  of  expansion  which  a  hot 
body  is  capable  of  producing  in  the  air  or  mercury  of  a  ther- 
mometer measures  what  we  term  its  temperature.  This  effect 
is  only  indirectly  connected  with  the  amount  of  heat  which  the 
body  contains.  If  different  masses  of  water,  of  mercury,  of  iron, 
or  of  wood  produce  each  the  same  expansion  in  the  air  or  mer- 
cury of  the  thermometer,  we  say  that  they  all  have  the  same 
temperature,  although,  as  we  shall  hereafter  see,  they  may  con- 
tain very  different  amounts  of  heat.  The  thermometer,  there- 
fore, is  an  instrument  for  measuring  the  temperature  of  a  body, 
and  not  the  amount  of  heat  which  it  contains.  It  gives  us, 
though  more  accurately,  the  same  kind  of  information  as  the 
sense  of  touch,  indicating  that  condition  of  a  body  which  pro- 
duces the  sensation  of  heat  and  cold.  It  gives  that  information 
which  is  alone  wanted  in  the  practical  affairs  of  life  ;  for  it  does 
not  concern  us  generally,  how  much  heat  a  body  contains,  but 
only  what  effect  its  heat  will  produce  on  our  bodies. 

The  temperature  of  a  body  depends  on  two  conditions :  first, 
on  the  amount  of  heat  which  the  body  contains ;  secondly,  on  the 
affinity  of  the  body  for  heat,  or,  in  other  words,  on  the  power 
with  which  it  holds  the  heat.  In  illustration  of  these  principles, 
several  well-known  facts  may  be  adduced.  Two  thermometers  in- 
troduced, the  one  into  a  wine-glass  and  the  other  into  a  pail,  each 
of  which  is  filled  with  water  just  drawn  from  a  well,  will  indicate 
the  same  temperature  in  both  ;  simply  because,  although  the 
water  in  the  pail  contains  several  hundred  times  as  much  heat 
as  the  water  in  the  wine-glass,  it  also  holds  the  heat  with  a  pro- 
portionally greater  force,  and  therefore  gives  up  no  more  to  the 
bulb  of  the  thermometer  than  the  smaller  amount  of  water  in  the 
wine-glass.  Again,  two  thermometers,  introduced,  the  one  into 
a  glass  containing  a  kilogramme  of  water,  and  the  other  into  a 
glass  containing  a  kilogramme  of  mercury,  the  glasses  having 
been  standing  together  for  some  time,  will,  in  like  manner,  indi- 
cate the  same  temperature  in  both  ;  for  although,  as  will  soon  be 
shown,  the  water  contains  thirty  times  as  much  heat  as  the  mer- 
cury, it  holds  it  with  thirty  times  as  much  power. 

(230.)  Thermal  Equilibrium.  —  If,  as  is  sometimes  the  case 
in  a  room,  the  heat  is  distributed  through  the  different  articles 


464  CHEMICAL  PHYSICS. 

of  furniture  in  proportion  to  their  affinity  for  the  imponderable 
agent,  it  is  evident  that  we  shall  have  a  condition  of  thermal 
equilibrium ;  for  there  will  be  no  tendency  for  the  heat  to  pass 
from  one  body  to  another.  If  we  now  bring  a  thermometer  in 
contact  with  the  various  articles  of  furniture,  we  shall  find  that 
they  all  have  the  same  temperature.  Let  us  next  suppose  that 
the  stove  suddenly  receives  an  accession  of  heat ;  we  shall  then 
find  that  it  will  indicate  a  higher  temperature  than  before,  be- 
cause it  is  in  a  condition  to  impart  more  heat  to  the  mercury  of 
the  thermometer.  In  the  course  of  a  short  time,  however,  this 
accession  of  heat  will  be  distributed  in  various  ways  through  the 
different  bodies  in  the  room,  in  proportion  to  their  relative  affini- 
ties, when  it  will  be  found  that  all  again  have  the  same  tempera- 
ture, although  a  little  higher  than  before.  It  therefore  appears, 
first,  that  when  bodies  are  at  the  same  temperature  they  are  in  a 
state  of  thermal  equilibrium ;  secondly,  that  when  they  are  at 
different  temperatures,  the  warmer  will  impart  heat  to  the  colder 
until  an  equilibrium  of  temperature  has  been  established ;  that 
is,  until  the  heat  has  been  distributed  through  all  in  proportion 
to  their  relative  affinities. 

(231.)  Unit  of  Heat. — In  one  condition  only  the  thermom- 
eter becomes  a  direct  measure  of  the  amount  of  heat ;  and  that 
is  in  the  case  of  the  same  weight  of  the  same  substance.  Thus, 
if  we  take  one  kilogramme  of  water,  it  is  true  that,  if  a  given 
amount  of  heat  will  raise  its  temperature  one  degree,  twice  the 
amount  of  heat  will  raise  its  temperature  two  degrees,  etc. 
Here,  then,  we  have  a  unit  for  measuring  amounts  of  heat ; 
and  it  has  been  generally  agreed  to  assume,  as  the  unit  of  heat, 
the  amount  of  heat  required  to  raise  the  temperature  of  one 
kilogramme  of  water  one  Centigrade  degree,  in  the  same  way 
that  a  metre  has  been  taken  as  a  unit  of  length,  and  a  minute  as 
a  unit  of  time. 

(232.)  Specific  Heat.  —  Assuming,  then,  this  unit  of  heat,  we 
shall  be  able  to  ascertain  the  relative  amounts  of  heat  which  differ- 
ent substances  contain  at  the  same  temperature,  or,  what  amounts 
to  the  same  thing,  their  relative  affinities  for  heat.  For  this  pur- 
pose, let  us  in  the  first  place  take  two  vessels,  one  containing 
one  kilogramme  and  the  other  ten  kilogrammes  of  water,  and  let 
us  expose  them  both  to  such  a  source  of  heat  that  equal  quan- 
tities of  heat  must  enter  each  vessel  during  the  same  time.  We 


HEAT.  465 

shall  find  that,  when  a  thermometer  in  the  first  vessel  indicates 
that  the  temperature  of  the  one  kilogramme  of  water  has  risen 
ten  degrees,  a  thermometer  in  the  second  vessel  will  have  risen 
only  one  degree.  Since  ten  units  of  heat  have,  by  our  assump- 
tion, entered  the  water  in  each  vessel,  it  follows  that  it  requires 
ten  times  as  much  heat  to  raise  the  temperature  of  ten  kilo- 
grammes of  water  one  degree  as  is  required  to  raise  the  temper- 
ature of  one  kilogramme  of  water  to  the  same  extent.  Sim- 
ilar results  would  be  obtained  with  any  other  substance,  and 
hence  we  may  conclude  that  the  amounts  of  heat  required  to 
raise  the  temperature  of  unequal  weights  of  the  same  substance 
one  degree,  are  proportional  to  these  weights. 

As  a  second  experiment,  we  will  take  five  vessels,  containing 
respectively  one  kilogramme  of  water,  one  kilogramme  of  sul- 
phur, one  kilogramme  of  iron,  one  kilogramme  of  silver,  one 
kilogramme  of  mercury,  and  we  will  expose  them  all  to  such 
a  source  of  heat  that  equal  amounts  must  enter  each  vessel 
during  the  same  interval.  If,  now,  we  observe  thermometers 
placed  in  these  vessels,  we  shall  find,  when  the  temperature  of 
the  water  has  risen  one  degree  and  consequently  when  one 
unit  of  heat  has  entered  each  vessel,  that  the  temperatures  of  the 
other  substances  have  increased  by  the  number  of  degrees  given 
in  the  second  column  of  the  following  table.  By  the  principle 
just  established,  it  follows  that,  if  one  unit  of  heat  will  raise  the 
temperature  of  one  kilogramme  of  mercury  thirty  degrees,  it  will 
only  require  one  thirtieth  as  much,  or  0.033  of  a  unit  of  heat, 
to  raise  the  temperature  of  the  same  weight  one  degree.  In 
like  manner,  the  fractional  parts  of  a  unit  of  heat  required  to 
raise  the  temperatures  of  one  kilogramme  of  each  of  the  other 
substances  one  degree  can  be  easily  calculated,  and  are  given  in 
the  third  column  of  the  table.  This  fraction  is  commonly  called 
the  specific  heat  of  the  substance. 


Water,    .       V 
Sulphur, 
Iron,       .-       ••« 

Temperature. 

;:;'%;  j  *   .    1.0 

'  V;     V'  O        •          4.9 

.-  "--*       '    /          ;"      8.8 

Unit  of  Heat. 

1.000 
0.203 

0.114 

Silver, 
Mercury, 

•  .  .  \  \;  ;;-    ..       17.5 

.    30.0 

0.057 
0.033 

Water,  then,  at  the  same  temperature,  contains  4.9  times  as 


466 


CHEMICAL  PHYSICS. 


much  heat  as  the  same  weight  of  sulphur,  8.8  times  as  much 
as  the  same  weight  of  iron,  17.5  times  as  much  as  the  same 
weight  of  silver,  and  30  times  as  much  as  the  same  weight  of 
mercury ;  and  in  like  manner  we  should  find  that,  at  the  same 
temperature  and  for  equal  weights,  water  contains  more  heat 
than  any  solid  or  liquid  known.  Hence,  the  specific  heat  of 
solid  or  liquid  substances  is  always  expressed  by  fractions. 
These  fractions,  as  determined  by  Regnault  for  the  chemical  ele- 
ments, are  given  in  the  following  table.  The  numbers  in  each 
case  denote  the  fractional  part  of  a  unit  of  heat  required  to  raise 
the  temperature  of  one  kilogramme  of  the  substance  one  degree. 
They  also  represent  the  relative  proportions  in  which  heat  is  dis- 
tributed among  equal  weights  of  these  substances  when  in  the 
state  of  thermal  equilibrium,  and  therefore  indicate  their  relative 
affinities  for  the  imponderable  agent. 

Specific  Heat  of  the  Elements. 


Names  of  Substances. 

Specific  Heat. 

Names  of  Substances. 

Specific  Heat. 

Preliminary  Data. 

Brass,  .... 

0.093910 

Water, 

1.008000 

Glass,       .        . 

0.197680 

Oil  of  Turpentine,  . 

0.425930 

Elements. 

Iron,    . 

0.113790 

Platinum  plate, 

0.032430 

Zinc,     '  'j<  •'.'.  ••  V  " 

0.095550 

sponge,    . 

0.032930 

Copper, 

0.095150 

Palladium, 

0.059270 

Mercury,  . 

0.033320 

Gold,       .        .    ,  .f> 

0.032440 

Solid  Mercury,     . 

0.032410 

Sulphur,     . 

0.202590 

Cadmium, 

0.056690 

Selenium,       '.        .    ' 

0.083700 

Silver,  .!:  '  •  *;  '  .   . 

0.057010 

Tellurium,.     >:^-?!  '*•'- 

0.051550 

Arsenic,    .        .    ,,...? 

0.081400 

Potassium,      .      !/•?:.$•»• 

0.169560 

Lead,    .... 

0.031400 

Bromine,  liquid,     •    .  .- 

0.110940 

Bismuth,  .        .... 

0.030840 

solid  (—28°), 

0.084320 

Antimony,    .         .        . 

0.050770 

Iodine, 

0.054120 

Tin,          .        .        . 

0.056230 

Carbon,  .        .      '  •'. 

0.241110 

Nickel,          .        .        .   ' 

0.108630 

Phosphorus, 

0.188700 

Cobalt,     . 

0.106960 

(233.)  Determination  of  the  Specific  Heat  of  Solids  and 
Liquids.  —  There  are  two  methods  usually  employed  for  this 
purpose.  The  first  method  is  called  the  method  of  cooling, 


HEAT.  467 

and  is  based  upon  the  axiom,  that  the  time  required  for  equal 
weights  of  different  substances  to  cool  through  the  same  num- 
ber of  degrees,  under  exactly  the  same  conditions,  will  be  pro- 
portional to  the  quantity  of  heat  which  they  respectively  contain, 
or,  in  other  words,  to  their  specific  heat.  The  only  difficulty  in 
applying  this  principle  to  practice  consists  in  securing  precisely 
the  same  conditions  for  all  substances.  In  order  to  attain  this 
object,  Regnault  contrived  a  very  ingenious  apparatus,  which  is 
described  at  length  in  the  Annales  de  Chimie  et  de  Physique, 
3e  Sdrie,  Tom.  IX.  ;  but  notwithstanding  the  utmost  precautions 
and  most  persevering  efforts,  this  very  skilful  experimenter  could 
not  obtain  satisfactory  results  by  this  method.  We  shall  not, 
therefore,  enlarge  upon  it  here. 

The  second  method,  which  is  called  the  method  of  mixture, 
consists  in  heating  a  substance  to  a  known  temperature,  and 
then  throwing  it  into  a  vessel  containing  a  known  weight  of 
cold  water.  The  amount  of  heat  communicated  to  the  water 
will  be  proportional  to  the  specific  heat  of  the  given  substance, 
and  gives  us  the  data  for  calculating  it.  This  last  method,  which 
is  by  far  the  most  accurate  of  all  the  methods  yet  devised,  re- 
quires further  illustration. 

Example  1.  If  we  mix  one  kilogramme  of  mercury  at  20° 
with  one  kilogramme  of  water  at  0°,  we  shall  find  that  the 
temperature  of  the  mixture  will  be  0°.639.  The  water,  there- 
fore, has  gained  0.639  of  a  unit  of  heat.  This  amount  of  heat, 
also,  is  evidently  sufficient  to  raise  the  temperature  of  one  kilo- 
gramme of  mercury  from  0°.639  to  20°,  that  is,  through  19°.361. 
Hence,  the  amount  of  heat  required  to  raise  the  temperature 
of  one  kilogramme  of  mercury  one  degree  must  be  equal  to 
§|£  =  0.033  of  one  unit. 

Example  2.  If  we  mix  0.685  of  a  kilogramme  of  sulphur  at  60° 
with  4.573  kilogrammes  of  water  at  12°,  we  shall  find  that  the 
temperature  of  the  mixture  will  be  13°. 42.  The  temperature 
of  4.573  kilogrammes  of  water  has  risen  1°.42,  and  hence  the 
water  has  acquired  4.573  X  1.42  =  6.493  units  of  heat.  These 
6.493  units  of  heat  were  sufficient  to  raise  the  temperature  of 
0.685  of  a  kilogramme  of  sulphur  from  13°.42  to  60°,  or  through 
46°. 58.  They  would,  therefore,  raise  the  temperature  of  one  kilo- 
gramme of  sulphur  through  46°.58  X  0.685  =  31°. 9.  Hence,  it 
would  require  |~f  =  0.203  of  a  unit  of  heat  to  raise  the  tempera- 


468  CHEMICAL  PHYSICS. 

ture  of  one  kilogramme  of  sulphur  one  degree.     In  like  manner 
all  similar  problems  may  be  solved. 

These  solutions  may  easily  be  made  general,  and  reduced  to 
an  algebraic  form,  in  the  following  way.  Let 

W  =  weight  of  water.  w    =  weight  of  substance. 

T°   =  temperature  of  water.  T°  =  temperature  of  substance. 

6°  =  temperature  of  mixture.  x    ==.  specific  heat  required. 

Then  we  shall  have, 

W  =  units  of  heat  required  to  raise  temperature  of  water 

used  one  degree. 

wx  =  units  of  heat  required  to  raise  temperature  of  sub- 

stance used  one  degree. 

(6  —  T)°  =  number  of  degrees  through  which  temperature  of  water 
has  been  raised. 

( T —  0)°  =  number  of  degrees  through  which  temperature  of  sub- 
stance has  fallen. 

(6  —  T)°  W    =  units  of  heat  water  has  gained. 

(T — 6)°  wx  =  units  of  heat  substance  has  lost. 

Since  the  gain  and  the  loss  must  be  equal,  it  follows  that 

(r  —  6)°wx  =  (6  —  T)°JF; 
whence 

*  =  [rafT-  c157-] 

The  results  obtained  from  this  formula  would  be  accurate, 
were  it  not  for  the  fact,  that  the  vessel  which  holds  the  water 
changes  its  temperature  with  that  of  the  water,  so  that  the  heat 
lost  by  the  substance  not  only  raises  the  temperature  of  the  water 
(0  —  T)°,  but  also  the  temperature  of  the  vessel,  by  the  same 
amount.  If  we  know  the  weight  of  the  vessel  and  the  specific 
heat  of  the  substance  of  which  it  is  made,  we  can  easily  estimate 
the  amount  of  heat  required  for  this  purpose.  The  vessel  used 
is  generally  made  of  brass  or  silver,  very  light  and  brightly  pol- 
ished, so  that  these  data  can  be  readily  obtained. 

Let  iv'  =  weight  of  the  vessel,  and  c  =  specific  heat  of  the 
vessel;  then 

uf  c  =  amount  of  heat  required  to  raise  its  temperature  one  de- 

gree. 
(6  —  T}°W'C  =  amount  of  heat  required  to  raise  its  temperature  (6  —  T)°. 


HEAT.  469 

Since  the  heat  lost  by  the  substance  is  equal  to  that  gained  by  the 
water  plus  the  amount  gained  by  the  vessel,  it  follows  that 


(T—  6)°wx=(0  —  r) 

(d  —  r)°  (W+w'c) 
hence,  x  =  ±  —  >,±^-  '->  .  [158.] 

If,  as  is  usually  the  case,  the  substance  is  enclosed  in  a  glass 
tube  on  a  small  basket  of  wire-work,  it  is  also  necessary  to  pay 
regard  to  the  weight  and  specific  heat  of  these  envelopes  in  the 
calculation.  Representing,  then,  by  w"  and  c'  the  weight  and 
specific  heat  of  the  envelope  respectively,  we  shall  have,  evi- 
dently, 

(  T  —  0)°w"c'  =  units  of  heat  the  envelope  has  lost 

Hence  we  obtain, 

(T—6)0w"c'  +  (T—6)°wx  =  (0  —  T)°  (W+w'c), 

and  also 

(0_T)°  (W+w'c)  —  (T  —  efw''*  n,    - 

(T—$fw 

The  above  method  of  determining  the  specific  heat  of  solids 
and  liquids  admits  of  great  accuracy,  but  its  practical  appli- 
cation requires  many  precautions  and  great  delicacy  of  ma- 
nipulation. Regnault,  who  adopted  this  method  in  his  very 
extended  investigations  on  specific  heat,  used,  in  making  the 
determinations,  the  apparatus  represented  in  Fig.  364.*  This 
apparatus  consists,  first,  of  the  vessel  m,  in  which  the  heated 
substance  is  mixed  with  water  ;  secondly,  of  a  peculiarly  con- 
structed steam-bath,  VP  V,  by  which  the  substance  is  previously 
heated  to  a  known  temperature  of  about  100°. 

The  substance  to  be  examined  is  placed  in  a  small  basket  of 
brass  wire,  P.  If  it  is  solid,  it  is  broken  into  small  lumps  ;  but 
if  liquid,  it  is  enclosed  in  tubes  of  glass,  whose  weight  and  spe- 
cific heat  are  known.  In  the  axis  of  the  basket  there  is  fastened 
a  small  cylinder  of  wire-netting,  which  receives  the  bulb  of  a 
delicate  thermometer  for  determining  the  temperature  of  the 
basket  and  its  contents.  During  the  process  of  heating,  the 
basket  is  suspended  by  means  of  silk  cords  in  the  interior  of  a 

*  Annales  de  Chimie  ct  de  Physique,  2e  Serie,  Tom.  LXXIII.  p.  20. 
40 


470 


CHEMICAL  PHYSICS. 


steam-bath,  formed  of  three  concentric  cylinders  of  tin  plate. 
The  space  P,  in  which  the  basket  is  suspended,  is  filled  with  air, 
and  opens  below  into  the  chamber  M  by  means  of  the  slide  r  r, 
which  can  be  withdrawn  at  pleasure.  The  space  V  is  filled  with 


Fig.  364. 

steam,  which  is  constantly  supplied  from  the  boiler  C,  and  after- 
wards  condensed  in  the  worm  s ;  and,  lastly,  the  space  between 
the  steam-chamber  and  the  outer  cylinder  is  filled  with  air,  which, 
being  a  non-conductor,  diminishes  the  loss  of  heat  by  the  bath, 
and  thus  tends  to  keep  its  temperature  constant. 

A  cylindrical  vessel,  w,  made  of  very  thin  sheet-brass,  contains 
the  water  with  which  the  substance  is  to  be  mixed.  It  is  sus- 
pended, by  means  of  silk  cords,  to  a  movable  support,  which 
slides  in  a  groove,  so  that  the  vessel  may  be  readily  moved  into 
the  chamber  M,  under  the  steam-bath.  A  delicate  thermometer, 
t,  gives  very  accurately  the  temperature  of  the  water,  and  a 
second  thermometer,  T,  that  of  the  air.  These  thermometers 
are  observed  by  means  of  a  telescope  placed  several  feet  distant, 
and  every  precaution  is  taken  to  protect  them  from  extraneous 
influences. 

In  making  a  determination  of  the  specific  heat  of  a  substance, 
we  wait  until  the  thermometer  P  indicates  a  constant  tempera- 
ture, which  requires  about  two  hours.  Then,  in  order  to  be  sure 
that  the  substance  has  the  same  temperature  throughout,  we 
wait  at  least  an  hour  longer,  and  carefully  observe  the  thermom- 
eters t  and  T.  Having  removed  the  screen  e,  we  now  push  the 
vessel  m  into  the  chamber  M,  and,  withdrawing  the  slide  r  ry 


HEAT.  471 

quickly  drop  the  basket  containing  the  substance  into  the  water. 
The  vessel  is  then  at  once  returned  to  its  former  position,  and, 
while  an  assistant  stirs  up  the  water,  we  observe  the  elevation  of 
temperature  indicated  by  the  thermometer  t,  which  reaches  its 
maximum  in  one  or  two  minutes. 

In  calculating  the  specific  heat  of  a  substance  from  these 
results  by  means  of  [159] ,  it  is  necessary  to  take  into  the  ac- 
count the  quantity  of  heat  received  by  the  vessel  m  from  the  air 
or  neighboring  bodies  during  the  course  of  the  experiment,  as 
well  as  that  which  it  loses  during  the  same  time.  The  variation 
of  temperature  arising  from  this  cause  is  ascertained  by  means 
of  a  series  of  preliminary  experiments,  made  under  the  same 
conditions  as  the  final  determination,  and  the  observed  tempera- 
ture of  t  corrected  accordingly  ;  but  as  the  value  of  this  correc- 
tion is  necessarily  somewhat  uncertain,  it  is  made  very  small  by 
reducing  as  much  as  possible  the  duration  of  the  experiments, 
and  also  by  so  regulating  the  temperature  of  the  water  that  it 
may  be  for  an  equal  length  of  time  above  and  below  the  temper- 
ature of  the  air.  Moreover,  during  the  few  seconds  that  the 
vessel  of  water  is  in  the  chamber  M,  it  is  protected  from  the  heat 
of  the  steam-bath  by  the  cold  water  which  fills  the  space  within 
the  hollow  walls  D  D  ;  and  when  outside  of  the  chamber,  it  is 
also  protected  by  the  screen  e. 

In  order  to  test  the  accuracy  of  this  process,  Regnault  deter- 
mined the  specific  heat  of  water  with  the  apparatus  just  described. 
In  two  experiments,  in  which  the  liquid  was  heated  to  97°,  he 
obtained  the  values  1.00709  and  1.00890,  thus  showing  that  the 
specific  heat  of  water  increases  with  the  temperature,  and  also 
confirming  the  accuracy  of  the  method. 

(234.)  General  Results.  —  From  the  numerous  investigations 
which  have  been  made  on  the  specific  heat  of  solid  and  liquid 
substances,  several  important  general  truths  have  been  deduced. 

First.  The  specific  heat  of  substances  is  a  distinguishing  prop- 
erty, closely  connected  with  their  atomic  weights  or  combining 
proportionals.  The  relation  which  exists  between  these  two 
qualities  of  matter  has  already  been  discussed  in  (215  bis)  and 
will  also  appear  on  solving  Prob.  292. 

Secondly.  The  specific  heat  of  the  same  substance  increases 
with  the  temperature.  This  is  true  even  in  the  case  of  water, 
which  has  been  selected  as  the  standard  to  which  the  specific 


472 


CHEMICAL   PHYSICS. 


heat  of  other  substances  is  referred.  The  unit  of  heat,  it  will 
be  remembered,  is  the  quantity  of  heat  required  to  raise  the 
temperature  of  one  kilogramme  of  water  one  Centigrade  degree. 
Now  it  might  be  supposed  that  the  same  quantity  of  heat  would 
raise  the  temperature  of  a  kilogramme  of  water  one  degree  at  all 
parts  of  the  thermometric  scale  ;.  but  this  is  not  the  case  :  to 
raise  the  temperature  of  one  kilogramme  of  water  from  100°  to 
101°  requires,  for  example,  1.0130  units  of  heat,  and,  as  a  general 
rule,  the  amount  required  is  greater  the  higher  the  temperature. 
This  is  shown  by  the  following  table.  In  the  second  column, 
headed  c,  opposite  to  each  temperature,  is  given  the  specific  heat 
of  water  at  that  temperature ;  in  other  words,  the  number  of 
units  of  heat  required  to  raise  the  temperature  of  one  kilo- 
gramme of  water  from  t°  to  (t  -f- 1)°.  In  the  third  column, 
headed  C,  are  given  the  mean  specific  heats  for  the  interval  of 
temperature  between  0°  and  t°. 


t. 

c. 

C. 

t. 

c. 

C. 

0 

0 

1.0000 

1.0000 

100 

.0130 

1.0050 

20 

1.0012 

1.0005 

120 

.0177 

1.0067 

40 

1.0030 

1.0013 

140 

.0232 

1.0087 

60 

1.0056 

1.0023 

160 

.0294 

1.0109 

80 

1.0089 

1.0035 

180 

.0364 

1.0133 

It  will  be  noticed  that,  within  the  ordinary  range  of  atmos- 
pheric temperatures,  the  specific  heat  of  water  increases  only 
very  slightly  ;  so  that,  in  determinations  of  the  specific  heat  of 
other  substances  by  the  method  of  mixtures,  that  of  water  may 
be  regarded  as  constant  between  0°  and  20°.  But  above  this 
temperature  the  increase  of  the  specific  heat  of  water  can  no 
longer  be  disregarded,  and  we  must  therefore  modify  slightly  our 
definition  of  the  unit  of  heat.  Accurately  speaking,  the  unit 
of  heat  is  the  quantity  of  heat  required  to  raise  the  temperature 
of  a  kilogramme  of  water  from  0°  to  1°. 

What  is  shown  by  the  above  table  to  be  true  of  water,  is  also 
true  of  all  other  solids  and  liquids.  Dulong  and  Petit  made 
experiments  on  a  number  of  metals  up  to  300°,  employing  the 
method  of  mixtures,  and  obtained  the  results  given  in  the  follow- 
ing table  :  — 


HEAT. 


473 


Mean  Specific  Heat. 

Mean  Specific  Heat 

Name  of 
Metal. 

Between      Between 

T. 

Metal. 

Between 

Between 

T. 

0°  &  100°    0°  &  300°. 

0°  &  100°. 

0°  &  300°. 

Iron, 

0.1098 

0.1218 

332^2 

Silver, 

0.0557 

0.0611 

32:>!3 

Mercury, 

0.0330 

0.0350 

318.2 

Copper, 

0.09J9 

0.1013 

320.0 

Zinc, 

0.0927 

0.1015 

328.5 

Platinum, 

0.0335 

0.0355 

317.9 

Antimony, 

0.0507 

0.0549 

324.8 

Glass, 

0.1770 

0.1990 

322.2 

In  equation  [159],  the  temperature  T  is  supposed  to  be  given, 
and  from  it  we  can  calculate  the  specific  heat  of  the  substance ; 
but  we  may  evidently  reverse  this  calculation,  and,  when  the 
specific  heat  of  the  substance  is  known,  use  the  method  of  mix- 
tures for  determining  its  temperature.  Thus  this  method  fur- 
nishes a  very  simple  means  of  measuring  high  temperatures.  If, 
for  example,  we  wish  to  measure  the  temperature  of  a  furnace, 
we  expose  to  it  a  mass  of  platinum  of  known  weight ;  and  when 
the  mass  has  acquired  the  temperature  of  the  furnace,  we  transfer 
it  to  the  brass  vessel  m  (Fig.  364),  containing  a  known  weight  of 
water,  and  observe  the  elevation,  taking  all  the  precautions  men- 
tioned in  the  previous  section.  If  the  specific  heat  of  the  plati- 
num is  known,  we  then  have  all  the  elements  for  calculating  the 
temperature.  If  it  is  not  known,  we  can  make  two  determina- 
tions with  unequal  quantities  both  of  platinum  and  water,  and 
thus  obtain  two  equations,  from  which  we  can  eliminate  the 
specific  heat.  Or,  since  the  mean  specific  heat  of  platinum  is 
known  between  0°  and  different  high  temperatures,  we  can  also 
calculate  the  temperature  of  the  furnace  from  an  estimate  of  the 
value  of  the  specific  heat  for  the  unknown  temperature,  and 
afterwards  use  the  specific  heat  corresponding  to  the  tempera- 
ture thus  obtained  for  calculating  a  new  value  of  the  temperature, 
which  will  be  more  exact.  In  order  to  furnish  the  data  for  such 
calculation,  M.  Pouillet  has  determined  by  experiment  the  mean 
specific  heat  of  platinum  between  0°  and  different  high  tempera- 
tures, measured  by  the  air  thermometer.  His  results,  which 
are  given  in  the  following  table,  were  obtained  by  the  method 
of  mixtures. 

Mean  Specific  Heat  of  Platinum. 


0  to  100 

0  "  300 

0  «  500 

0  "  700 


0.03350 
0.03434 
0.03518 
0.03602 
40* 


0  to  1000  0.03728 
0  "  1200  0.03818 
0  "  1500  0.03938 


474 


CHEMICAL   PHYSICS. 


The  change  of  the  specific  heat  with  the  temperature  becomes 
very  marked  as  the  solid  approaches  its  melting  point ;  and  this 
is  especially  the  case  with  those  solids  which  soften  before  they 
melt.  Hence,  in  stating  the  specific  heat  of  a  substance,  it  is 
important  to  name  the  temperatures  between  which  the  deter- 
mination was  made. 

The  specific  heat  of  liquids  varies  with  the  temperature  to  a 
much  greater  extent  than  that  of  solids.  Thus  bromine,  according 
to  Regnault,  has  the  specific  heats  0.10513,  0.11094,  0.11294, 
between  the  temperatures  —6°  and  +10°,  11°  and  48°,  13°  and 
58°,  respectively.  So,  also,  oil  of  turpentine  has  the  specific  heat 
of  0.426  between  15°  and  20°,  and  0.4672  between  15°  and  100°. 

Regnault*  has  also  determined  the  specific  heat  of  a  large 
number  of  other  liquids  by  the  method  of  cooling,  which,  as  he 
found,  gives  more  accurate  results  with  liquid  than  with  solid 
substances.  Some  of  the  most  important  of  his  results  are  given 
in  the  following  table.  As  a  general  rule,  they  show  that  the 
specific  heat  increases  with  the  temperature.  But  the  difference 
between  the  extreme  temperatures  is  so  small,  that  the  slight 
increase  of  the  specific  heat  is,  in  some  cases,  more  than  over- 
balanced by  variations  arising  from  other  and  accidental  causes. 


Names  of  Liquids. 

Mean  Specific  Heat. 

5°  to  10°. 

10°  to  15°. 

15°  to  20°. 

Mercury,     ....   ;    ,.  •i(- 

0.0282 

0.0283 

0.0290 

Alcohol  at  36°,        .         .       ft 

0.6388 

0.6651 

0.6725 

Mcthylic  Alcohol,        .         .     ,    .  . 

0.5901 

0.5868 

0.6009 

Oxide  of  Ethyle,     .         .        ; 

0.5207 

0.5158 

0.5157 

Bromide  of  Ethyle,     .         .    :    %   ; 

0.2164 

0.2135 

0.2153 

Iodide  of  Ethyle,     .         »^-;j»Vr 

0.1587 

0.1584 

0.158  i 

Sulphide  of  Ethyle,    .  •  .  ...   »     ., 

0.4715 

0.4653 

0.4772 

Terebene,        ... 

0.4154 

0.4156 

0.4267 

Oil  of  Citron,      .  •     ..    '     .       '. 

0.4489 

0.4424 

0.4501 

Bichloride  of  Tin,  .        .  >     .    ; 

0.1421 

0.1402 

0.1J16 

Chloride  of  Silicon,     .        .    >   t 

0.1914 

0.1904 

0.1904 

Chloride  of  Phosphorus,          . 

0.2017 

0.1987 

0.1991 

Sulphide  of  Carbon,   . 

0.2179 

0.2183 

02206 

It  will  be  noticed  that  the  increase  of  the  specific  heat  with 
the  temperature  corresponds  to  the  increase  of  the  rate  of  expan- 
sion, and  it  is  probable  that  the  two  classes  of  phenomena  are 

*  Annales  de  Chimie  et  de  Physique,  3e  Serie,  Tom.  IX.  p.  336. 


HEAT. 


475 


closely  connected  together.  The  best  explanation  which  we  can 
give  of  the  facts  is  this.  If  the  volume  of  a  solid  or  liquid  mass 
of  matter  remained  the  same  at  all  temperatures,  it  is  probable 
that  it  would  require  exactly  the  same  quantity  of  heat  to  raise 
its  temperature  one  degree  at  all  parts  of  the  thermometric  scale. 
As,  however,  both  solid  and  liquid  matter  are  expanded  by  heat 
with  an  irresistible  force,  a  portion  of  the  quantity  of  heat  re- 
quired to  raise  the  temperature  of  a  given  mass  one  degree  is 
rendered  latent  in  producing  this  mechanical  effect ;  and  since 
the  rate  of  expansion  increases  with  the  temperature,  the  quan- 
tity of  heat  thus  rendered  latent,  and  hence  also  the  specific 
heat,  must  be  greater  at  high  than  at  low  temperatures. 

Thirdly.  All  substances  have  a  greater  specific  heat  in  the 
liquid  than  in  the  solid  state.  This  truth,  which  is  rendered 
evident  by  the  following  table,  is  probably  connected  with  the 
fact  that  the  rate  of  expansion  of  liquids  is  greater  than  that  of 
solids,  and  hence  the  quantity  of  heat  absorbed  in  producing  this 
mechanical  effect  is  also  greater. 


Xunie  of  Substance. 

Solid 

Liquid 

U 

Interval  of 
Temperature. 

Specific 
Heat. 

Interval  of 
Temperature. 

Specific 
Heat. 

0                               0 

0                             0 

Lead,  

0  to   100 

0.0314 

350    to   450 

0.0402 

Bromine,  .... 

-78    «   -20 

0.08432 

10    u      48 

0.1109 

0    «    100 

0.05412 

0.10822 

Mercury,  .... 

-78    u   -40 

0.0247 

0    u    100 

0.0333 

Sulphur,       .... 

0    «    100 

0.2026 

120    «    150 

0.234 

Bismuth,  .... 

0    «    100 

0.03084 

230    u    380 

0.0363 

Zinc,    

0    «    100 

0.0956 

Tin,           .... 

0    «    100 

0.0562 

250    «    350 

0.0637 

Phosphorus, 

10    «      30 

0.1887 

50    «    100 

0.212 

Water,      .... 

under    0 

0.502 

0    «      20 

1.0000 

Chloride  of  Calcium  (cryst), 

«       0 

0.315 

33    u      80 

0.555 

Nitrate  of  Soda, 

0  to   100 

0.27821 

320    «    430 

0.413 

Nitrate  of  Potassa,        . 

0    «    100 

0.23875 

350    «    435 

0.3319 

Fourthly.  The  specific  heat  varies  with  the  molecular  condi- 
tion of  a  substance,  and  we  can  say,  in  general,  that  all  causes 
which  increase  the  density  of  a  solid  diminish  its  specific  heat. 
Thus  the  specific  heat  of  artificially  prepared  sesquioxide  of  iron 
diminishes  in  proportion  as  its  density  is  increased  by  calcination, 
and  finally  becomes  equal  to  that  of  the  natural  iron  glance.  So 
also  copper,  when  annealed,  has  a  specific  heat  equal  to  0.09501; 


476  CHEMICAL  PHYSICS. 

but  after  its  density  has  been  increased  by  hammering,  the  spe- 
cific heat  is  found  to  be  only  0.09360.  On  the  other  hand,  the 
specific  heat  of  tin  or  lead  is  not  increased  by  mechanical  prej?- 
sure  ;  but  then  their  density  also  remains  unchanged. 

The  specific  heat  of  a  substance,  moreover,  is  not  the  same  in 
its  different  allotropic  modifications.  The  specific  heat  of  car- 
bon, for  example,  differs  very  greatly  in  its  three  allotropic  condi- 
tions, as  is  shown  by  the  following  results  of  Regnault.  It  will 
be  noticed  that  in  these  cases,  also,  the  specific  heat  diminishes 
with  the  density.  Similar  facts  were  observed  by  Regnault  *  in 
the  case  of  sulphur  and  carbonate  of  lime. 

Specific  Gravity.     Specific  Heat. 

Wood  Charcoal,     W|i|     .     **'£       .     0.300  0.2415 

Graphite,       .     Vtf*      .         .         .         2.300  0.2027 

Diamond,       '»' /i:     .         .      ,'.         .     3.500  0.1469 

Fifthly.  By  referring  to  the  tables  011  pages  466, 475,  it  will  be 
seen  that  liquid  water  has  the  greatest  specific  heat  of  any  of  the 
substances  mentioned.  In  fact,  for  the  same  temperature,  it 
contains  the  greatest  amount  of  heat  of  any  solid  or  liquid 
known.  This  property  of  water  makes  the  oceans  of  the  globe 
great  reservoirs  of  heat,  and  hence  the  important  influence  which 
they  exert  in  moderating  and  equalizing  the  climate  of  islands 
and  continents. 

On  the  other  hand,  it  will  be  noticed  that  mercury  has  a  very 
small  specific  heat.  It  is  therefore  rapidly  heated  or  cooled,  and 
is  in  this  respect  also,  as  in  others  (225),  well  adapted  for  its 
use  in  the  thermometer. 

(235.)  Specific  Heat  of  Gases.  —  The  determination  of  the 
specific  heat  of  gases  involves  the  greatest  practical  difficulties, 
and  although  several  extended  investigations  of  the  subject  have 
been  made  by  eminent  physicists,  yet  the  results  obtained  have 
been  generally  very  erroneous.  Within  a  few  years,  the  subject 
has  been  reinvestigated  by  Regnault,  and  his  determinations  of 
the  specific  heat  of  the  gases  are,  unquestionably,  far  more  accu- 
rate than  those  of  any  previous  experimenter.  Unfortunately, 
however,  as  no  description  of  the  process  employed  by  Regnault 
has  yet  been  published,  we  can  only  state  the  general  results  at 
which  he  has  arrived. 

The  specific  heat  of  a  gas  may  be  defined  in  two  ways  :   first, 

*  Annales  de  Chimie  et  de  Physique,  3e  Serie,  Tom.  I.  pp.  182  and  202. 


HEAT.  477 

as  the  amount  of  heat  required  to  raise  the  temperature  of  one 
kilogramme  of  the  gas  from  0°  to  1°,  allowing  the  gas  to  expand 
freely  and  in  such  a  manner  that  it  shall  preserve  a  constant 
elasticity  ;  and,  secondly,  as  the  amount  of  heat  required  to 
raise  the  temperature  of  one  kilogramme  of  the  gas  from  0°  to 
1°  when  the  gas  is  compelled  to  preserve  a  constant  volume,  the 
tension  of  course  increasing.  We  may  distinguish  the  specific 
heats  under  these  two  conditions  as  the  specific  heat  under  con- 
stant pressure,  and  specific  heat  under  constant  volume.  In  the 
case  of  liquids  and  solids  we  can  only  determine  the  specific 
heat  under  constant  pressure,  and  in  the  case  of  gases  it  is  only 
this  value  which  can  be  determined  by  direct  experiment. 

(236.)  Specific  Heat  of  Gases  under  Constant  Pressure.  —  As 
preliminary  to  the  determination  of  the  specific  heats  of  the  sepa- 
rate gases,  Regnault  has  established  two  important  principles :  — 

First.  The  specific  heat  of  a  gas  does  not  vary  sensibly  with 
the  temperature.  This  is  illustrated  by  the  following  table,  which 
gives  the  specific  heat  of  air  between  different  limits  of  temperature. 

Interval  of  Temperature.  Specific  Heat. 

_30°     to    +10°  0.2377 

10°     "       100°  0.2379 

100°     «       225°  0.2376 

It  will  be  noticed  that  the  differences  are  inconsiderable,  and  the 
same  was  found  to  be  true  of  other  gases. 

Secondly.  The  specific  heat  of  a  gas  does  not  vary  with  the 
pressure,  and  hence  is  the  same  for  all  densities.  Regnault  ex- 
perimented on  air  and  on  other  gases  under  pressures  which 
varied  from  one  to  ten  atmospheres,  and  found  no  sensible  differ- 
ence in  the  quantity  of  heat  which  the  same  weight  of  a  gas 
lost,  when  under  these  different  pressures,  in  cooling  the  same 
number  of  degrees.  Nevertheless,  he  thinks  it  possible  that 
slight  differences  may  exist. 

The  specific  heats  of  the  different  gases  and  vapors,  as  de- 
termined by  Regnault,  are  given  in  the  following  table.  The 
numbers  in  the  column  headed  "  Specific  Heat  by  Weight " 
correspond  to  those  given  in  all  the  preceding  tables  of  specific 
heats,  and  denote  in  each  case  the  number  of  units  of  heat  re- 
quired to  raise  the  temperature  of  one  kilogramme  of  the  gas 
from  0°  to  1°,  assuming  that  the  gas  is  allowed  to  expand  freely, 
and  that  the  pressure  is  constant. 


478 


CHEMICAL  PHYSICS. 


Specific  Heat  of  Gases  and  Vapors. 


Name  of  Gas  or  Vapor. 

Specific  Heat. 

Specific 
Gravity. 

By  Weight. 

By  Volume. 

Simpk  Gases. 

Air 

0  2*177                   ft  OOTT 

1.0000 

Oxygen,      '-'-^    -  i  ''<>  ••>-•'  ;-"'-  .  '• 

Vr.£O  4  f 

0.2182 

0.2412 

1.1056 

0.2440 

0.2370 

0.9713 

Hydrogen,       .... 

3.4046 

0.2356 

0.0692 

0.1214 

0.2962 

2.4400 

Bromine,     '  V   ';",  '/'./'.     ' 

0.0552 

0.2992 

5.39 

Compound  Gases. 

Protoxide  of  Nitrogen, 

0.2238 

0.3413 

1.5250 

Deutoxide  of  Nitrogen,  . 

0.2315 

0.2406 

1.0390 

Oxide  of  Carbon, 

0.2479 

0.2399 

0.9674 

Carbonic  Acid,      --«•;'  fi  * 

0.2164 

0.3308 

1.5290 

Sulphide  of  Carbon,  . 

0.1575 

0.4146 

2.6325 

Sulphurous  Acid,    . 

0.1553 

0.3489 

2.2470 

Chlorohydric  Acid,    . 

0.1845 

0.2302 

1.2474 

Sulphohydric  Acid, 

0.2423 

0.2886 

1.1912 

Ammonia  Gas,    .... 

0.5080 

0.2994 

0.5894 

Marsh  Gas,     .... 

0.5929 

0.3277 

0.5527 

Olefiant  Gas  

0.3694 

0.3572 

0.9672 

Vapors. 

0  4750 

OOQKf) 

0.6210 

V.'d  4  O\J 
04C-I  O 

•MftfU 
07-1  71 

IEoqn 

Ether,      -  -^     .        .        .       i 

•  4Olo 

04Q  1  A 

.  /  1  /  1 

i   oonr* 

•  Ool/v/ 

2K  C/?O 

Cyanohydric  Ether, 

.48  1U 
0.4255 

I«9BM 
0.8293 

.oouo 
1.9021 

Chlorohydric  Ether,  .        .     '.    . 

0.2737 

0.6117 

2.2350 

Bromohydric  Ether,        .        i  ' 

0.1816 

0.6777 

3.7316 

Sulphohydric  Acid,    .        .     •  -A  U 

0.4005 

1.2568 

3.1380 

Acetic  Acid,    .        .    v;>        .;}", 

0.4008 

1.2184 

3.0400 

Chloroform,        .     .  ,     •>.       ,j 

0.1568 

0.8310 

5.30 

Dutch  Liquid,         .        .        . 

0.2293 

0.7911 

3.45 

01  |OK 

n  8Q.li 

9  fl990 

Benzole,          .... 

•  41^0 

0.3745 

U.oo41 

1.0114 

£t*\j£L\) 

2.6943 

Oil  of  Turpentine,      . 

0.5061 

2.3776 

4.6978 

Terchloride  of  Phosphorus,    . 

0.1346 

0.6386 

4.7445 

Terchloride  of  Arsenic, 

0.1122 

0.7013 

6.2510 

Chloride  of  Silicon, 

0.1329 

0.7788 

5.86 

Bichloride  of  Tin, 

0.0939 

0.8639 

9.2 

Bichloride  of  Titanium,  . 

0.1263 

0.8634 

6.8360 

HEAT.  479 

The  specific  heat  of  a  substance,  whether  it  be  a  solid,  a  liquid, 
or  a  gas,  is  always,  properly  speaking,  the  number  of  units  of 
heat  required  to  raise  the  temperature  of  one  kilogramme  from 
0°  to  1° ;  and  the  term  is  invariably  used  in  this  sense  in  relation 
to  both  solids  and  liquids.  But  in  the  case  of  gases  some  im- 
portant truths  have  been  discovered  by  comparing  together  the 
amounts  of  heat  required  to  raise  the  temperature  of  equal  vol- 
umes from  0°  to  1°,  irrespective  of  their  weight.  The  number  of 
units  required  can  in  any  case  be  readily  calculated  from  the 
specific  heat  and  the  specific  gravity  of  the  gas,  and  this  quantity 
is  usually  called  the  specific  heat  by  volume. 

By  referring  to  Table  II.,  it  will  be  found  that  one  cubic  metre 
of  air  at  0°,  and  under  a  pressure  of  76  c.  m.,  weighs  1.29206 
kilogrammes.  Hence,  by  [100],  one  cubic  metre  of  air  at  0°, 
and  under  a  pressure  of  58.75  c.  m.,  will  weigh  exactly  one  kilo- 
gramme ;  and  one  cubic  metre  of  any  other  gas  as  much  more 
or  less  than  one  kilogramme  as  its  specific  gravity  is  greater  or 
less  than  1.  In  other  words,  the  number  which  stands  for  the 
specific  gravity  also  expresses  the  weight  of  one  cubic  metre 
under  the  above  conditions  of  temperature  and  pressure.  Now, 
since  the  quantity  of  heat  required  to  raise  the  temperature  of 
any  mass  of  matter  from  0°  to  1°  may  be  found  by  multiplying 
the  specific  heat  of  the  substance  by  its  weight  (232),  it  is  evi- 
dent that  we  can  find  the  quantity  of  heat  required  to  raise  from 
0°  to  1°  the  'temperature  of  one  cubic  metre  of  any  gas  under 
the  pressure  of  58.75  c.  m.,  by  multiplying  together  the  specific 
heat  of  the  gas  and  the  number  representing  its  specific  gravity. 
For  example,  the  specific  heat  of  hydrogen  is  3.4046,  and  its 
specific  gravity  0.0692.  The  product  of  these  two  numbers 
equals  0.2356,  which  is  the  fractional  part  of  a  unit  of  heat 
required  to  raise  the  temperature  of  one  cubic  metre  of  hydro- 
gen, measured  under  a  pressure  of  58.75  c.  m.,  from  0°  to  1°. 
In  like  manner  all  the  numbers  in  the  column  of  the  last  table 
headed  "  Specific  Heat  by  Volume  "  were  obtained.  These 
numbers  evidently  represent  the  relative  quantities  of  heat  re- 
quired to  raise  the  temperature  of  equal  volumes  of  different 
gases  from  0°  to  1°,  and  the  absolute  number  of  units  of  heat 
required  to  raise  the  temperature  of  one  cubic  metre  of  the  dif- 
ferent gases  measured  under  a  pressure  of  58.75  c.  m.  from 
0°  to  1°. 


480  CHEMICAL  PHYSICS. 

By  comparing  the  numbers,  it  will  be  seen  that  the  specific 
heats  by  volume  of  the  simple  gases  differ  but  slightly  from  each 
other.  Indeed,  the  difference  is  so  small,  that  some  experiment- 
ers have  concluded  that  the  specific  heats  of  all  the  simple  gases 
are  the  same.  The  results  of  Regnault  do  not  confirm  this 
theory  ;  for  although  the  specific  heats  by  volume  of  oxygen, 
nitrogen,  and  hydrogen  are  by  his  'determinations  very  nearly 
equal,  those  of  chlorine  and  bromine  are  much  greater  than  the 
rest,  although  equal  to  each  other.  These  differences,  moreover, 
are  too  large  to  be  accounted  for  by  errors  of  observation,  and 
probably  depend  on  inherent  qualities  of  the  gases  themselves. 

(237.)  Specific  Heat  of  Gases  under  Constant  Volume.  —  It 
was  stated  in  (234),  that  a  portion  of  the  quantity  of  heat  re- 
quired to  raise  the  temperature  of  a  given  mass  of  matter  one 
degree  was  rendered  latent  in  producing  the  mechanical  effect 
of  expansion,  and  that,  if  this  expansion  could  be  prevented,  the 
same  quantity  of  heat  would  probably  cause  the  same  elevation 
of  temperature  at  all  parts  of  the  thermometer-scale.  In  the 
case  of  solids  and  liquids  it  is  evidently  impossible  to  verify  this 
theory,  since  they  expand  with  an  irresistible  force.  We  do  not 
meet  with  the  same  difficulty  in  the  case  of  gases.  They  are 
easily  compressed,  so  that  their  volume  can  be  kept  constant 
by  enclosing  them  in  an  unyielding  vessel ;  and  we  should  there- 
fore naturally  expect  to  be  able  to  put  our  theory  to  the  test  of 
experiment.  Now  it  is  a  perfectly  well-known  fact,  that  a  cer- 
tain amount  of  heat  is  rendered  latent  in  producing  the  expansion 
of  a  given  mass  of  gas,  and  that,  on  condensing  the  gas  to  its 
original  volume,  the  same  amount  of  heat  is  set  free.  Indeed, 
the  temperature  of  a  confined  mass  of  air  can  be  raised  by  sudden 
mechanical  condensation  sufficiently  high  to  ignite  tinder. 

If  we  could  measure,  then,  the  quantity  of  heat  set  free  by 
mechanical  condensation,  we  should  be  able  to  determine  the 
quantity  absorbed  during  the  equivalent  expansion ;  and  since 
we  know  the  quantity  of  heat  required  to  raise  the  temperature 
of  one  kilogramme  of  gas  from  0°  to  1°  when  allowed  to  expand 
freely,  we  should  be  able  to  determine  the  quantity  of  heat  re- 
quired to  raise  its  temperature  from  0°  to  1°  when  confined  and 
not  allowed  to  expand,  by  simply  subtracting  the  amount  ab- 
sorbed during  expansion. 

It  has  been  stated  that  at  0°,  and  under  a  pressure  of  58.75 


HEAT.  481 

c.m.,  one  cubic  metre  of  air  weighs  one  kilogramme  ;  and  it  has 
been  shown  that,  in  order  to  raise  the  temperature  of  this  mass 
of  air  one  degree,  (the  pressure  remaining  the  same,)  we  must 
impart  to  it  0.2377  unit  of  heat.  But  it  is  also  true  that,  in 
consequence  of  the  increase  of  temperature,  the  volume  of  the 
one  kilogramme  has  increased  ^1^,  that  is,  from  1  to  I^i3  cubic 
metres  (216).  If  now,  by  increasing  the  pressure,  we  condense 
the  gas  to  its  initial  volume  of  one  cubic  metre,  a  certain  amount 
of  heat  will  be  set  free,  sufficient,  as  we  will  assume,  to  raise  the 
temperature  of  the  kilogramme  of  air  from  1°  to  1°.42.  This 
shows  that  although  0.2377  unit  of  heat  will  raise  the  tempera- 
ture of  one  kilogramme  of  air  only  one  degree,  when  allowed  to 
expand  under  a  constant  pressure,  it  will  raise  the  temperature 
of  the  same  mass  of  air  1°.42  when  confined  and  preserving  a 
constant  volume.  If,  then,  0.2377  unit  of  heat  will  raise  the 
temperature  of  one  kilogramme  of  air  1°.42,  it  is  easy  to  calcu- 
late how  much  will  be  required  to  raise  its  temperature  one  de- 
gree by  means  of  the  proportion  1.42  :  1  =  0.2377  :  x  =  0.1674. 
This  quantity  is  the  specific  heat  of  air  under  constant  volume, 
and  the  difference  between  0.1674  and  0.2377,  or  0.0703  unit,  is 
the  amount  of  heat  rendered  latent  in  producing  the  expansion 
when  the  air  is  under  constant  pressure. 

It  is  evident  from  the  above  illustration,  that,  if  we  represent 
by  S  the  specific  heat  of  a  gas  under  constant  pressure,  and  by  t 
the  small  increase  of  temperature  which  a  mass  of  gas  undergoes 
when  condensed  ?$x  of  its  volume,  we  can  always  calculate  the 
specific  heat  under  constant  volume,  or  /S',  by  the  proportion 
1  -f  t  :  1  =  S  :  S',  which  gives  for  the  value  of  S', 


An  obvious  method  of  determining  experimentally  the  specific 
heat  of  a  gas  under  constant  volume  would  then  be  to  condense 
the  gas  by  mechanical  means,  and  observe  the  increase  of  tem- 
perature. Such  experiments  have  been  made,  but  the  results 
have  been  in  all  cases  erroneous,  in  consequence  of  the  unavoid- 
able loss  of  heat,  which  was  absorbed  by  the  walls  of  the  con- 
taining vessel.  —  In  like  manner,  when  we  attempt  to  determine 
the  specific  heat  of  gases  under  constant  volume  by  other  direct 
methods,  we  are  met  at  once  by  practical  difficulties  of  a  similar 
41 


482  CHEMICAL  PHYSICS. 

kind,  and  no  process  has  as  yet  been  discovered  which  will  give 
accurate  results.  We  are  therefore  obliged  to  resort  to  indirect 
methods  ;  and  fortunately  such  a  method  is  furnished  by  the 
principles  of  acoustics. 

By  analyzing  the  condition  of  an  elastic  fluid  during  the  trans- 
mission of  a  sonorous  wave,  Newton  obtained,  for  the  value  of  the 
velocity  of  sound  in  any  gas,  the  expression 


in  which  g-  represents  the  intensity  of  gravity,  H  the  height  of 
the  barometer,  and  d  the  specific  gravity  of  the  gas  referred  to 
mercury  as  unity.  This  formula  gives  for  the  velocity  of  sound 
in  dry  air,  at  0°  and  when  H  =  76  c.  m.,  the  value  t)  =  279.3 
metres,  which  is  less  than  332.25  metres,  the  true  value  as  ascer- 
tained by  experiment,  by  over  one  sixth  of  the  whole.  The  cause 
of  this  great  discrepancy  between  the  observed  and  calculated 
velocity  remained  for  a  long  time  unexplained,  until  Laplace 
showed  that  the  alternate  expansion  and  contraction  of  the 
elastic  fluid,  constituting  the  sound-wave,  must  produce  a  change 
of  temperature,  which  would  increase  the  velocity  of  the  trans- 
mission of  the  wave  itself.  In  order  to  take  into  account  the 

TT 

effect  thus  produced,  Laplace  multiplied  the  quantity  g  .  —  in 
the  formula  of  Newton  by  the  quotient  -^7,  obtained  by  dividing 

the  specific  heat  of  the  gas  under  constant  pressure  by  the  spe- 
cific heat  under  constant  volume.-  As  thus  corrected,  the  formula 
of  Newton  becomes 


H     S_ 
=  *'*  '  T"  S1' 

By  transformation,  we  easily  obtain  from  this  equation  the  ex- 
pression, 

S'  =sSL'-H'-_?,  [163.] 

t)2<5 

by  which  we  can  calculate  the  specific  heat  of  a  gas  under  con- 
stant volume,  when  the  velocity  of  sound  in  the  medium  and 
the  other  constants  are  known.  Now  the  velocity  of  sound  in 
air  has  been  several  times  carefully  determined  by  direct  experi- 
ment, and  is  probably  known  within  a  metre  ;  and  starting  from 


HEAT. 


483 


the  velocity  in  air,  the  science  of  acoustics  furnishes  the  means 
of  determining  the  velocity  in  other  gases.  Thus  it  is  that  we 
have  been  able  to  determine  some  of  the  most  refined  data  con- 
nected with  the  thermal  condition  of  matter,  by  means  of  phe- 
nomena which  at  first  sight  seem  entirely  independent  of  the 
action  of  heat. 

The  specific  heat  under  constant  volume  of  several  gases,  as 
determined  by  Dulong  by  means  of  the  method  just  described, 
is  given  in  the  second  column  of  the  following  table ;  but  these 
values  must  be  regarded  as  only  approximations.  The  corre- 
sponding values  of  specific  heat  under  constant  pressure  are 
given  in  the  first  column,  repeated  from  the  table  on  page  472, 
for  the  sake  of  comparison.  The  third  column  shows  the  differ- 
ence between  the  specific  heat  under  the  two  circumstances,  and 
the  last  gives  the  value  of  1  -{-  t  in  formula  [160] . 

Specific  Heat  of  Equal  Volumes. 


Name  of  Gas. 

Under  Con- 
stant Pressure. 
S. 

Under  Con- 
stant Volume. 
#. 

Difference. 
S—S. 

l  +  <. 

Air,    

0.2377 

0.1673* 

0.0704 

.421 

Oxygen, 

0.2412 

0.1705 

0.0707 

.415 

Hydrogen,  .... 

0.2356 

0.1675 

0.0681 

.407 

Oxide  of  Carbon,    . 

0.2399 

0.1681 

0.0718 

.428 

Carbonic  Acid,  . 

0.3308 

0.2472 

0.0836 

.338 

Olefiant  Gas,:  . 

0.3572 

0.2880 

0.0692 

.240 

The  numbers  in  the  first  column  of  the  above  table  repre- 
sent the  fractional  part  of  one  unit  of  heat  required  to  raise  the 
temperature  of  one  cubic  metre  of  each  gas  (measured  under 
a  pressure  of  58.75  c.  m.)  from  0°  to  1°,  the  pressure  remain- 
ing constant,  the  gas  being  allowed  to  expand  freely,  and  in- 
creasing in  volume  2fT  of  a  cubic  metre.  The  numbers  in  the 
second  column  represent  the  corresponding  quantity  of  heat 
required  when  the  volume  is  kept  constant  by  increasing  the 
pressure.  The  difference  of  these  quantities,  or  S —  S',  is,  then, 
the  quantity  of  heat  absorbed  by  one  cubic  metre  of  each  gas, 
measured  as  above  described,  in  expanding  ^fa  of  its  initial 
volume. 


*  By  using  the  more  recently  determined  constants,  we  should  obtain,  for  the  value 
of  >S',  0.1678,  and  for  1  + 1  the  value  1.417. 


484  CHEMICAL  PHYSICS. 

By  comparing  the  quantity  of  heat  thus  rendered  latent  in 
the  case  of  air  with  that  which  remains  free,  and  consequently 
raises  the  temperature  of  the  gas,  it  will  be  found  that  they  stand 
to  each  other  very  nearly  in  the  proportion  of  2  to  5.  Hence,  of 
seven  units  of  heat  imparted  to  a  mass  of  free  air  for  the  pur- 
pose of  increasing  its  temperature, —  as,  for  example,  in  warming 
the  air  of  a  room,  —  two  units  are  absorbed  in  expanding  the 
air,  so  that  the  elevation  of  temperature  results  entirely  from 
the  remaining  five. 

By  comparing  the  values  of  S —  £>',  it  will  be  noticed  that  the 
quantity  of  heat  absorbed  by  equal  volumes  of  these  different 
gases,  in  expanding  to  an  equal  extent,  is  very  nearly  the  same 
in  all  cases.  Dulong  has  verified  this  principle  in  the  case  of  a 
large  number  of  gases  not  included  in  the  above  table,  and  has 
stated  the  law  in  the. following  simple  terms  :  — 

1.  Equal  volumes  of  all  gases,  measured  at  the  same  tempera- 
ture and  pressure,  set  free  or  absorb  the  same  quantity  of  heat 
when  they  are  compressed  or  expanded  the  same  fractional  part 
of  their  volume. 

If  the  specific  heat  of  the  gases  were  all  equal,  the  same 
change  of  volume,  and  consequently  the  same  absorption  or 
liberation  of  heat,  would  cause  the  same  change  of  temperature. 
This,  however,  is  not  the  case,  except  with  oxygen,  hydrogen,  and 
nitrogen.  The  specific  heats  of  the  compound  gases  differ  very 
considerably  from  each  other,  and  the  change  of  temperature 
caused  by  the  same  change  of  volume  is  smaller  in  proportion  as 
the  specific  heat  of  the  gas  is  greater.  Hence  the  second  law  of 
Dulong,  which  should  be  read  in  connection  with  the  first. 

2.  The  variations  of  temperature  which  result  are  in  the  in- 
verse ratio  of  the  specific  heats  under  constant  volume. 

Whether  these  empirical  laws  of  Dulong  are  the  exact  expres- 
sions of  the  truth,  or  whether  they  are  merely  close  approxima- 
tions, remains  yet  to  be  ascertained  by  further  investigation. 

(238.)  Mechanical  Equivalent  of  Heat.  —  The  doctrine  of  the 
conservation  of  the  physical  forces  has  furnished,  through  the 
investigations  of  Joule  on  the  mechanical  equivalent  of  heat,  a 
most  remarkable  confirmation  of  the  results  of  the  last  section. 
According  'to  this  doctrine,  there  is  an  exact  equivalency  of  cause 
and  effect  between  all  the  forces  of  nature.  Thus,  in  the  case 
af  heat,  it  would  assume  that  a  given  mechanical  effect  would, 


HEAT. 


485 


under  all  circumstances,  be  accompanied  by  the  absorption  of 
the  same  amount  of  heat ;  and  conversely,  that  the  same  quantity 
of  heat  should,  under  all  conditions,  do  the  same  amount  of 
mechanical  work  —  for  example,  should  raise  a  given  weight 
through  the  same  height  —  in  whatever  way  it  may  be  applied. 
It  is  a  well-known  fact,  that  friction  is,  under  all  circum- 
stances, attended  with  evolution  of  heat.  Now,  since  friction 
represents  the  expenditure  of  force,  it  follows  that  the  quantity 
of  heat  evolved  by  friction  is  the  equivalent  of  the  mechanical 
force  expended  in  overcoming  it.  Joule  was  therefore  able  to 
fix  the  mechanical  equivalent  of  heat,  by  measuring  the  quantity 
of  heat  generated  by  friction,  and  comparing 
this  with  the  power  (42)  expended  in  over- 
coming the  friction.  The  heat  was  generated 
by  the  friction  of  water,  and  the  apparatus  he 
used  for  the  purpose  is  represented  in  Fig. 
365.  It  consisted  of  a  brass  paddle-wheel, 
furnished  with  eight  sets  of  revolving  arms, 
working  between  four  sets  of  stationary  vanes 
affixed  to  a  framework,  also  of  sheet-brass. 
This  frame  fitted  firmly  into  a  copper  vessel 
containing  from  six  to  seven  kilogrammes  of 
water.  In  the  lid  of  the  vessel  there  were  two  necks,  the  first  for 
the  axis  to  revolve  in  without  touching,  the  second  for  the  inseiv 
tion  of  the  thermometer.  The  paddle-wheel  was  set  in  motion 


Fig.  305. 


Fig.  366. 


by  means  of  two  weights  connected  with  its  axis  by  a  system  of 
cords  and  pulleys,  as  represented  in  Fig.  366.  In  making  the 
experiments,  the  weights  were  wound  up  by  means  of  the  handle 
vy  attached  to  the  wooden  cylinder  v  s,  and  after  observing  the 
41* 


486  CHEMICAL  PHYSICS. 

temperature  of  the  water  in  the  vessel,  the  cylinder  was  fixed  to 
the  axis  of  the  paddle,  which  was  then  made  to  revolve  by  the  fall 
of  the  weights  to  the  floor  of  the  laboratory,  causing  a  friction 
against  the  water  in  the  vessel.  The  cylinder  was  then  removed 
from  the  axis,  the  weights  wound  up  again,  and  the  friction  re- 
newed. After  this  had  been  repeated  twenty  times,  the  experi- 
ment was  concluded  with  another  observation  of  the  temperature 
of  the  water.  The  mean  temperature  of  the  laboratory  was 
determined  by  observations  made  at  the  beginning,  middle,  and 
end  of  the  experiment,  and  the  quantity  of  heat  which  the  vessel 
lost  by  radiation  and  other  causes  was  determined  in  every  case 
by  means  of  a  second  experiment,  made  under  precisely  the  same 
circumstances  as  the  first,  with  the  apparatus  at  rest.  It  was 
then  easy  to  calculate,  by  means  of  [159] ,  the  number  of  units 
of  heat  developed  by  the  friction  of  the  water,  since  the  weights 
of  the  copper  vessel,  of  the  brass  paddle  and  frame,  and  of  the 
water,  as  well  as  their  several  capacities  for  heat,  and  the  increase 
of  temperature  caused  by  the  friction  of  the  particles  of  water, 
were  known.  This  quantity  of  heat  was,  then,  evidently  the 
equivalent  of  the  mechanical  force  expended  in  moving  the 
paddles  and  overcoming  the  friction.  In  order  to  estimate 
the  mechanical  force  thus  expended,  the  value  of  the  weights, 
the  height  through  which  they  fell,  and  the  velocity  of  the 
fall,  were  accurately  measured. 

In  one  series  of  experiments,  the  value  of  the  weights  was 
406,152  grains,  the  total  fall  in  inches  1,260.248,  and  the  ve- 
locity 2.42  inches  per  second.  The  weight,  starting  from  the  state 
of  rest,  soon  acquired  the  velocity  of  2.42  inches,  and  afterwards 
moved  with  a  uniform  motion  until  it  reached  the  ground,  where 
the  velocity  was  destroyed.  During  the  uniform  motion,  it  is 
evident  that  the  intensity  of  the  force  of  gravity  acting  on  the 
weights  was  entirely  expended  in  overcoming  the  friction  of  the 
water  (42)  ;  but  before  the  motion  became  uniform,  a  portion 
of  the  force  was  expended  in  imparting  velocity  to  the  weights. 
The  whole  mechanical  power  expended  in  overcoming  the  fric- 
tion of  the  water,  and  thus  generating  heat,  is  then  the  power  gen- 
erated by  the  force  of  gravity  acting  on  the  mass  of  the  weights 
through  the  whole  distance  fallen,  less  the  power  generated  by 
the  same  force  acting  through  the  distance  required  to  impart 
a  velocity  of  2.42  inches.  By  [6],  we  find  that  a  fall  through 


HEAT.  487 

0.0076  of  an  inch  would  impart  a  velocity  of  2.42  ;  and  since  the 
weights  were  wound  up  twenty  times  in  each  experiment,  a  fall 
through  twenty  times  0.0076,  or  0.152  inch,  would  represent 
the  entire  loss  due  to  the  increase  of  velocity.  Hence  the  me- 
chanical power  expended  in  overcoming  the  friction  of  the  water 
was  a  force  having  the  intensity  of  406,152  grains,  acting  through 
1,260.096  inches.  Compare  (63). 

We  have  assumed,  in  this  estimate,  that  the  intensity  of  the 
force  of  gravity  was  entirely  expended  in  overcoming  the  friction 
of  the  whole  ;  but  this  was  not  the  case,  for  a  portion  of  the  force 
was  used  in  overcoming  the  friction  of  the  pulleys  and  the  rigid- 
ity of  the  cord.  This  was  ascertained  by  a  separate  experiment, 
in  which  the  pulleys  and  cord  were  disconnected  from  the  paddle- 
wheel,  to  be  equal  to  2,837  grains  acting  during  the  whole  time, 
which,  deducted  from  the  value  of  the  weights,  gives  403,315 
grains  for  the  actual  force  overcome  by  the  friction.  This 
force,  acting  through  1,260.096  inches,  is  equivalent  to  a  force  of 
6,050.186  pounds  acting  through  one  foot,  or,  using  the  technical 
expression,  to  6,050.186  foot-pounds.  But  in  order  to  obtain  the 
whole  power  overcome  by  the  friction,  we  must  add  to  this  amount 
16.928  foot-pounds  for  the  force  developed  by  the  elasticity  of 
the  string  after  the  weights  touched  the  ground,  making  the 
whole  mechanical  force  expended  in  overcoming  friction,  and 
thus  developing  heat,  equal  to  6,067.114  foot-pounds,  as  the  mean 
of  all  the  experiments  of  the  series.  The  same  series  of  experi- 
ments gave,  for  the  mean  value  of  the  quantity  of  heat  evolved, 
7.842299  English  units  ;  *  and  hence,  ^jj££  =  773.64  foot- 
pounds will  be  the  force  which  is  equivalent  to  one  English 
unit  of  heat. 

In  these  experiments  a  portion  of  the  force  is  used  in  over- 
coming the  resistance  of  the  air,  and,  making  the  correction 
necessary  to  reduce  the  results  to  a  vacuum,  and  omitting  the 
fraction,  we  get  772  foot-pounds  as  the  mechanical  equivalent, 
which  Joule  regards  as  the  most  probable  value.  Similar  experi- 
ments, in  which  the  friction  was  produced  by  an  iron  paddle- 
wheel  revolving  in  mercury,  and  others,  in  which  it  was  produced 
by  two  cast-iron  wheels,  gave  for  the  mechanical  equivalent  of  heat 
774  foot-pounds, —  a  number  which  is  surprisingly  near  the  first. 

*  The  English  unit  of  heat  is  the  quantity  of  heat  required  to  raise  one  avoirdupois 
pound  of  water  one  Fahrenheit  degree  between  55°  and  60°. 


488  CHEMICAL  PHYSICS. 

"We  have  given  the  above  calculation  in  English  weights  and 
measures,  because  it  is  so  given  in  the  original  memoir,*  to 
which  we  would  refer  for  further  details.  In  the  French  system, 
these  results  correspond  to  423  and  424  kilogramme-metres, 
or,  in  other  words,  the  unit  of  heat  is  equivalent  to  a  force  of 
423  kilogrammes  acting  through  one  metre. 

Let  us  now  see  in  what  way  these  results  of  Joule  confirm 
those  stated  in  the  last  section.  It  will  be  remembered  that  the 
value  of  the  specific  heat  of  air  under  constant  volume  was  de- 
duced from  the  velocity  of  sound.  This  value  furnishes  us  with 
all  the  data  required  for  calculating  the  mechanical  equivalent 
of  heat ;  and  if  the  doctrine  of  the  conservation  of  forces  is  cor- 
rect, the  equivalent  calculated  from  the  velocity  of  sound  ought 
to  agree  with  that  determined  by  Joule  from  his  experiments  on 
friction.  Such  an  agreement  would  not  only  confirm  the  value 
which  has  been  assigned  to  the  specific  heat  of  air,  but  it  would 
also  tend  to  confirm  the  doctrine  in  question. 

Let  us  suppose  that  we  have  a  cylinder,  the  area  of  whose  base 
equals  1  cTm.2,  filled  to  the  height  of  273  c.  m.  with  air  at  0°  and 
under  a  pressure  of  76  c.  m.  By  Table  II.  the  weight  of  this 
mass  of  air  would  be  equal  to  0.3531  gramme.  If  we  raise  the 
temperature  of  this  air  from  0°  to  1°,  it  will  expand  2^3  of  its 
volume ,  and  will  rise  in  the  cylinder  one  centimetre,  thus  lift- 
ing the  weight  of  the  atmosphere  on  the  base  of  the  cylinder  — 
1,033.3  grammes — through  this  distance.  The  quantity  of  heat 
required  to  raise  the  temperature  of  0.3527  gramme  of  air  from 
0°  to  1°  is,  by  (236),  equal  to  0.3527  X  0.000237,  or  0.0000836 
unit.  Of  this  amount,  a  part  only  is  consumed  in  expanding 
the  air,  the  rest  remaining  free  and  increasing  the  temperature 
of  the  mass  of  gas.  By  (237),  the  part  which  does  the  mechan- 
ical work  is  equal  to  the  difference  between  the  specific  heat  under 
constant  pressure  and  the  specific  heat  under  constant  volume. 
Hence,  in  the  present  case,  it  is  equal  to  [160] 

0.0000836  —  (0.0000836  -~  1.417)  =  0.0000246  unit  of  heat 

It  follows,  then,  that  in  the  expansion  of  air  0.0000246  unit  of 
heat  will  raise  1,033.3  grammes  one  centimetre,  or,  what  is  equiv- 
alent to  this,  one  unit  of  heat  will  raise  419  kilogrammes  oiie 

*  Philosophical  Transactions,  London,  1850,  Part  I.  p.  61. 


HEAT.  489 

metre.  The  difference  between  this  value  of  the  mechanical 
equivalent  of  heat  and  that  obtained  by  Joule  (423  kilogramme- 
metres)  is  very  small,  considering  the  entirely  heterogeneous 
data  which  enter  into  the  calculation. 

Assuming,  then,  that  the  doctrine  of  the  mechanical  equiva- 
lency of  heat  is  established,  it  follows  that  the  law  of  Dulong 
(237)  holds  in  all  cases  where  the  same  mechanical  power,  act- 
ing on  equal  volumes  of  different  gases,  causes  the  same  amount 
of  condensation.  But,  as  we  have  seen,  this  is  not  always  the 
case ;  hence  the  law  of  Dulong  must  be  subject  to  the  same  limi- 
tation as  that  of  Mariotte  (165).  Indeed,  the  law  of  Dulong  is 
probably  only  an  imperfect  expression  of  the  mechanical  equiva- 
lency of  heat,  and  is  true  so  far  as  the  same  expansion  or  com- 
pression represents  the  same  amount  of  mechanical  work. 

PROBLEMS. 
Specific  Heat. 

291.  How  much  heat  is  required  to  raise  the  temperature  of 

500  kilogrammes  of  water      from        4°  C.  to  94°  ? 

235           "          "        sulphur      "          20°       "  100°? 

336           "          "        charcoal    "            5°       "  500°? 

9.467   grammes   of       alcohol       "            3°       "  20°? 

10.234           "          "        ether          "      —20°       "  13°? 

292.  Calculate  the  quantity  of  heat  which  is  required  to  raise  the  tem- 
perature of  the  weight  of  the  different  elements  represented  by  their  chem- 
ical equivalents  one  degree. 

293.  The  following  quantities  of  water  were  mixed  together :  — 

2  kilogrammes  of  water  at  10°  C., 

5  "  "  "        30°, 

6  "  *'  "        20°, 

7  «  «  «         12°. 

What  was  the  temperature  of  the  mixture  ? 

294.  The  quantities  of  water  w^  w^  w3,  wt,  at  the  respective  tempera- 
tures of  t°t  *2°,  *3°,  24°,  were  mixed  together.     What  was  the  tempera- 
ture of  the  mixture  ? 

295.  How  much  water  at  99°  and  how  much  water  at  11°  must  be 
mixed  together,  in  order  to  obtain  20  kilogrammes  of  water  at  30°  ? 

296.  Determine  the  temperature  of  a  mixture  of  one  kilogramme  of 
water  at  100°  and  one  kilogramme  of  mercury  at  0°  ;  also  of  one  kilo- 
gramme of  mercury  at  100°  and  one  kilogramme  of  water  at  0°. 

297.  How  many  kilogrammes  of  mercury  at  100°  must  be  added  to  one 


490  CHEMICAL  PHYSICS. 

kilogramme  of  water  at  0°  in  order  that  the  temperature  of  the  mixture 
may  be  50°  ?  Also,  how  much  water  at  100°  must  be  added  to  one  kilo- 
gramme of  mercury  at  0°  to  raise  its  temperature  to  50°  ? 

298.  Equal  volumes  of  mercury  at  100°  and  water  at  0°  are  mixed 
together.     Required  the  temperature  of  the  mixture. 

299.  A  mass  of  matter  weighing  6.17  kilogrammes  at  the  temperature 
of  80°  is  mixed  with  25.45  kilogrammes  of  water  at  the  temperature  of 
12°.5.     The  mixture  is  found  to  have  the  temperature  of  14°. 17.     What 
is  the  specific  heat  of  the  body  ? 

300.  How  many  kilogrammes  of  gold  at  45°  would  be  required  to  raise 
the  temperature  of  1,000  grammes  of  water  from  12°.3  to  15°.7  ? 

301.  The  specific  heat  of  an  alloy  containing  one  equivalent  of  lead 
(103.6  parts)  and  one  equivalent  of  tin  (58.8  parts)  was  found  by  experi- 
ment to  be  0.0407.     How  does  this  value  correspond  with  that  which  may 
be  calculated  on  the  assumption  that  the  alloy  is  a  mechanical  mixture  of 
the  two  metals  ? 

302.  The  specific  heat  of  sulphide  of  mercury  (Hg  S)  was  found  by 
experiment  to  be  0.0512.     How  does  this  value  agree  with  that  calculated 
on  the  assumption  made  in  the  last  problem  ? 

303.  A  piece  of  iron  weighing  20  grammes  at  the  temperature  of  98° 
is  dropped  into  a  glass  vessel  weighing  12  grammes,  and  containing  150 
grammes  of  water  at  10°.     The  temperature  of  the  water  is  thus  raised  to 
11°.29.     Required  the  specific  heat  of  iron,  knowing  that  the  specific  heat 
of  glass  is  0.19768. 

304.  The  weights  of  different  substances,  wt ,  w%,  w3,  w4,  at  the  re- 
spective temperatures  ^°,  £2°,  £3°,  £4°,  and  having  the  respective  specific 
heats  <?!,  c2,  c3,  c4,  are  supposed  to  be  mixed  together.     Required  the  tem- 
perature of  the  mixture  in  terms  of  the  other  values. 

305.  Calculate  the  specific  heat  of  oil  of  turpentine  from  the  follow- 
ing data :    42.57  grammes  of  the  oil  at  33°.7  were  mixed  with  470.3 
grammes  of  water  at  12°.23  ;  the  temperature  of  the  mixture  was  found 
to  be  13°.07 ;  the  oil  was  enclosed  in  a  glass  tube  weighing  5.25  grammes 
and  having  a  specific  heat  equal  to  0.177  ;  lastly,  the  water  was  contained 
in  a  copper  vessel  weighing  45.25  grammes,  and  having  a  specific  heat 
equal  to  0.095. 

306.  A  platinum  ball  weighing  150  grammes  is  heated  to  1,000°,  and 
then  plunged  into  one  kilogramme  of  water  at  10°.     After  an  equilibrium 
is  established,  how  high  is  the  temperature  of  the  water,  assuming  that 
the  water  receives  all  the  heat  which  the  platinum  ball  loses  ?     If  the 
water  is  contained  in  a  brass  vessel  weighing  200  grammes,  how  high 
would  be  the  temperature  of  the  water  ? 

307.  A  platinum  ball  weighing  100  grammes,  after  having  been  ex- 
posed for  some  time  to  the  heat  of  a  furnace,  is  thrown  into  a  brass  vessel 


HEAT.  491 

containing  750  grammes  of  water  at  5°.  The  weight  of  the  brass 
amounted  to  150  grammes,  and  the  temperature  of  the  water  after  the 
equilibrium  was  established  to  15°.  What  was  the  temperature  of  the 
furnace,  assuming  that  no  heat  was  lost  from  the  vessel  and  water  during 
the  experiment  ? 

308.  How  much  heat  is  required  to  raise  the  temperature  of  one  cubic 
metre  each  of  air,  oxygen,  carbonic  acid,  and  hydrogen  from  0°  to  15°,  as- 
suming that  the  gas  is  allowed  to  expand  freely,  and  that  the  pressure  is 
constant  at  76  c.  m. 

309.  A  room  measures  7  metres  by  6  on  the  floor,  and  is  4  metres  high. 
How  much  heat  is  required  to  raise  the  temperature  of  the  air  in  that 
room  from  5°  to  18°  when  the  barometer  stands  at  76  c.  m.  ?     How  much 
heat  is  lost  in  expanding  the  air  of  the  room  ? 

310.  How  much  heat  would  be  required  to  raise  1,000  kilogrammes  of 
water  100  metres,  if  the  full  effect  of  the  heat  were  realized? 


EXPANSION. 

(239.)  Coefficient  of  Expansion.  —  It  has  already  been  stated 
(216)  that  the  first  effect  of  heat  on  matter,  in  either  of  its  three 
states,  is  to  expand  it ;  and  we  have  also  examined  the  most 
important  means  by  which  the  effects  of  expansion  are  used  as  a 
measure  of  temperature.  We  will  now  study  the  phenomena  of 
expansion  more  in  detail ;  but,  first,  we  will  establish  a  few  for- 
mulae by  which  the  amount  of  expansion  can  be,  in  any  case, 
readily  calculated. 

Linear  Expansion.  —  The  small  fraction  of  its  length  by 
which  a  rod  of  iron,  or  of  any  other  solid,  one  metre  long, 
expands,  when  heated  from  0°  to  1°,  is  called  the  Coefficient  of 
Linear  Expansion  of  the  solid.  A  bar  of  iron  one  metre  long  at 
0°  becomes  1.0000122  at  1°,  and  the  small  fraction  0.0000122  is 
the  coefficient  of  linear  expansion  of  iron.  If  we  assume  that 
the  expansion  is  proportional  to  the  temperature,  then  a  bar  of 
iron  one  metre  long  at  0°  becomes  1.00122  metres  long  at 
100°,  1.00244  at  200°,  1.0061  at  500°,  etc.  Hence  a  bar  of 
iron  26.354  metres  long  at  0°  would  become  1.0061  X  26.354 
=  26.515  at  500°.  To  make  the  solution  general,  let  k  =  co- 
efficient of  expansion  ;  then  1  +  k  —  increased  length  of  a  rod 
which  is  one  metre  long  at  0°,  when  heated  to  1°,  and  (1  ~{-t  k}  •= 
increased  length  at  t°.  Hence  /  (1  -f-  /  &)  =  increased  length  of 


492  CHEMICAL  PHYSICS. 

a  rod  at  t°  which  is  /  metres  long  at  0°.  Representing,  then,  by 
/',  this  increased  length,  we  have 

/'  =  /(!  +  <&);  [164.] 

by  which  we  can  easily  calculate  the  length  of  a  rod  of  any 
metal  at  t°,  when  its  length  at  0°  and  its  coefficient  of  expansion 
are  given.  The  coefficients  of  expansion  of  the  solids  most  fre- 
quently used  in  the  arts  are  given  in  Table  XV. 

It  is  frequently  the  case  that  we  do  not  know  the  length  of 
the  rod  at  0°,  but  only  at  some  other  temperature,  £,  and  it  is 
required  to  determine  the  length  at  a  second  temperature,  t', 
which  may  be  either  higher  or  lower  than  t.  To  obtain  a  formula 
for  the  purpose,  denote  by  /  the  unknown  length  of  the  rod  at  0°, 
by  /'  the  known  length  at  £°,  and  by  /"  the  required  length  at  t'°. 
We  have  then,  as  above, 


and         /"  = 
By  combining  these  equations,  we  obtain 

v  1    *  (e  ~ 


All  the  terms  of  the  quotient  after  the  first  may  be  neglected, 
because  they  contain  powers  of  the  already  very  small  fraction  k. 

We  have  assumed  that  the  expansion  of  solids  is  proportional 
to  the  temperature,  but  this  is  not  strictly  true  ;  for  the  rate 
of  expansion  of  solids,  like  that  of  mercury  (219),  increases, 
although  but  very  slightly,  as  the  temperature  rises.  The  co- 
efficient of  expansion  is  not,  therefore,  absolutely  the  same  at 
all  parts  of  the  thermometer-scale  ;  but  the  difference  is  so  small 
that  we  can  neglect  it,  except  in  the  most  refined  investiga- 
tions, more  especially  if  we  use,  not  the  coefficient  observed  at 
any  particular  temperature,  but  a  mean  coefficient  obtained  by 
dividing  by  100  the  total  amount  of  expansion  between  0°  and 
100°,  by  which  means  we  average  the  error. 

Cubic  Expansion.  —  The  small  fraction  of  its  volume  by 
which  one  cubic  centimetre  of  a  solid,  liquid,  or  gas  increases 
when  heated  from  0°  to  1°,  is  called  the  Coefficient  of  Cubic 
Expansion  of  that  substance.  The  coefficient  of  expansion  of 
mercury,  for  example,  is  0.00018  ;  that  is,  one  cubic  centimetre 
of  mercury  at  0°  becomes  1.00018  ~^?  at  1°.  Assuming  then 


HEAT.  493 

that  the  expansion  is  proportional  to  the  temperature,  we  obtain, 
by  the  same  course  of  reasoning  as  above,  the  formula 

F'=  F(l  +  *  JT);  [166.] 

by  which  the  increased  volume  (  F')  of  any  mass  of  matter  may 
be  calculated,  when  the  volume  at  0°  (F),  the  temperature  (£), 
and  the  coefficient  of  cubic  expansion  (jK"),  are  known.  In  like 
manner  we  easily  obtain  the  formula 

V"  =  V  [1  +  K  (i1  —  0  ] ,  [167.] 

which  will  enable  us  to  calculate  the  volume  of  a  body  at  t'  °  from 
the  volume  at  t°  and  the  coefficient  of  expansion. 

(240.)  The  Coefficient  of  Cubic  Expansion  is  three  times  as 
great  as  the  Coefficient  of  Linear  Expansion.  — The  truth  of  this 
simple  principle,  which  enables  us  to  calculate  one  coefficient 
when  the  other  is  given,  can  easily  be  proved.  For  this  purpose, 
let  us  suppose  that  we  have  a  cube  of  glass  measuring  one  cen- 
timetre on  each  edge  at  0°  ;  and  let  us  inquire  what  will  be  its 
increased  volume  at  1°,  assuming  that  the  coefficient  of  linear 
expansion  is  known.  At  1°  each  edge  of  this  glass  cube  will 
be  (1  +  k)  c.  m.  long.  Hence  the  increased  volume  of  the  cube 
wiU  be  equal  to  (1  +  &)3  =  1  +  3  k  +  3  k*  +  k3  ;  but  as  k 
is  an  exceedingly  small  fraction,  k1  and  /c3  may  be  neglected 
in  comparison  without  any  sensible  error,  so  that  the  volume 
of  a  cube  of  glass  which  is  one  cubic  centimetre  at  0°  becomes 
(1  -f-  3  &)  ^m.3  at  1°.  Since  by  [166]  the  volume  of  this  same 
cube  at  1°  would  also  be  expressed  by  (1  -f-  JC)  cTm?,  it  follows 
that  K=  3  /c,  which  was  to  be  proved. 

(241.)  The  increased  capacity  of  a  hollow  vessel,  in  conse- 
quence of  the  expansion  of  its  wall,  may  be  found  by  calculat- 
ing- the  increased  volume  of  a  solid  mass  of  the  same  substance 
which  would  just  Jill  the  interior  of  the  vessel.  —  A  moment's 
reflection  will  show  the  truth  of  this  statement.  Let  the  hollow 
vessel  be  a  glass  globe,  and  let  us  conceive  of  it  as  filled  with  a 
solid  globe  of  glass.  If  this  mass  be  heated,  it  is  evident  that 
the  glass  vessel  will  expand  just  as  if  it  formed  the  outside  shell 
of  a  solid  globe  ;  the  same  must  be  true  when  the  interior  core  is 
not  present. 

42 


494 


CHEMICAL  PHYSICS. 


Expansion  of  Solids. 

(242.)  Measurement  of  Linear  Expansion.  —  The  earliest 
accurate  determinations  of  the  coefficients  of  linear  expansion  of 
solids  were  made  by  Lavoisier  and  Laplace  with  the  apparatus 
represented  in  perspective  by  Fig.  367,  and  in  section  by  Fig.  368. 
This  apparatus  consisted  of  two  parts :  first,  of  a  copper  tank, 
in  which  a  bar  made  of  the  solid  whose  coefficient  was  to  be 
determined  was  heated  to  a  uniform  temperature  by  immersing 
it  in  heated  oil  or  water  ;  and,  secondly,  of  four  stone  posts  sup- 
porting an  ingenious  contrivance  for  measuring  the  increase  of 


Fig.  367. 

length.  The  solid  bar,  about  two  metres  in  length,  rested  in  the 
tank  on  rollers,  with  one  end  bearing  against  an  upright  immov- 
able glass  bar,  ^(see  Fig.  368),  firmly  fastened  by  cross-pieces  to 
the  two  stone  posts  on  the  left-hand  side  of  Fig.  367,  and  with 
the  other  end  bearing  against  the  lever,  D.  The  upper  end  of 


Fig.  368. 

this  lever  was  attached  to  a  horizontal  axis  turning  in  sockets 
inserted  into  the  two  stone  pillars  on  the  right  of  Fig.  367,  and 
having  at  one  end  the  telescope,  (7,  adjusted  with  its  axis  perpen- 
dicular to  the  lever  D.  The  telescope  was  furnished  with  a 
micrometer  eye-piece,  and  as  it  was  turned  by  the  expansion  of 
the  bar,  the  cross-wires  moved  over  the  divisions  of  a  scale,  A  B, 
placed  in  a  vertical  position  at  the  distance  of  fifty  metres  or 
more  from  the  instrument. 


HEAT.  495 

The  apparatus  was  used  in  the  following  manner.  The  bar 
having  been  placed  in  position,  the  tank  was  filled  with  ice-cold 
water,  and  the  observer  noted  the  division  of  the  scale  on  which 
the  cross-wire  of  the  telescope  was  projected.  The  cold  water 
was  then  withdrawn  by  a  stopcock,  and  its  place  supplied  with 
boiling  water.  The  temperature  soon  became  stationary  and 
was  ascertained  by  thermometers  placed  at  the  side  of  the  bar, 
when  the  observer  again  noted  the  division  on  the  scale  with 
which  the  cross-wire  of  the  telescope  coincided.  Knowing,  now, 
the  distance  A  B  on  the  scale  over  which  the  cross-wire  had 
moved,  also  the  distance  A  G  of  the  scale  from  the  axis  of  ro- 
tation of  the  telescope,  and,  lastly,  the  length  of  the  lever  G  H, 
it  was  easy  to  determine  the  value  of  H  C,  the  elongation  of. 
the  bar.  The  two  triangles  A  B  G  and  H  C  G  are  similar 
by  construction,  and  we  have  H  C  :  H  G  =  A  B  :  A  G,  or 

TT  S^l  TT  f^ 

H  C  =  A  B  -j-£.  The  value  of  -^  depends,  evidently,  on 
the  dimensions  of  the  apparatus.  In  that  used  by  Lavoisier 
and  Laplace  it  was  about  T£T,  so  that  HC=  =TT,  and  hence 

any  error  in  the  measurement  of  A  B  was  divided  744  times  in 
the  result. 

The  length  of  the  bar  at  0°  being  known,  and  the  elongation 
corresponding  to  an  observed  number  of  degrees  having  been 
measured  as  just  described,  it  was  easy  to  determine  the  coeffi- 
cient of  expansion  by  dividing  the  elongation  in  fractions  of  a 
metre  by  the  length  of  the  bar  in  metres  and  by  the  number  of 
degrees.  For  example,  let  us  suppose  that  the  length  of  the  bar 
at  0°  was  1.786  m.,  and  that  the  elongation  corresponding  to  80° 
was  0.004  ;  the  coefficient  of  expansion  would  then  be  0.004  -T- 
(1.786  X  80)  =  0.000028. 

Since  the  experiments  of  Lavoisier  and  Laplace,  the  linear 
coefficient  of  expansion  of  glass  and  of  the  metals  most  used  in 
the  arts  has  been  redetermined  by  a  number  of  physicists,  and 
with  various  methods ;  but  as  these  methods  do  not  involve  the 
application  of  any  new  principle,  it  is  not  important  to  describe 
them. 

(243.)  Determination  of  Coefficient  of  Cubic  Expansion.  — 
We  have  already  seen  that  the  coefficient  of  cubic  expansion  is 
three  times  that  of  linear  expansion,  so  that  the  cubic  expansion 
of  a  homogeneous  solid  can  always  be  easily  calculated  from  the 


496  CHEMICAL  PHYSICS. 

linear  expansion.  In  many  cases,  however,  the  coefficient  of 
cubic  expansion  can  be  measured  with  more  accuracy  than  the 
other,  and  it  is  then  best  to  reverse  the  calculation.  The  coeffi- 
cient of  cubic  expansion  of  several  solids  can  be  determined  with 
great  accuracy,  by  means  of  a  process  based  on  the  apparent 
expansion  of  mercury,  which  will  be  described  in  (254)  .  It  can 
also  be  determined  in  the  following  manner  from  the  specific 
gravity  of  the  solid  taken  at  different  temperatures  :  — 

Let  (Sp.  Gr.)  and  (Sp.  Gr.)'  represent  the  specific  gravity  of  the  solid 
at  the  temperatures  t  and  t1  respectively.  Also  let  W  represent  the 
weight  of  the  solid  mass  used  in  the  experiment,  V  the  volume  at  0°, 
and  K  the  unknown  coefficient  which  we  wish  to  determine.  We  have 
then,  by  [166],  for  the  volume  of  the  solid  body  at  t°  and  Z'°,  the  values 
V(l-\-tK)  and  V(l  -\-f  K)  ;  by  substituting  these  values  in  [55]  we 
obtain,  for  the  value  of  the  specific  gravity  at  the  two  temperatures, 


Combining  these  two  equations,  and  reducing,  we  get  for  the  value  of  the 
coefficient  of  cubic  expansion, 

_       (Sp.Gr.)  -  (Sp.Gr.y  rl6g  , 

-  - 


Kopp  has  determined,  by  the  above  method,  the  coefficient 
of  cubic  expansion  of  a  number  of  solids,  and  his  results  are 
included  in  Table  XY. 

(244.)  General  Results.  —  By  examining  Table  XY.  it  will 
be  seen  that  the  increase  of  length  which  a  solid  bar  undergoes 
when  heated  from  0°  to  100°  is  at  most  very  small,  amounting  in 
the  case  of  zinc,  the  most  expansible  of  all  solids  hitherto  ob- 
served, to  only  -s%v  of  the  length  at  zero.  The  difference,  how- 
ever, between  different  solids  is  very  great,  zinc  expanding  over 
three  times  as  much  as  glass  for  the  same  increase  of  temper- 
ature. 

The  relative  expansibility  of  solids  seems  to  be  more  nearly 
related  to  their  relative  compressibility  than  to  any  other  physical 
quality  ;  for  we  find,  as  a  general  rule,  that  those  metals  are 
the  most  expansible  which  have  the  smallest  coefficients  of  elas- 
ticity (101)  and  are  therefore  most  easily  compressed.  This 
fact  is  shown  by  the  two  following  series,  in  which  the 


HEAT.  497 

metals  are  arranged  in  the  order  of  expansibility  and  compres- 
sibility :  — 

Zinc,  Lead,  Tin,  Silver,  Gold,  Palladium,  Copper,  Platinum,  Steel,  Iron, 
Glass. 

Lead,  Tin,  Gold,  Silver,  Zinc,  Palladium,  Platinum,  Copper,  Steel,  Iron, 
Glass. 

Although  these  two  series  are  not  perfectly  parallel,  they  are 
sufficiently  so  to  indicate  a  close  connection  between  the  two 
properties.  This  connection  is  also  seen  in  the  fact,  that  the 
diminution  of  the  coefficient  of  elasticity  with  the  increase  of 
temperature,  already  noticed  (101),  is  accompanied  with  a  cor- 
responding increase  of  the  rate  of  expansion. 

The  increase  of  the  coefficient  of  expansion  between  0°  and 
100°  is  hardly  perceptible  in  solids ;  but  when  the  change  of 
temperature  amounts  to  several  hundred  degrees,  it  is  necessary 
to  take  account  of  it  in  delicate  physical  measurements.  This 
is  especially  the  case  with  the  glass  vessels  which  are  used  for 
air  thermometers  or  in  determining  the  specific  gravity  of  va- 
pors ;  and  in  order  to  furnish  the  necessary  data  for  such  experi- 
ments, Regnault  has  determined  the  mean  coefficients  of  cubic 
expansion  of  the  common  Paris  glass,  when  blown  into  hollow 
ware,  between  zero  and  different  temperatures.  His  results  are 
as  follows :  — 

Between  0°  and  100°  .         .        .  K=  0.0000  276. 

"        «  «      150  ;'           «     0.0000284. 

«        «  «      200  ...       «     0.0000291. 

«        "  «     250  ...           "     0.0000298. 

«        «  "300  ..."     0.0000306. 

«        «  «     350  ...           "    0.0000313. 

From  the  fact  that  the  rate  of  expansion  of  a  solid  increases 
with  the  temperature,  we  should  naturally  infer  that  the  rate  for 
any  given  solid  would  be  greatest  just  below  its  melting-point ; 
and  of  several  solids  taken  at  the  temperature  of  the  air,  we 
should  expect,  other  things  being  equal,  that  those  would  be  the 
most  expansible  which  are  nearest  their  melting-points  at  this 
temperature,  or,  in  other  words,  which  are  the  most  fusible. 
This  we  find,  as  a  general  rule,  to  be  true ;  the  easily  fusible 
solids,  like  zinc  and  lead,  being  more  expansible  than  the 
42* 


498  CHEMICAL   PHYSICS. 

difficultly  fusible,  like  iron  and  platinum :  but  there  is  by  no 
means  a  perfect  parallelism  between  the  order  of  fusibility  and 
that  of  expansibility  ;  nor  ought  we  to  expect  it,  for  different 
metals  are  not  equally  expansible  at  temperatures  equally  dis- 
tant from  their  melting-points. 

(245.)  Expansion  of  Crystals.  —  We  have  hitherto  assumed 
that  solid  bodies  expand  equally  in  all  directions,  and  this  is 
true  of  all  homogeneous  solids  ;  but  it  is  not  necessarily  the  case 
with  crystals.  Only  tht>se  crystals  which  belong  to  the  Regular 
System  expand  equally  in  all  directions.  Those  belonging  to 
the  other  systems  expand  unequally  in  the  direction  of  the  un- 
equal axes.  This  inequality  in  the  expansion  of  crystals  in  the 
directions  of  unequal  axes  can  be  readily  detected,  because  an 
alteration  in  the  relative  length  of  the  axes  must  change  the  inter- 
facial  angles  of  the  crystal,  which  can  be  measured  with  great 
accuracy  (96).  Professor  Mitscherlich,*  of  Berlin,  who  has  very 
carefully  studied  this  subject,  found  that  the  interfacial  angles  of 
all  crystals,  except  those  belonging  to  the  regular  system,  were 
slightly  affected  by  changes  of  temperature.  The  rhombohedral 
angle  of  calc-spar,  for  example,  (page  150,)  varies  eight  and  a 
half  minutes  between  the  freezing  and  boiling  points  of  water. 
Indeed,  Mitscherlich  has  shown  that,  while  a  crystal  is  expanding 
in  length  by  heat,  it  may  actually  be  contracting  in  another  di- 
mension. These  facts  are  in  entire  harmony  with  the  principles 
of  the  last  section  ;  for,  since  the  elasticity  of  crystals  is  different 
in  different  directions  (108),  we  should  naturally  expect  that  the 
rate  of  expansion  would  be  different  also. 

In  investigating  the  laws  of  expansion  of  solids,  it  is  evidently 
advisable  to  make  choice  of  crystallized  bodies ;  for  when  the 
substance  is  not  crystallized,  the  expansion  of  different  specimens 
may  not  be  precisely  the  same,  owing  to  variations  of  internal 
structure.  This  is  probably  the  cause  of  the  discrepancies  which 
we  find  between  the  coefficients  of  expansion  of  the  same  sub- 
stance as  given  by  different  experimenters.  These  discrepancies, 
indeed,  are  the  most  marked  in  the  case  of  substances  like  glass, 
in  which  we  should  naturally  expect  the  greatest  variations  of 
structure. 

The  expansion  of  glass  has  been  more  carefully  studied  than 

*  Poggendorff's  Annalen,  I.  125,  X.  137,  XLI.  213. 


HEAT.  499 

that  of  any  other  substance,  on  account  of  its  use  in  physical 
apparatus.  Regnault  has  found,  not  only  that  the  expansion  of 
glass  varies  with  its  composition,  but  also  that  it  varies  with  the 
manner  in  which  it  has  been  worked.  Thus,  the  same  glass  ex- 
pands more  in  the  form  of  a  solid  rod  than  in  that  of  a  tube,  and 
a  large  vessel  frequently  expands  at  a  different  rate  from  a  small 
vessel  made  of  precisely  the  same  material.  Indeed,  Regnault 
has  shown  that  the  coefficient  of  the  same  glass  vessel  is  not 
always  absolutely  the  same  between  the  same  limits  of  temper- 
ature, especially  if  between  two  observations  it  has  been  exposed 
to  great  and  sudden  thermal  changes.  These  variations  are 
probably  due  to  changes  in  the  molecular  condition  of  the  glass, 
and  are  similar  to  those  which  cause  the  change  in  the  zero  point 
of  the  thermometer  (220). 

It  follows  from  the  above  facts,  that,  where  very  great  accuracy 
is  required,  it  is  important  to  determine  the  rate  of  expansion  of 
the  actual  vessel  which  is  to  be  used  in  the  experiment. 

(246.)  Force  of  Expansion.  —  The  force  with  which  a  body 
expands  is  equal  to  the  resistance  which  it  would  oppose  to  a 
compression  of  an  equal  amount ;  we  have  already  seen  (101) 
how  very  great  this  resistance  is.  A  bar  of  iron  one  metre  long 
expands  0.0012  m.  if  heated  100°.  If  now  we  assume  that  the 
area  of  the  section  of  the  bar  is  equal  to  2,500  m.  m.2,  and  that 
the  coefficient  of  elasticity  of  iron  is  equal  in  round  numbers  to 
21,000,  we  can  readily  calculate  by  [66]  the  weight  which  would 
be  required  to  compress  the  bar  0.0012.  This  weight  would  be 
21,000  X  2,500  X  0.0012  =  63,000  kilogrammes,  and  it  would 
be  necessary  to  apply  this  enormous  force  in  order  to  prevent 
a  bar  of  iron  measuring  5  c.  m.  on  each  side  from  expanding, 
when  heated  from  0°  to  100°.  It  is  not,  therefore,  at  all  won- 
derful that  iron  bars  used  in  buildings  frequently  destroy  the 
masonry  they  were  intended  to  strengthen,  where  care  has  not 
been  taken  to  allow  for  the  expansion. 

The  force  with  which  a  solid  contracts  when  cooled  is  equal  to 
that  with  which  it  expands  when  heated.  This  force  was  first 
used  at  the  Conservatoire  des  Arts  et  Metiers,  in  Paris,  for  draw- 
ing together  the  walls  of  an  arched  gallery  which  had  bulged 
outward  from  the  pressure  of  the  roof,  and  the  experiment  has 
since  been  successfully  repeated  in  several  other  buildings. 
Stout  iron  rods  were  placed  across  the  building,  and  their  ends 


500  CHEMICAL  PHYSICS. 

secured  to  the  outside  of  the  walls  by  means  of  plates  and  nuts. 
Half  of  the  number  of  rods  were  then  strongly  heated  by  char- 
coal furnaces,  and  when  they  were  expanded  the  plates  were 
screwed  firmly  up  to  the  walls.  As  the  bars  cooled,  they  con- 
tracted and  drew  the  walls  somewhat  nearer  together.  The  same 
process  was  then  repeated  with  the  other  half  of  the  rods,  and 
so  continued  until  the  walls  were  restored  to  a  perpendicular 
position. 

Applications  of  this  same  force  may  be  seen  in  many  of  the 
trades.  The  wheelwright  binds  the  parts  of  a  wheel  together  by 
putting  on  the  iron  tire  while  hot,  and  allowing  it  to  contract 
round  the  wood  ;  and  even  the  large  wrought-iron  tires  round 
the  wheels  of  locomotive  engines  are  fastened  in  the  same  way. 
The  cooper  insures  the  tightness  of  a  cask  by  surrounding  it 
with  heated  iron  hoops,  which,  by  contracting,  unite  the  staves 
more  firmly ;  and  steam-boilers  are  riveted  with  red-hot  rivets, 
which,  on  cooling,  draw  the  plates  together  more  securely  than 
any  other  means  could. 

(247.)  Illustrations.  —  The  expansion  of  solids  by  heat  may 
be  illustrated  by  a  great  variety  of  experiments,  but  we  shall 

only  be  able  to  describe  a  few  of  the 
most  striking. 

The  cubic  expansion  may  be  shown 
by  means  of  the  apparatus  represent- 
ed in  Fig.  369.  The  brass  ball  a  is 
made  so  that  it  will  just  pass  through 
the  ring  m,  when  both  have  the  same 
temperature.  If  then  we  heat  the 
ball,  it  will  no  longer  pass  through  in 
Fig  369.  any  position,  thus  indicating  an  in- 

crease of  volume. 

In  order  to  illustrate  the  linear  expansion  of  solids,  we  make 
use  of  a  class  of  instruments  called  pyrometers.  One  of  the 
simplest  and  most  convenient  of  these  is  represented  in  Fig.  370. 
It  consists  essentially  of  the  metallic  rod  J,  one  end  of  which  is 
firmly  secured  to  a  brass  pillar  by  means  of  the  clamp-screw  jB, 
while  the  other  end,  which  is  free  to  expand,  plays  against  the 
shorter  arm  of  a  needle,  K,  moving  on  a  graduated  arc.  The 
rod  is  heated  by  an  alcohol  lamp  of  peculiar  construction,  and 
its  expansion  is  rendered  visible  by  the  motion  of  the  needle  over 


HEAT. 


501 


the  graduated  arc.  Instruments  constructed  on  the  same  prin- 
ciple have  been  employed  by  Daniels  and  others  for  measuring 
high  temperatures  ;  but  since  they  have  been  superseded  by  the 


Kg.  370. 

far  more  accurate  methods  of  the  present  day,  it  is  not  necessary 
to  describe  them  in  detail. 

The  unequal  expansion  of  different  metals  is  best  illustrated 
by  a  compound  bar,  made  by  riveting  together  two  bars  of  iron 
and   copper   at   different  points 
through   their  whole  length,  as  rig.  an. 

represented  in  Fig.  371.     When      *—*--  •'-  -C-^-T-T— r-r- ?  .  .  .•   •  -_^ 
such  a  bar  is  heated,  the  copper 

expands    more    than    the    iron,       ^-^^T^— ^'-^— ^^^-^^^ 
and   the   bar  curves,   as   repre-  Kg.  372. 

sented  in  Fig.  372,  in  order  to 

accommodate  the  inequality  of  length  which  thus  results.     If  the 
bar  is  cooled,  it  again  curves,  but  in  the  opposite  direction. 

The  expansion  of  solids  is  also  illustrated  by  many  phe- 
nomena of  e very-day  life.  A  nail  driven  into  a  brick  wall  be- 
comes loose  after  a  time,  because  the  iron  expands  in  summer 
and  contracts  in  winter  more  than  the  mortar,  and  thus  the 
opening  is  enlarged.  Clocks  go  faster  in  winter  and  slower 
in  summer,  because  the  pendulum  elongates  in  summer,  and 
consequently  vibrates  more  slowly  ;  while  in  winter  it  becomes 
shorter,  and  vibrates  more  rapidly.  The  pitch  of  a  piano  or  harp 
rises  in  a  cold  room,  in  consequence  of  the  contraction  of  the 
metallic  strings.  A  closely-fitting  iron  gate,  which  can  be  easily 
opened  on  a  cold  day,  can  only  be  opened  with  difficulty  on  a 
warm  day,  because  both  the  gate  and  the  adjoining  railings  have 
become  expanded  by  the  heat.  When  iron  pipes  are  employed 


502  CHEMICAL  PHYSICS. 

to  conduct  steam  through  a  factory,  they  are  never  allowed  to 
abut  against  a  wall  or  other  obstacle,  which  they  might  injure  in 
expanding ;  and,  for  the  same  reasons,  the  rails  of  a  railroad  are 
always  laid  at  a  little  distance  apart.  A'  kilometre  of  rails 
expands  seven  metres  between  — 20°  and  40°,  and  this  allow- 
ance must  be  made  in  the  construction  of  the  road.  When  a 
metal  is  soft,  and  its  expansion  or  contraction  at  all  resisted,  it 
may  become  permanently  expanded  when  repeatedly  heated.  A 
waste  steam-pipe  of  lead  has  been  elongated  several  inches  in  a 
few  weeks,  and  the  zinc  or  lead  linings  of  bath  tubs  are  fre- 
quently gathered  in  ridges  from  the  same  cause. 

The  walls  of  buildings  are  also  sensibly  expanded  by  the  action 
of  the  sun's  rays.  Bunker  Hill  Monument,  an  obelisk  of  granite 
two  hundred  and  twenty-one  feet  high,  moves  at  the  top  so  as  to 
describe  an  irregular  ellipse  with  the  sun's  motion.  Professor 
Horsford,  who  had  an  opportunity  of  studying  the  action  of  the 
sun's  rays  on  this  structure,  noticed  that  the  movement  com- 
menced early  in  the  morning  on  a  simny  day,  and  attained  its 
maximum  in  the  afternoon.  In  a  cloudy  day  no  motion  takes 
place,  and  a  shower  restores  the  shaft  to  its  position,  —  showing 
that  the  heat  which  produces  the  deflection  penetrates  but  a  short 
distance.*  A  similar  fact  is  also  noticed  when  astronomical  in- 
struments are  placed  on  elevated  buildings,  from  the  derangement 
which  they  undergo  by  the  unequal  expansion  of  the  walls. 

"When  hot  water  is  poured  on  a  thick  plate  of  glass,  the  upper 
surface  is  expanded  before  the  heat  reaches  the  under  surface  of 
the  plate.  There  is,  therefore,  an  unequal  expansion,  and  the 
plate  tends  to  bend,  like  the  compound  bar,  with  the  hot  surface 
on  the  outside  of  the  curve  ;  and  since  the  particles  of  glass  do 
not  readily  yield  to  such  displacement,  the  glass  breaks.  Hence 
is  explained  the  fact,  that  hot  vessels  of  glass  or  porcelain  are 
liable  to  break  when  cold  water  is  poured  into  them,  or  when  set 
down  on  a  cold  surface  which  is  at  the  same  time  a  good  con- 
ductor of  heat.  Such  accidents  are  avoided  by  resting  the  vessel 
on  rings  of  straw,  or  other  poor  conductors,  and  having  them 
made  as  thin  on  the  bottom  as  is  consistent  with  the  necessary 
strength. 

This  effect  of  heat  on  glass  is  used  in  the  laboratory  for  dividing 

*  Silliman's  Philosophy,  p.  329. 


HEAT.  603 

glass  vessels  which  have  been  cracked  or  otherwise  damaged, 
since  a  crack  once  started  may  be  conducted  in  any  direction 
by  means  of  an  iron  rod  heated  to  redness,  or,  still  better,  by 
means  of  a  burning  slow-match  prepared  expressly  for  the  pur- 
pose.* In  like  manner  the  round  necks  of  glass  retorts,  flasks, 
and  other  chemical  vessels,  can  be  cut  off  by  means  of  an  iron 
ring,  which  is  first  heated  to  a  red  heat  in  a  furnace,  and  then 
held  for  a  few  moments  around  the  neck.  As  soon  as  the  neck 
is  thus  heated,  a  few  drops  of  water  let  fall  upon  the  heated  part 
will  cause  the  neck  to  crack  off. 

But  by  far  the  most  remarkable  illustration  of  the  expansion 
of  solids  by  heat  is  furnished  by  the  Britannia  Tubular  Bridge. 
This  bridge  consists  of  two  rectangular  iron  tubes  (made  of  boiler 
plates  firmly  riveted  together)  1,510  feet  1|  inches  long  at  32°  F., 
and  varying  from  23  feet  in  height  at  either  end  to  30  feet  at  the 
centre.  These  tubes,  which  are  placed  parallel  to  each  other, 
are  secured  permanently  to  the  central  stone  pier  of  the  bridge, 
called  the  Britannia  Tower  ;  but  at  the  other  points  of  support 
they  rest  on  friction  rollers,  and  the  free  ends  move  backwards 
or  forwards  as  the  length  of  each  tube  changes  with  the  tem- 
perature. An  increase  of  temperature  of  26°,  viz.  from  32°  to 
58°  F.,  gives  an  increase  of  3J  inches  in  the  whole  length  of  the 
bridge,  and  the  daily  expansion  and  contraction  varies  from  half 
an  inch  to  three  inches,  usually  attaining  its  maximum  and 
minimum  about  three  o'clock  in  the  afternoon  and  morning. 
Since  the  tubes  are  immovably  secured  in  the  centre,  only  one 
half  of  this  motion  is  visible  at  either  end.  "  But  the  most  in- 
teresting effect  is  that  produced  by  the  sun  shining  on  one  side 
of  the  tube  or  on  the  top,  while  the  opposite  side  and  the  bottom 
remain  shaded  and  comparatively  cool.  The  heated  portions  of 
the  tube  expand,  and  thereby  warp  or  bend  the  tube  towards  the 
heated  side,  the  motion  being  sometimes  as  much  as  two  and  a 
half  inches  vertically  and  two  and  a  half  inches  laterally."!  The 
same  phenomena  may  be  seen  at  the  Victoria  Tubular  Bridge, 
recently  built  at  Montreal ;  but  as  the  tubes  of  this  bridge  are 

*  For  a  recipe  by  which  these  slow-matches  may  be  prepared,  see  Mohr's  Phar- 
macy. 

t  For  a  very  interesting  and  detailed  account  of  these  phenomena,  see  the  large  work 
on  the  Britannia  and  Conway  Tubular  Bridges,  by  Edwin  Clark,  Resident  Engineer. 
2  vols.  and  Atlas,  London,  1856. 


504 


CHEMICAL  PHYSICS. 


Fig.  373. 


much  shorter  than  those  of  the  Britannia  bridge,  the  extent  of 
the  motion  is  not  so  great. 

(248.)  Applications  of  the  Expansion  of  Solids.  —  Bre*guet's 
metallic  thermometer  (Fig.  373)  is  an  application  of  the  principle 

of  the  compound  bar.  The  essen- 
tial part  of  the  instrument  is  a 
spiral,  formed  of  a  metallic  ribbon 
which  is  constructed  in  the  fol- 
lowing way.  Three  small  bars, 
one  each  of  platinum,  gold,  and 
silver,  are,  in  the  first  place,  sol- 
dered together  throughout  their 
whole  length.  This  compound 
bar  is  next  rolled  out  in  a  rolling- 
mill  until  it  is  reduced  to  a  rib- 
bon not  more  than  one  sixtieth 
of  a  millimetre  in  thickness,  and 
from  one  to  two  millimetres  broad. 
The  ribbon  thus  prepared  is  wound 

into  a  spiral,  having  the  silver  face  towards  the  interior,  and  this 
spiral  is  suspended  to  the  upright  arm  of  the  instrument.  To 
its  lower  end  there  is  fastened  a  needle,  which  traverses  an  arc 
graduated  into  Centigrade  degrees,  and  the  whole  instrument  is 
covered  with  a  glass  bell  for  protection. 

Although  the  ribbon  is  rolled  out  to  the  extreme  degree  of 
thinness  just  stated,  yet  the  continuity  of  the  three  metals  re- 
mains unbroken  ;  so  that  the  spiral  may  be  regarded  as  consist- 
ing of  three  spirals  of  different  metals  united  throughout  their 
whole  length.  The  silver  spiral,  which  is  the  most  dilatable,  is 
surrounded,  first,  by  a  gold  spiral,  which  expands  less  than  the 
silver,  and  lastly  by  a  platinum  spiral,  which  expands  the  least 
of  all.  As  the  temperature  rises,  the  silver  expanding  more  than 
the  platinum  or  the  gold,  each  coil  of  the  spiral  tends  to  unbend, 
and  the  effect  is  evidently  partially  to  uncoil  the  whole,  causing 
the  needle  to  move  over  the  graduated  arc  from  left  to  right  in 
the  above  figure.  The  opposite  effect  ensues  when  the  tempera- 
ture falls.  The  gold  band  is  placed  between  the  two  others, 
because  it  has  an  intermediate  rate  of  expansion.  Were  plati- 
num and  silver  used  alone,  the  great  inequality  of  their  rates 
of  expansion  might  cause  the  bands  to  separate.  On  account 


HEAT. 


505 


of  the  small  mass  of  metal  of  which  the  spiral  consists,  Bre*guet's 
thermometer  is  exceedingly  sensitive  to  very  slight  changes  of 
temperature,  and  may  be  used  in  some  cases  with  great  ad- 
vantage. 

Some  of  the  most  ingenious  applications  of  the  expansion  of 
metals  are  to  be  found  among  the  numerous  contrivances  for 
retaining  the  pendulums  of  clocks  of 
an  invariable  length  at  all  tempera- 
tures. One  of  these,  called  Harrison's 
gridiron  pendulum,  is  represented  in 
Fig.  374.  The  large  disk  of  this  pen- 
dulum is  suspended  by  a  series  of  steel 
and  brass  rods,  alternating  with  each 
other,  and  connected  at  the  ends  by 
cross-pieces.  The  manner  in  which 
these  are  arranged  will  be  best  -under- 
stood by  studying  the  figure,  in  which 
the  steel  rods  are  distinguished  from 
the  brass  by  being  shaded.  The  length 
of  the  pendulum  is  evidently  equal  to 
the  sum  of  the  lengths  of  the  steel  rods, 
including  the  steel  ribbon,  6,  which  sup- 
ports the  whole  pendulum  and  bends  at 
each  oscillation,  less  the  sum  of  the 
lengths  of  the  brass  rods.  Moreover, 
it  will  also  be  seen,  by  examining  the 
figure,  that,  while  the  expansion  of  the 
steel  rods  lengthens  the  pendulum,  the 
expansion  of  the  brass  rods  shortens  it. 
If,  then,  the  lengths  of  the  rods  are  so 
adjusted  that  the  expansion  in  one  di- 
rection will  just  balance  that  in  the  other,  the  pendulum  will 
remain  of  an  invariable  length.  It  is  easy  to  determine,  ap- 
proximatively,  the  length  required  to  produce  this  compen- 
sation. 

Representing  by  L  and  L1  the  sum  of  the  lengths  of  the  steel  and  the 
brass  rods  respectively,  and  by  k  and  k1  their  coefficients  of  expansion,  we 
should  have,  since  the  amount  of  expansion  is  the  same  in  both, 


fig.  374 


—  L1  1J. 


43 


506 


CHEMICAL   PHYSICS. 


Moreover,  since  at  the  latitude  of  Paris  the  length  of  the  seconds  pendu- 
lum is  0.99394  metre  (58),  we  must  also  have 

L  —  L'  =  0.99394. 

Combining  these  two  equations,  and  substituting  for  k  and  k'  their  values 
from  Table  XV.,  we  should  find  that  the  pendulum  would  remain  of  an 
invariable  length  when  the  sum  of  the  lengths  of  the  steel  rods,  or 
L,  •=.  2.31919  metres,  and  when  the  sum  of  the  lengths  of  the  brass  rods, 
or  L',  —  1.32525  metres.  It  is  evident,  therefore,  that  compensation 
could  not  be  effected  with  fewer  rods  than  are  represented  in  the  figure, 
namely,  three  of  steel  and  two  of  brass. 

The  above  calculation,  however,  only  gives  approximate  re- 
sults, since  the  virtual  length  of  the  pendulum  depends  on  the 
position  of  the  centre  of  oscillation,  and  may  vary,  even  when  the 
apparent  length  remains  the  same  (54).  In  practice,  the  rods 
are  constructed  as  nearly  as  possible  of  the  required  length,  and 
the  compensation  is  afterwards  completed  by  varying  tlie  position 
of  the  weight  o,  until,  after  successive  trials,  the  right  point  is 
attained. 

A  clockmaker  by  the  name  of  Martin  effected  the  compensa- 
tion in  pendulums  by  means  of  a  compound  bar  of  iron  and 
copper,  fixed  transversely  on  the  pendulum  rod,  as  represented 
in  Fig.  375.  To  the  ends  of  this  compound  bar  small  weights 
are  attached,  movable  on  a  screw,  and  the  bar  is  so  placed  that 
the  copper  is  lowest.  Hence,  when  the  temperature  rises,  its  ends 


Fig.  375. 


Fig.  376. 


curve  upwards,  as  represented  in  Fig.  376  ;  and,  on  the  other 
hand,  they  curve  downwards,  as  in  Fig.  377,  when  the  tempera- 
ture falls.  The  rising  and  falling  of  these  masses  of  matter  will 
evidently  change  the  virtual  length  of  the  pendulum,  by  raising  or 
lowering  the  centre  of  oscillation.  Moreover,  this  change  will  be 
just  the  reverse  of  that  caused  by  the  action  of  heat  on  the  pen- 


HEAT.  507 

dulum  itself ;  and,  by  varying  the  position  of  the  small  weights 
on  the  transverse  bar,  the  two  changes  may  be  made  exactly  to 
counteract  each  other. 

An  arrangement  precisely  similar  to  that  of  Martin  has  long 
been  employed  for  compensating  the  balance-wheels  of  chronom- 
eters and  watches.     It  is  well  known  that  the 
motion  of  a  watch  is  regulated  by  a  balance- 
wheel,  as  that  of  a  clock  is  by  the  pendulum, 
and  that  the  oscillations  of  this  balance-wheel 
are  maintained  by  a  fine  spiral  spring,  whose 
elasticity  takes  the  place  of  the  force  of  grav- 
ity acting  on  the  pendulum  of  the  clqck.    Now, 
the  duration  of  an  oscillation  of  a  balance-  Fig  373. 

wheel  depends  on  the  elasticity  of  the  spring, 
on  the  radius  of  the  wheel,  and  on  the  mass  of  matter  in  its  rim. 
The  effect  of  heat  is  to  increase  the  radius,  and  thus  to  retard 
the  watch  by  increasing  the  duration  of  each  oscillation.  This 
effect,  however,  can  be  entirely  counteracted  by  the  arrangement 
represented  in  Fig.  378.  The  three  metallic  arcs,  a,  a,  a,  are  each 
made  of  two  metals,  the  most  expansible  being  placed  outside ; 
and  as  the  temperature  rises,  they  curve  in  and  carry  the  three 
small  masses  of  matter,  n,  n,  n,  nearer  to  the  axis  of  the  wheel, 
thus  diminishing  the  virtual  length  of  the  radius  as  much  as  the 
expansion  increased  it.  The  position  of  the  small  masses  n,  n,  n, 
in  which  the  effect  of  expansion  is  just  compensated,  is  found  by 
trial ;  and  they  are  adjusted  by  turning  them  on  the  small  screws 
which  form  the  extremities  of  the  arcs. 

Expansion  of  Liquids. 

(249.)  Absolute  and  Apparent  Expansion.  —  In  considering 
the  expansion  of  a  liquid,  it  is  important  to  distinguish  between 
the  absolute  expansion  and  the  apparent  expansion  when  the 
liquid  is  enclosed,  in  a  glass  vessel.  From  the  very  nature  of  a 
liquid,  it  is  evident  that  its  absolute  expansion  cannot  be  directly 
observed,  but  must  be  determined  by  indirect  methods.  It  is 
also  evident,  that  the  absolute  expansion  must  be  equal,  in  any 
case,  to  the  apparent  expansion,  increased  by  the  amount  of  ex- 
pansion of  the  glass  vessel  containing  the  liquid;  compare  (219) 
and  (241) ;  and  hence,  when  any  two  of  these  quantities  arc 
known,  the  third  can  always  be  calculated. 


508 


CHEMICAL   PHYSICS. 


(250.)  Absolute  Expansion  of  Mercury.  —  The  coefficient  of 
absolute  expansion  of  mercury  is  one  of  the  most  important 
constants  of  physics ;  for  not  only  does  it  enter  indirectly  into  the 
determination  of  the  expansion  of  most  other  substances, — solids, 
liquids,  and  gases  (254),  —  but  it  also  has  a  direct  bearing  on 
the  theory  and  use  of  both  the  thermometer  and  barometer 
(219)  and  (160).  It  is  therefore  essential  that  this  constant 
should  be  determined  with  the  greatest  care. 

The  most  accurate  method  of  determining  the  coefficient  of 
absolute  expansion  of  mercury  is  based  upon  the  principle  in 
hydrostatics  (131),  that,  when  two  tubes  filled  with  different 
liquids  communicate  together,  the  heights  of  the  two  liquid  col- 
umns if  in  equilibrium  are  inversely  proportional  to  the  specific 
gravities  of  the  liquids.  What  is  true  of  different  liquids  must 
also  be  true  of  the  same  liquid  at  different  temperatures  ;  and 
we  can  therefore  determine  the  relative  specific  gravity  of  mer- 
cury at  such  temperatures  by  measuring  the  heights  of  the  mer- 
cury-columns in  the  legs  of  an  inverted  siphon,  so  arranged 
that  each  column  may  be  exposed  to  the  temperature  required. 
When  the  specific  gravity  at  two  different  temperatures  has  been 
thus  determined,  we  can  easily  calculate  the  coefficient  of  expan- 
sion by  [168]. 

The  apparatus  used  by  Dulong  and  Petit,  who  determined  the 
absolute  expansion  of  mercury  by  the  hydrostatic  method,  is 


Fig.  379. 


represented  in  Fig.  379.  It  consisted  of  two  glass  tubes,  A  and 
J5,  supported  vertically  on  an  iron  basement,  and  united  below 
by  a  capillary  tube,  so  as  to  form  together  an  inverted  siphon. 


HEAT.  509 

The  two  tubes  were  each  enclosed  in  a  metallic  vessel.  The 
^allest  of  these,  Z),  was  filled  with  pulverized  ice,  and  the  other, 
E,  contained  oil,  which  was  gradually  heated  by  a  small  fur- 
nace, which  the  figure  represents  in  section,  in  order  to  show  the 
construction.  Lastly,  the  tubes  were  filled  with  mercury,  which 
preserved  the  same  level  in  both  as  long  as  the  tubes  were  ex- 
posed to  the  same  temperature,  but  which  rose  in  the  tube  B  in 
proportion  as  it  was  heated.  In  making  an  observation  with  this 
apparatus,  the  bath  was  first  heated  to  the  required  temperature, 
which  was  indicated  by  the  thermometer  P,  and  then  the  heights 
of  the  two  columns  were  measured  by  the  cathetometer  K. 

In  order  to  calculate  from  such  an  observation  the  coefficient 
of  absolute  expansion,  let  us  represent  by  H  and  (Sp.Gr.^)  the 
height  and  specific  gravity  of  the  mercury-column  A  at  0°,  and 
by  H'  and  (Sp.Gr.y  the  height  and  specific  gravity  of  the  mer- 
cury-column B  at  t°.  Then  we  have,  by  [81],  H  .  (Sp.Gr.)  = 
H'  (Sp.  Gr.y.  Moreover,  representing  the  coefficient  of  absolute 
expansion  of  mercury  by  K,  we  have,  by  [166]  and  [56], 

(^p.GV.)  =  (Sp.Gr.y  (l  +  Kt).  [169.] 

Combining  the  two  equations,  we  obtain,  for  the  value  of  K, 


By  this  method,  Dulong  and  Petit  found  that  the  mean  abso- 
lute expansion  of  mercury  between  0°  and  100°  was  ^v  = 
0.000  18018.  Regnault  has  since  redetermined  this  coefficient 
with  an  apparatus  based  on  the  same  principle,  but  very  greatly 
improved,  and  has  obtained,  for  the  mean  value  between  0°  and 
100°,  0.000  18153,  a  number  which  differs  but  little  from  that  of 
Dulong  and  Petit.  The  apparatus  of  Regnault,  although  very 
simple  in  principle,  is  quite  complicated  in  construction,  and  it 
would  require  more  space  to  describe  it  than  we  are  able  to 
give  ;  but  the  student  will  find  it  described  in  full  in  Regnault's 
memoir  on  the  subject.* 

As  has  already  been  stated  (219),  the  coefficient  of  expansion 
of  mercury  increases  with  the  temperature.  This  is  shown  by 
the  following  table,  which  contains  the  results  obtained  by  Reg- 
nault. 

*  Memoires  de  1'Academie  des  Sciences  de  1'Institut,  1847. 

43* 


CHEMICAL  PHYSICS. 


True  Tempera- 
ture by 
Air-Thermometer. 

0° 

Mean  Coefficient  of 
Expansion  of  Mercury 
from  0°  to  t°. 

0 

Actual  Coefficient 
of  Expansion 
from  t°  to  (t  -f-  1)°. 

0.00017905 

Volumes 
of 
Equal  Weights. 

1.0000000 

30 

0.00017976 

0.00018051 

1.0053928 

50 

0.00018027 

0.00018152     < 

10090135 

70 

0.00018078 

0.00018253 

1.0126546 

100 

0.00018153 

0.00018305 

1.0181530 

150 

0.00018279 

0.00018657 

1.0274185 

200 

0.00018405 

0.00018909 

1.0368100 

250 

0.00018531 

0.00019161 

1.0463275 

300 

0.00018658 

0.00019413 

1.0559740 

350 

0.00018784 

0.00019666 

1.0657440 

In  the  last  column  of  this  table  we  have  given  the  volume 
to  which  one  cubic  centimetre  of  mercury  will  expand  when 
heated  to  the  different  temperatures  indicated  in  the  first  column. 
This  volume  may  be  calculated  by  means  of  the  formula  F== 
1  -f- 1  k,  whenever  the  corresponding  mean  coefficient  between 
0°  and  t°  (as  given  in  the  second  column  of  the  table)  is  known ; 
and  for  temperatures  for  which  the  coefficient  has  not  been  de- 
termined, it  can  be  ascertained  sufficiently  near  by  interpolation. 
It  is  convenient,  however,  to  have  a  single  formula  by  which  the 
volume  can  be  calculated  at  once  for  any  temperature  ;  and  such 
a  formula  can  be  obtained  by  applying  the  principle  of  [130] . 

Since  the  volume  is  always  some  function  of  the  temperature, 
it  can  be  expressed  by  the  general  formula,  into  which  every 
algebraic  function  may  be  developed, 

F==  A  +  B  t  -f  Ct*  +  D  t3  +,  &G.  [171.] 

In  the  present  case,  A  is  equal  to  unity,  the  volume  when  the 
temperature  is  zero,  and  the  other  coefficients  can  be  found  by 
substituting  in  the  general  equation  [171]  the  value  of  -A,  and 
also  the  values  of  V  and  t  for  each  temperature  at  which  the 
volume  has  been  experimentally  determined.  We  shall  thus 
obtain  as  many  equations  as  there  are  determinations,  and  by 
combining  them  together  according  to  the  well-known  methods  of 
algebra  we  can  easily  calculate  the  coefficients  required.  Making 
use  of  Regnault's  results,  as  given  in  the  above  table,  we  should 
thus  obtain  for  the  volume  of  mercury  at  any  temperature,  t,  as 
indicated  by  an  air-thermometer,  the  value, 


HEAT.  511 

F=  1  -f  0.0001T9007  t  +  0.0000000252316  1*.      [172.] 

It  is  unnecessary  to  add  that  tins  formula  is  purely  empirical, 
and  can  only  be  trusted  for  temperatures  within  the  limits  be- 
tween which  the  experiments  were  made. 

(251.)  Correction  of  the  Observed  Height  of  the  Barometer 
for  Temperature.  —  Since  the  height  of  a  barometer  is  affected 
by  changes  of  temperature  (160),  it  becomes  essential,  before 
comparing  together  different  observations,  to  reduce  each  to  the 
standard  temperature  of  0°  ;  in  other  words,  to  calculate  what 
would  have  been  the  height  had  the  temperature  at  the  time  of 
the  observation  been  at  the  freezing-point.  The  principles  of 
the  last  section  furnish  us  with  a  ready  method  of  making  the 
reduction. 

The  pressure  of  the  air  being  constant,  it  follows  from  (158)  and  [81] 
that  the  height  of  a  mercury  barometer  at  different  temperatures  will  be 
inversely  proportional  to  the  specific  gravity  of  mercury  at  these  tempera- 
tures. Hence  we  shall  have  Hi  H'  =  (Sp.Gr.)'  :  (Sp.Gr.),  a  propor- 
tion in  which  /f  and  (Sp.Gr.)  represent  the  height  of  the  column  and  the 
specific  gravity  of  mercury  at  0°,  while  H'  and  (Sp.Gr.)1  represent  the 
same  values  at  f.  But  we  also  have  (Sp.Gr.)  =  (Sp.Gr.)1  (1  -f-  Kt), 
and  combining  this  with  the  last  proportion,  we  at  once  deduce  H1  = 
J5T(l-fjn),  and 


or,  substituting  for  K  its  mean  value  between  0°  and  100°  (0.00018  = 


The  last  term  of  the  above  formula  is  the  correction  which  must  be  sub- 
tracted from  the  observed  height,  in  order  to  reduce  the  observation  to 
zero. 

The  reduction  as  thus  made,  however,  would  not  be  quite  correct,  since 
we  have  not  taken  into  account  the  change  in  the  length  of  the  scale  of 
the  barometer  caused  by  the  expansion  of  the  material  on  which  it  is 
engraved.  If,  as  in  the  barometer  of  Fortin  (160),  this  scale  is  engraved 
on  the  brass  casing  of  the  tube,  which  extends  quite  down  to  the  cistern, 
it  is  easy  to  make  allowance  for  the  effect  of  its  expansion,  assuming  that 
the  scale  agrees  with  the  standard  of  length  at  0°.  Let  us  assume  that  the 
divisions  on  the  scale  are  in  centimetres.  It  is  evident  that  the  effect  of 


512  CHEMICAL  PHYSICS. 

heat  will  be  to  increase  the  length  of  each  division,  and  thus  to  make  the 
apparent  height  of  the  mercury-column  less  than  the  real  height.  If  the 
brass  expanded  as  much  as  the  mercury,  the  two  effects  would  balance 
each  other,  and  there  would  be  no  correction  to  make.  But  this  is  not  the 
case ;  and  the  expansion  of  the  brass  scale  only  in  part  compensates  for 
the  increased  height  of  the  mercury-column  caused  by  the  change  of  tem- 
perature. Representing  by  Ic  the  coefficient  of  expansion  of  brass,  we 
shall  have,  for  the  length  of  each  division  of  the  scale  at  t°,  the  value 
1  -j-  k  t ;  and  since  the  apparent  height  of  an  invariable  mercury-column 
must  be  inversely  proportional  to  the  length  of  the  divisions  of  the  scale, 
by  which  it  is  measured,  we  deduce  the  proportion  H:  ff0  =  1  :  1  -[-  k  t, 
in  which  H  and  HQ  represent  respectively  the  apparent  heights  of  the 
column  at  t°  and  0°  respectively.  Substituting  in  this  proportion  the 
value  of  H  [173],  we  readily  deduce 

H  _ .  -fji  Lufcif  -  -  H'  --  ft1  ^ ^-.          ri7^  i 

^-  Y+Kt-  'l+Kt   ' 

The  second  term  of  the  above  formula  gives  a  correction,  to  be 
subtracted  from  the  observed  height  of  a  mercury-column,  which 
eliminates  the  expansion  of  the  scale  as  well  as  that  of  the  column 
itself,  and  reduces  the  observations  strictly  to  0°.  The  value  of 
this  correction,  in  centimetres,  corresponding  to  one  degree  of 
temperature,  is  given  in  Table  XVIII.  for  every  five  millimetres 
in  the  height  of  the  mercury-column  from  0.5  c.  m.  to  100  c.  m., 
and  not  only  for  a  barometer  with  a  brass  scale,  but  also  for  a 
barometer  with  the  scale  engraved  on  the  glass  tube.  The  cor- 
rection for  any  given  temperature  is  found  by  multiplying  the 
number  from  the  table  opposite  to  the  observed  height  by  the 
number  of  degrees.  If  the  degrees  are  above  zero,  the  correc- 
tion is  to  be  subtracted  from  the  observed  height ;  if  below,  to  be 
added  to  it.  This  same  table,  as  well  as  the  formula  [175],  may 
also  be  used  for  reducing  to  0°  the  height  of  any  mercury- 
column  ;  for  example,  that  in  a  manometer-tube  (168),  or  in  a 
glass  bell  over  a  mercury  pneumatic  trough  (169).  If  the  height 
of  the  column  is  measured  by  means  of  a  cathetometer,  as  in 
Fig.  272,  it  is  equivalent  to  using  a  barometer  with  a  brass  scale, 
and  the  correction  must  be  taken  from  the  column  headed  "  Brass 
Scale  "  in  Table  XVIII.  If,  on  the  other  hand,  it  is  measured  by- 
means  of  graduation  on  the  glass  bell  or  tube  itself,  the  column 
headed  "  Glass  Scale  "  should  be  used. 


HEAT. 


513 


Fig.  380. 


(252.)  Apparent  Expansion  of  Mercury.  —  The  apparent  ex- 
pansion of  mercury  will  evidently  vary  with  the  nature  of  the 
vessel  in  which  it  is  enclosed.  But  since  the  vessels 
used  for  the  purpose  are  almost  invariably  made  of 
glass,  we  understand  by  the  term  apparent  expan- 
sion the  apparent  expansion  in  glass,  unless  it  is 
otherwise  stated.  The  apparent  expansion  of  mer- 
cury in  glass  can  readily  be  determined  experimen- 
tally by  means  of  the  apparatus  represented  in  Fig. 
380.  It  consists  of  a  cylindrical  reservoir  opening 
into  a  capillary  tube,  which  is  drawn  out  at  the  end 
to  a  fine  point,  and  bent  into  the  form  of  a  hook. 
The  apparatus  is  in  the  first  place  weighed,  and  then 
filled  with  pure  mercury,  like  a  thermometer-tube 
(Fig.  340),  taking  care  to  boil  the  mercury  in  the 
reservoir  in  order  to  expel  the  last  traces  of  air  and 
moisture.  It  is  next  surrounded  with  melting  ice, 
the  orifice  of  the  tube,  o,  dipping  under  mercury, 
which  is  thus  drawn  into  the  apparatus  as  the  temperature  falls 
until  the  whole  is  filled  with  mercury  at  0°.  Having  weighed 
the  apparatus  again,  and  subtracted  the  weight  of  the  glass, 
we  obtain  the  weight  of  the  mercury  at  0°,  which  we  will  repre- 
sent by  W.  Finally,  we  expose  the  apparatus  to  a  constant  and 
known  temperature,  £°,  (for  example,  to  that  of  the  steam  from 
boiling  water,)  and  collect  and  weigh  the  mercury  which  escapes. 
Call  this  weight  w  ;  then  W —  w  is  the  weight  of  mercury  which 
just  fills  the  apparatus  at  t°.  We  have  now  all  the  data  required 
for  calculating  the  apparent  coefficient  of  expansion. 

The  volume  of  W —  w  grammes  of  mercury  at  0°  is,  by  [56] , 

V=         ^     .      Neglecting   the   expansion   of   the   glass,   this 

weight  of  mercury  occupies  at  t°  the  same  volume  which  was 
filled  by  W  grammes  of  mercury  when  the  temperature  was 
zero ;  viz.  the  volume  of  the  apparatus.  Hence,  the  volume  of 

W 
W —  w  grammes  at  t°  is   V'  =     „    r  .  .      But  if  J£   repre- 


sents the  coefficient  of  apparent  expansion,  we  have,  by  (239), 
V  =  V  (1  +  K  0  ;  and  substituting  the  values  of  V  and  V, 
we  get,  by  reducing, 

K  =        w  n.76.1 

n        (TT—  w)t 


514  CHEMICAL   PHYSICS. 

Dulong  and  Petit  found,  by  this  method,  that  the  apparent 
coefficient  of  expansion  of  mercury  in  the  common  glass  of 
Paris  is  ^^ff  ;  but  evidently  this  coefficient  depends  on  the 
expansion  of  glass,  and  is  liable  to  all  its  variations  (245). 

(253.)  We  can  also  easily  determine  the  apparent  expansion 
of  mercury  by  a  thermometer-tube,  whose  stem  has  been  divided 
into  parts  of  equal  capacity  (221).  For  this  purpose,  we  in 
the  first  place  ascertain  the  relation  between  the  volume  of  the 
reservoir  and  that  of  one  of  the  divisions  of  the  tube  in  the  fol- 
lowing way  :  — 

The  tube,  having  been  weighed,  is  partially  filled  with  mer- 
cury, and  the  point  on  the  lower  part  of  the  stem  at  which  the 
mercury  stands  in  melting  ice  is  carefully  marked.  Now  re- 
weighing  the  tube,  we  find  the  weight  of  mercury  which  the  tube 
and  bulb  contain  below  this  index-mark.  Call  this  weight  W. 
An  additional  quantity  of  mercury  is  then  introduced,  so  that, 
when  the  apparatus  is  again  immersed  in  ice-water,  the  column 
stands  at  the  wth  division  above  the  mark.  A  third  weighing  now 
gives  the  weight  of  mercury  occupying,  at  0°,  n  divisions  of  the 

rtrt 

tube.      Call  this  weight  w  ;    then  —  is  the  weight  of  mercury 

which  fills  one  division  of  the  tube.  Assuming  the  volume  of 
one  division  of  the  tube  as  our  unit  of  measure,  and  representing 
by  N'  the  number  of  such  units  of  volume  which  the  bulb  and 
tube  contain  below  the  index-mark,  we  have 


and  knowing  the  number  of  these  arbitrary  units  of  volume 
below  the  index-mark  on  the  tube,  we  can  by  simple  addition 
or  subtraction  find  the  number  below  any  other  division.  Let  us 
represent  this  number  in  general  by  N. 

The  bulb  and  tube  having  been  thus  gauged,  in  order  to  meas- 
ure the  apparent  expansion  of  mercury  we  have  only  to  deter- 
mine the  two  fixed  points,  as  in  making  a  thermometer  (218). 
The  number  of  divisions  on  the  stem  between  these  points  is  the 
niimber  of  units  of  volume  which  N  units  of  volume  expand  be- 
tween 0°  and  100°.  Representing  by  n  the  number  of  divisions 
between  the  fixed  points,  we  have,  by  [166], 

100),    whence     fi  =  ~'y      [178.] 


HEAT.  515 

which  is  the  coefficient  required.  This  method,  although  not  so 
accurate  in  the  case  of  mercury  as  the  one  described  in  the  last 
section,  is  much  the  more  accurate  of  the  two  for  other  liquids. 

(254.)  Relation  between  the  Apparent  and  Absolute  Coeffi- 
cient of  Expansion.  —  It  has  already  been  stated  (249),  that  the 
apparent  increase  of  volume  of  mercury  in  a  glass  vessel  is  equal 
to  the  actual  increase  of  volume  diminished  by  the  amount  of 
expansion  of  the  glass.  A  simple  algebraic  calculation  will  show 
that  the  apparent  coefficient  of  expansion  of  mercury  is  also  equal 
to  the  absolute  coefficient  diminished  by  the  coefficient  of  expan- 
sion of  the  glass.  Representing  these  quantities  respectively  by 
l\,  JT,  and  K1,  we  have,  in  every  case, 

it  =  K  —  K'     (1),      or         K1  =  K—  K    (2)  ;    [179.] 

so  that  we  can  always  calculate  either  coefficient  when  the  other 
two  are  known.  Now  the  absolute  coefficient  of  mercury  is 
known  with  great  accuracy,  and  we  can  therefore  use  the  pro- 
cesses described  in  the  last  two  sections  for  determining  the 
coefficient  of  expansion  of  glass.  Indeed,  this  is  much  the  most 
accurate  method  we  have,  and  the  careful  determinations  made 
by  Regnault  of  the  coefficients  of  expansion  of  different  kinds  of 
glass,  and  of  the  same  glass  under  different  circumstances,  were 
made  in  this  way. 

We  can  also  use  the  method  of  (252)  for  determining  the 
coefficient  of  expansion  of  any  solid  not  acted  on  by  mercury, 
when  the  coefficient  of  the  glass  used  is  known.  For  this  pur- 
pose, a  weighed  amount  of  the  solid  (either  in  fragments  or 
in  the  form  of  a  bar)  is  introduced  into  a  glass  tube  closed 
at  one  end,  and  the  other  end  is  then  heated  in  a  lamp  and 
drawn  out  into  the  form  represented  in  Fig.  380.  The  tube  is 
next  filled  with  mercury,  and  the  experiment  conducted  in  all 
respects  as  described  in  (252).  We  shall  then  have  the  follow- 
ing data  for  calculating  the  coefficient  of  expansion  of  the  solid : 

1.  the  weight  of  the  solid  (W^),  and  its  specific  gravity  (#) ; 

2.  the  weight  of  mercury  in  the  tube  at  0°  (  W'),  and  its  specific 
gravity  (5')  ;  3.  the  weight  of  mercury  in  the  tube  at  t°  (  W1 — w)\ 
4.  the  coefficients  of  mercury  and  glass  (K  and  A"'),     Represent- 
ing also  by  x  the  unknown  coefficient  of  the  solid,  we  can  easily 
obtain  it  from  the  following  equation,  remembering  that  the  vol- 
ume of  the  tube  either  at  0°  or  t°  must  be  equal  to  the  volume  of 


516  CHEMICAL  PHYSICS. 

the  enclosed  solid  plus  the  volume  of  the  mercury  it  contains 
at  the  temperature.     See  also  [56]  and  [166]  . 

=  7  (1  +  x  °  +  ""a7"  (*  +  *<>•    [130.] 
From  this  we  obtain  the  value  of  the  coefficient, 


1       S  w    ,    («<  —  P1Q1  -. 

=  7'¥W~          ~d'W~  ~6rW~ 

This  method  of  determining  the  coefficient  of  expansion  of 
solids  admits,  in  many  cases,  of  great  accuracy.  It  was  used  by 
Dulong  and  Petit  for  determining  the  coefficients  of  cubic  expan- 
sion of  iron,  platinum,  and  copper. 

(255.)  Laws  of  the  Expansion  of  Liquids.  —  The  fullest  in- 
vestigations on  the  expansion  of  liquids  have  been  made  by 
Kopp,*  in  Germany,  and  by  Pierre,f  in  France.  These  experi- 
menters followed  essentially  the  same  method.  They  deter- 
mined, in  the  first  place,  the  apparent  expansion  by  means 
of  a  thermometer-tube,  as  described  in  (253),  and  afterwards 
corrected  the  results  for  the  expansion  of  the  glass.  The  follow- 
ing are  the  most  important  facts  which  are  known  in  regard  to 
the  expansion  of  this  class  of  bodies. 

Liquids,  like  solids,  expand  with  an  almost  irresistible  force, 
which  may  be  measured  by  the  mechanical  effort  required  to 
condense  the  expanded  liquid  to  its  initial  volume  (118).  For 
the  same  increase  of  temperature,  all  liquids  expand  more  than 
the  most  expansible  solid.  This  we  should  naturally  expect, 
from  (244),  because  liquids  are  more  compressible  than  solids  ; 
and  in  support  of  the  same  principle,  we  find  that  the  order  of 
expansibility  of  different  liquids  is  nearly  the  same  as  the  order 
of  compressibility,  although  by  no  means  identical  with  it.  It 
may  also  be  stated  as  a  general  rule,  but  one  to  which  there  are 
many  exceptions,  that  the  most  expansible  liquids  are  those 
which  have  the  lowest  boiling-points  ;  this  is  especially  true 
in  regard  to  liquids  which  are  allied  in  their  chemical  proper- 

*  Poggendorff,  Annalen,  Band  LXXIL  S.  223.  Also  Ann.  Chern.  und  Pharm., 
Band  XCIV.  S.  257  ;  Band  XCV.  S.  307. 

t  Annales  de  Chimie  et  de  Physique,  3«  Serie,  Tom.  XV.,  XIX.,  XX.,  XXI., 
XXXL,  XXXIII. 


HEAT. 


517 


ties.  The  difference  between  the  coefficients  of  expansion  of 
different  liquids  for  the  extreme  cases  is  very  great.  Thus, 
while  the  coefficient  of  mercury  is  only  0.00019  at  the  boiling- 
point,  that  of  aldehyde  is  0.002025,  only  one  third  less  than  that 
of  air.  The  amount  of  expansion  of  different  liquids  for  the 
same  interval  of  temperature  may  therefore  differ  immensely. 

The  rate  of  expansion  of  all  liquids  increases  with  the  tempera- 
ture ;  but  it  varies  according  to  different  laws  with  different  sub- 
stances, and  these  laws  appear  to  be  very  complicated.  Of  all 
liquids,  the  coefficient  of  expansion  of  mercury  increases  the  most 
slowly,  that  of  water  the  most  rapidly, —  the  difference  between 
the  mean  rate  of  increase  in  the  two  cases  being  (according  to 
Regnault  and  Kopp)  as  28  to  1,408.  The  following  table,  which 
includes  also  a  few  of  the  results  of  Pierre's  investigation,  will 
illustrate  these  facts. 


Name  of  Liquid. 

Coefficient  of 
lIx|>:uiM<m  at 
Boiling-Point. 

Coefficient  of 
Expansion 
atO°. 

M.-.iii  1'atoof 
Increase  l>etween 
O3  and  Boiling- 
Poiut,  for  1°. 

Boiling- 
Point. 

0 

Mercury, 

0.000197* 

0.000179* 

0.023 

360 

Chloride  of  Amylc,     . 

O.OOKJ93 

0.001171 

0.158 

101.75 

Terebene, 

0.001328 

0.000896 

0.299 

161 

Ethylic  Alcohol,  . 

0.001347 

0.001049 

0.364 

78.3 

Methylic  Alcohol,  . 

0.001491 

0.001185 

0.409 

63 

Bromine, 

0.001318 

0.001033 

0.429 

63.04 

Terchloride  of  Phosphorus, 

0.001589 

0.001129 

0.521 

78.34 

Chloroform, 

0.001488 

0.001107 

0.543 

'     63.oO 

Amylic  Alcohol, 

0.001606 

0.000890 

0.611 

131.8 

B  mm  id  e  of  Methyle,  . 

0.001559 

0.001415 

0.7S2 

13 

Chloride  of  Silicon, 

0.001978 

0.001294 

0.896 

59 

Sulphurous  Acid, 

0.001820 

0.00l496f 

1.J54 

-3 

Aldehyde, 

0.002121 

0.001653 

1.2S3 

22 

Water, 

0.000765 

o.oooooot 

100 

It  has  been  found  in  a  few  cases,  that,  starting  from  the  boiling- 
point,  the  volumes  of  liquids  belonging  to  the  same  chemical 
group  diminish,  as  the  temperature  falls,  very  nearly  at  the 
same  rate.  By  this  is  meant,  that,  starting  with  equal  volumes 
of  such  chemically  allied  liquids  at  their  boiling-points,  the  vol- 
umes also  will  be  equal  at  temperatures  equally  distant  from  these 
points.  At  least,  this  was  observed  to  be  true  by  Pierre  in  five 


*  Calculated  from  Renault's  formula  [172]. 
t   This  coefficient  of  sulphurous  acid  is  taken  at 
J  At  4°  or  point  of  maximum  density. 


-25°.  85. 


518 


CHEMICAL   PHYSICS. 


separate  instances  ;  but  unfortunately  these  groups  consisted  of 
only  two  or  three  liquids,  and  hence  110  general  conclusions  can 
be  drawn  from  the  facts. 

The  expansion  of  most  liquids  can  be  represented  by  a  formula 
of  the  general  form  [171]  ,  with  the  same  numerical  coefficients 
for  all  temperatures  between  the  limits  of  the  experiment.  The 
following  are  the  formulae  for  alcohol,  ether,  and  oil  of  turpentine, 
as  calculated  by  Kopp  from  the  results  of  his  own  experiments  :  — 

Alcohol,    Sp.  Gr.  =  0.80950  ;  B.  P.  =  78°.4  ;  0°  to  79°.6. 

V=  1  +  0.00104139  1  +  0.0000007836  12  -f  0.00000001  7G18  13. 
Ether,    Sp.  Gr.  =  0.73658  ;   B.  P.  =  34°.9  ;  0°  to  33°. 

V=  1  -f  0.00148026  1-\-  0.00000350316^-f-  0.000000027007  *3. 
Oil  of  turpentine,    Sp.  Gr.  =  0.884  ;   B.  P.  —  156°  ;    9°.3  to  105°.6. 
F  =  I  -f  0.0009003*  +  0.0000019595  12  -f  0.0000000045  1*. 

In  each  case  are  given  the  specific  gravity,  the  boiling-point,  and 
the  limits  of  temperature  between  which  the  experiments  from 
which  the  formula  is  deduced  were  made. 
Strictly  speaking,  the  formula  only  holds 
between  these  limits  ;  but,  nevertheless, 
it  can  be  used  without  any  important 
error  for  temperatures  a  few  degrees 
either  above  or  below  the  extreme  lim- 
its, as,  for  example,  to  determine  the 
volume  of  a  liquid  at  the  boiling-point. 
The  law  of  expansion  which  any  given 
liquid  obeys  may  also  be  expressed  by 
means  of  a  curve  applying  the  principle 
already  explained  in  (195).  Fig.  881 
represents  three  such  curves,  those  of 
mercury,  water,  and  alcohol.  Here  the 
numbers  on  the  horizontal  axis  indicate 
degrees  of  temperature,  and  the  numbers 
on  the  vertical  axis  the  corresponding 
amount  of  expansion,  expressed  in  frac- 
tions  of  the  unit  of  volume.  These 
curves  illustrate  several  of  the  facts  just 
stated.  It  is  evident,  for  example,  that  alcohol  expands  much 
more  rapidly  than  either  of  the  other  two  liquids.  It  will  also 


HEAT. 


519 


be  noticed,  that,  although  above  40°  water  expands  more  rap- 
idly than  mercury,  yet  below  this  temperature  the  order  is  re- 
versed. Moreover,  it  will  be  seen  that  the  curve  of  mercury  is  a 
straight  line,  showing  that  the  amount  of  its  expansion  is  propor- 
tional to  the  temperature,  or,  in  other  words,  that  the  rate  is  uni- 
form. (The  small  variation  which  actually  exists  is  not  sensible, 
on  account  of  the  reduced  scale  of  the  figure.)  The  curve  of 
alcohol,  on  the  other  hand,  bends  in  towards  the  vertical  axis, 
indicating  that  its  rate  of  expansion  increases  with  the  tempera- 
ture ;  and  the  curve  of  water,  bending  much  more  strongly, 
points  to  a  still  more  rapid  variation. 

(256.)  Expansion  of  Liquids  above  the  Boiling- Point.  —  It 
is  a  well-known  fact,  that,  when  a  liquid  is  confined  in  a  strong 
and  hermetically-sealed  vessel,  its  temperature  may  be  raised  very 
greatly  above  its  boiling-point ;  and  it  becomes  a  very  interesting 
subject  of  inquiry,  whether  the  rate  of  expansion,  which  increases 
so  rapidly  as  we  approach  this  point,  increases  with  equal  rapid- 
ity above  it.  This  subject  has  recently  been  investigated  by 
C.  Drion,*  and  he  has  arrived  at  the  very  remarkable  conclusion, 
that  under  these  circumstances  the  coefficient  of  expansion  of  a 
liquid  not  only  increases  at  a  constantly  accelerated  rate,  but  also 
that  it  may  even  surpass  the  coefficient  of  expansion  of  the  gases. 
The  experiments  of  Drion  were  made  on  chloride  of  ethyle, 
hyponitric  acid,  and  sulphurous  acid,  and  his  results  are  given  in 
the  following  table,  which  shows  the  coefficients  of  expansion  of 
all  three  liquids  at  the  temperatures  indicated. 


Temperature. 

Coefficient  of  Expansion. 

Chloride  of  Ethyle. 
B.  P.  =  11°. 

Sulphurous  Acid. 
B.  P.  =  —8°. 

Ilvpouitric  Acid. 
B.  P.  =  22J. 

0° 

0.001482 

0.001734 

0.001445 

20 

0.001699 

0.002029 

0.001596 

40 

0.001919 

0.002371 

0.001847 

60 

0.002202 

0.002846 

0.002230 

80 

0.002625 

0.003608 

0.002768 

90 

0.002910 

0.004147 

0.003081 

100 

0.003250 

0.004859 

110 

0.003690 

0.005919 

120 

0.004306 

0.007565 

130 

0.003031 

0.009571 

Coefficient  of  expansion  of  air  =  0.003665. 


*  Annales  de  Chimie  et  de  Physique,  3"  Se'rie,  Tom.  LVI. 


520  CHEMICAL  PHYSICS. 

It  will  be  noticed  that  the  coefficients  of  all  three  liquids  in- 
crease with  very  great  rapidity  above  their  boiling-points,  and  that 
those  of  the  first  two  soon  exceed  the  coefficient  of  air.  The 
same  is  undoubtedly  the  case  with  hyponitric  acid  ;  but  it  was 
impossible  to  push  the  experiment  above  90°,  because  the  deep 
color  of  the  vapor  obscured  the  position  of  the  summit  of  the 
liquid  column  in  the  thermometer-tube. 

These  results  confirm  the  following  observation  made  by  Thi- 
lorier,  in  1835,  in  regard  to  the  expansion  of  liquid  carbonic 
acid,  which  has  been  hitherto  received  with  great  mistrust  on 
account  of  its  paradoxical  nature,  but  which  is  now  shown  by 
Dripn  to  be  in  perfect  harmony  with  the  laws  of  liquid  expan- 
sion :  — 

"This  liquid  presents  the  strange  and  paradoxical  fact  of  a 
liquid  more  expansible  than  the  gases ; in  a  word,  its  ex- 
pansion is  four  times  greater  than  air,  which  between  0°  and  30° 
expands  only  ^y,  while  the  expansion  of  liquid  carbonic  acid 
reduced  to  the  same  scale  amounts  to  ££f ."  * 

(257.)  Expansion  of  Water.  —  The  expansion  of  water  is  far 
more  irregular  than  that  of  any  known  liquid,  although  the  total 
amount  of  expansion  between  0°  and  100°  is  comparatively  small. 

This  fact  is  shown  by  the  table  on  page  517,  from  which  it 
appears  that  the  coefficient  of  water  increases  as  the  temperature 
rises  vastly  more  rapidly  than  that  of  any  other  liquid  mentioned, 
although  this  coefficient,  even  at  the  boiling-point,  is  the  smallest 
in  the  table  with  the  single  exception  of  that  of  mercury ;  and  not 
only  does  the  coefficient  increase  with  this  unparalleled  rapidity, 
but  also  the  rate  of  increase  varies  so  irregularly,  that  it  has  been 
found  impossible  to  express  the  volume  of  water  at  different 
temperatures  by  any  single  empirical  formula.  All  this  is  true 
of  the  expansion  of  water  between  10°  and  100°,  and  below  10° 
the  expansion  is  still  more  irregular  than  it  was  above ;  for  water 
alone  of  all  liquids  has  a  point  of  maximum  density  above  its 
freezing-point  (4°  C.),  and  from  this  temperature  it  expands, 
whether  it  be  heated  or  cooled. 

(258.)  Point  of  Maximum  Density.  —  This  last  fact,  which  is, 
so  far  as  we  know,  a  unique  property  of  water,  and  seems  to 
be  a  special  adaptation  in  the  plan  of  creation,  can  be  very  well 

*  Annales  de  Chimie  et  de  Physique,  2e  Se'rie,  Tom.  LX.  p.  427. 


HEAT. 


521 


illustrated  by  means  of  the  apparatus  represented  in  Fig.  382. 
The  apparatus   is  essentially  a  largo  water  thermometer,  —  a 
glass  flask  of  about  one  litre  capacity  form- 
ing the  bulb,  and  the  tube  being  secured 
by  leather  packing  in  a  brass  cap,  which 
screws  into  a  collar  of  the   same   metal, 
cemented  to  the  neck  of  the  flask  (see  Fig. 
383).     The   temperature  of  the  water  in 
the  flask  is  given  by  a  thermometer  sus- 
pended from  a  hook  on  the  under  side  of 
the  cap,  and  the  height  of  the  column  in 
the  tube  is  observed  by  means  of  a  wooden 
scale   divided    into    millimetres,   counting 
from  a  zero-point  near  the 
lower  end. 

If  this  apparatus  is  placed 
in  a  cold  room,  whose  tem- 
perature is  below  the  freez- 
ing-point, and  carefully 
watched,  the  column  of 
water  in  the  tube  will  be 
seen  to  fall,  until  the  ther- 
mometer in  the  flask  marks 
about  G°.  It  will  then  be 
at  its  lowest  point ;  for  as 
the  temperature  falls  still 
lower,  the  liquid  column 

will  begin  to  rise  in  the  tube,  and  continue  to  rise  until  the 
water  freezes,  although  by  keeping  the  apparatus  perfectly  still 
the  water  may  be  cooled  several  degrees  below  its  normal  freez- 
ing-point before  this  takes  place. 

The  course  of  this  very  remarkable  phenomenon  may  be  best 
represented  to  the  eye  by  means  of  a  curve.  In  Fig.  384,  the 
abscissas  of  the  curve  a  b  c  represent  degrees  of  temperature, 
and  the .  ordinates  the  corresponding  height  of  the  column  of 
water  in  the  tube  of  the  apparatus  (Fig.  382),  measured  from 
the  zero-mark  on  the  scale ;  and  it  will  be  noticed  that  the  curve 
bends  towards  the  axis  of  abscissas,  reaching  its  lowest  point  at 
the  temperature  of  about  6°.  This  curve  does  not,  however, 
represent  faithfully  the  variation  in  the  volume  of  the  water, 


Fig  3C3 


tig.  382. 


522 


CHEMICAL   PHYSICS. 


since  the  height  of  the  liquid  column  in  the  tube  depends  on  the 
expansion  of  the  glass  as  well  as  on  that  of  the  enclosed  liquid. 
But  since  we  know  the  volume  of  the  glass  flask  and  its  coeffi- 
cient of  expansion,  it  is  easy  to 
calculate  the  effect  produced  by 
its  expansion  ;  and  thus  we  can 
reduce  the  observed  heights  of  the 
column  of  water  to  what  they 
would  be,  were  the  volume  of  the 
vessel  absolutely  constant.  If,  then, 
we  construct  a  curve  with  these 
corrected  heights,  we  shall  obtain 
the  curve  adf,  which  represents 
accurately  the  variation  in  the  vol- 
ume of  water  between  0°  and  16°  ; 
and  it  will  be  seen  that  the  liquid 
has  the  smallest  volume  (or  is  most 
dense)  at  4°. 

There  is  another  singular  fact 
connected  with  this  phenomenon. 
Starting  from  the  point  of  maxi- 
mum density,  the  rate  of  expansion 

of  water  increases  with  very  nearly  equal  rapidity,  whether  we 
heat  or  cool  the  liquid.  This  is  illustrated  by  the  water  ther- 
mometer (Fig.  385),  in  which,  as  before  described  (219),  the 
d agrees  have  been  proportioned  to  the  rate  of  expansion.  In  this 
thermometer,  as  in  the  apparatus  of  Fig.  382,  the  water  will  be 
at  the  lowest  point  at  6°,  and  from  this  temperature  the  water  will 
rise  whether  the  instrument  be  heated  or  cooled,  the  length  of 
the  degrees  in  either  case  rapidly  increasing.  The  temperatures 
below  6°  are  marked  in  the  figure  on  the  left-hand  side  of  the 
scale  of  the  instrument ;  but  here,  as  before,  the  phenomenon  is 
obscured  by  the  expansion  of  the  glass,  so  that  the  rate  of  expan- 
sion on  either  side  of  the  point  of  maximum  density  cannot  be 
directly  compared.  It  is  evident,  however,  that  it  increases  in 
both  cases  with  great  rapidity  ;  and  were  the  tube  and  bulb  inex- 
pansible,  the  lowest  point  on  the  scale  would  be  4°,  and  the 
degrees  on  either  side  would  be  of  equal  lengths. 

The   fact   that  water  has   a  point  of  maximum  density  was 
first  noticed  by  the  Florentine  Academicians  as  early  as  1670  ; 


Fig.  384. 


HEAT. 


523 


but  the  phenomenon  was  first  carefully  inves- 
tigated by  Lefebre  Gineau,  while  determining 
the  French  unit  of  weight,  at  the  close  of  the 
last  century  (12).  He  fixed  the  point  of  maxi- 
mum density,  by  weighing  a  mass  of  brass  in 
water  (135)  and  comparing  the  loss  of  weight  at 
different  temperatures,  —  taking  care  to  reduce 
the  results  to  what  they  would  have  been  if  the 
volume  of  the  brass  had  remained  absolutely 
constant.  He  found  that  water  was  most  dense 
at  4°.5  C.,  and  this  result  was  confirmed  subse- 
quently by  Hallstrom,*  who,  using  essentially 
the  same  process,  fixed  the  point  of  maximum 
density  at  4°.l.  Still  later,  Despretz,f  in  a  very 
extended  investigation,  published  in  1839,  on 
the  expansion  of  water  from  — 9°  to  +100°,  al- 
so fixed  the  point  of  maximum  density  at  4°. 
Despretz  used  in  his  experiment  thermometer- 
tubes,  and  measured  the  change  of  volume  by 
the  method  described  in  (253),  correcting,  of 
course,  the  observed  results  for  the  expansion 
of  the  glass.  These  observations  were  evidently 
exposed  to  all  the  uncertainties  connected  with 
the  expansion  of  glass,  already  noticed  (245)  ; 
and  since,  near  the  point  of  maximum  density, 
the  expansion  of  glass  bears  a  very  large  propor- 
tion to  that  of  water,  a  small  error  in  the  de- 
termination of  this  quantity  may  have  caused 
an  important  error  in  the  final  result.  In  order 
to  avoid  this  source  of  error,  Pliicker  and  Geiss. 
ler, J  who  have  made  the  most '  recent  investi- 
gations on  this  subject,  used  thermometer-tubes 
very  ingeniously  contrived  so  that  the  expansion 
of  mercury  should  correct  that  of  the  glass. 
They  found  it,  however,  impossible  to  deter- 
mine with  absolute  accuracy  the  point  of 

*  Annales    do    Chimie    et    de    Physique,   2«    Serie,    Tom. 
XXVIII.  p.  56. 

t  Comptes  Rcndus,  Tom.  IV.  p.  124  ;    Tom.  X.  131 
J  Poggendorff's  Annalen,  Band  LXXXVL 


18 


Fig.  385. 


524 


CHEMICAL   PHYSICS. 


maximum  density  by  direct  observation  ;  but  they  concluded 
that  it  must  be  very  near  3°. 8,  and  that  it  might  be  regarded 
for  all  practical  purposes  as  at  4°  without  sensible  error.  In- 
deed, it  is  impossible  with  our  present  methods  of  observation 
to  fix  the  point  of  maximum  density  within  a  quarter  of  a 
Centigrade  degree  ;  nor  is  this  important,  since  the  volume  of 
water  does  not  vary  perceptibly  for  a  degree  on  either  side  of 
this  point. 

Fig.  386  gives  a  graphic  delineation  of  the  expansion  of  water 
between  — 4°  and  +12°,  according  to  the  method  of  analytical 


Fig.  386. 

geometry.  The  curve  drawn  with  a  heavy  line  has  been  plotted 
from  the  results  of  Pliicker  and  Geissler,  and  that  with  a  light 
line  from  those  of  Despretz.  The  abscissas  of  the  curves  are 
tho  degrees  of  temperature,  and  the  ordinates  are  the  amounts  of 
expansion,  —  the  number  on  the  vertical  axis  being  in  each  case 


HEAT.  525 

so  many  million tlis  of  the  volume  at  0°.  It  will  be  noticed  that 
the  two  branches  of  the  curve  on  either  side  of  the  abscissa  of 
4°  are  similar,  showing,  as  stated  above,  that  the  expansion 
increases  at  the  same  rate  from  the  point  of  maximum  density, 
whether  the  water  be  heated  or  cooled. 

This  provision  in  the  constitution  of  water,  that  its  point  of 
maximum  density  is  four  degrees  above  the  freezing-point,  is  one 
of  great  importance  in  the  economy  of  nature  ;  for  were  it  not 
for  this  apparent  exception  to  an  otherwise  universal  law,  all  the 
ponds  and  lakes  of  our  northern  climates  would  be  converted 
every  winter  into  a  solid  mass  of  ice.  It  must  be  remembered, 
that  all  liquids  are  poor  conductors  of  heat,  and  that  they  can 
only  be  heated  or  cooled  by  a  circulation  of  their  particles,  by 
which  each  in  its  turn  is  brought  in  contact  with  some  hot  or 
cold  surface.  Jlence  we  cannot  cool  a  liquid  by  removing  the 
heat  from  below.  The  lowest  stratum  of  liquids,  it  is  true, 
readily  yields  its  heat ;  but  since  its  density  is  thus  increased,  it 
remains  persistently  at  the  bottom,  and  then  its  poor  conducting 
power  comes  into  play,  and  prevents  the  escape  of  the  heat  from 
the  great  mass  of  the  liquid  above.  We  can  easily,  however, 
cool  a  liquid  by  removing  the  heat  from  the  upper  surface,  for 
then  the  particles  of  liquid  sink  as  fast  as  they  are  cooled,  until 
the  whole  mass  is  reduced  to  a  uniform  temperature. 

Such  a  circulation  as  this  takes  place  in  every  pond  as  the 
winter's  cold  increases,  and  continues  until  the  temperature  of 
the  mass  of  water  has  been  reduced  to  4° ;  but  as  the  tempera- 
ture approaches  the  point  of  maximum  density,  the  circulation 
slackens,  and  is  entirely  arrested  when  that  point  is  fully  reached. 
The  surface  water  cools  still  lower,  and  finally  freezes  ;  but  then 
the  ice,  being  a  poor  conductor  of  heat,  and  floating  on  the  sur- 
face, serves  as  a  cloak  to  the  pond,  so  that  during  the  coldest 
winter  a  thermometer  will  always  indicate  a  temperature  of  4° 
if  sunk  only  a  few  feet  below  the  ice. 

If  water  had  been  constituted  like  other  liquids,  the  circula- 
tion just  described  would  have  continued  down  to  the  freezing- 
point,  and  the  ice,  being  now  heavier  than  the  water,  would  have 
first  formed  at  the  bottom  of  the  pond,  and  gradually  accumu- 
lated until  the  whole  mass  of  water  was  frozen.  On  such  a  body 
of  ice  the  hottest  summers  would  have  produced  but  little  effect  ; 
and  as  now  during  the  winter  the  water  freezes  only  to  the  depth 


526  CHEMICAL   PHYSICS. 

of  a  few  feet,  so  then  during  the  summer  the  ice  would  only  have 
melted  on  the  surface.  Thus  it  is  that  the  order  of  creation  de- 
pends on  an  apparent  exception  to  a  general  law,  so  slight  and  so 
limited  in  its  extent  that  it  can  only  be  detected  by  the  most 
refined  experiments. 

A  point  of  maximum  density  has  not  been  observed  with  cer- 
tainty in  any  liquid  except  water  ;  but,  nevertheless,  it  is  possible 
that  such  a  point  may  exist  in  a  few  melted  metals,  such  as  cast- 
iron,  antimony,  and  bismuth,  which,  like  water,  expand  on  becom- 
ing solid.  These  substances,  however,  are  liquid  only  at  high 
temperatures,  at  which  it  is  impossible  to  make  accurate  meas- 
urements. On  the  other  hand,  it  has  been  proved  in  the  case  of 
many  liquids,  which,  like  olive-oil,  contract  on  solidifying,  that 
there  is  no  point  of  maximum  density. 

Despretz  has  carefully  studied  *  the  effect  of  §alts  dissolved  in 
water  on  its  point  of  maximum  density.  He  found,  in  general, 
that  aqueous  solutions  have  a  point  of  maximum  density,  which 
may  be,  however,  below  the  normal  freezing-point  of  the  solution 
when  the  quantity  of  salt  dissolved  is  considerable.  The  point 
of  maximum  density  sinks  very  nearly  in  proportion  to  the  quan- 
tity of  salt  dissolved,  and  more  rapidly  than  the  freezing-point, 
so  as  finally  to  fall  below  it  (271).  A  table  will  be  found  in  the 
memoir  just  referred  to,  giving  the  point  of  maximum  density, 
as  well  as  the  freezing-point,  in  solutions  of  various  salts  at  dif- 
ferent degrees  of  concentration. 

(259.)  Volume  of  Water  at  different  Temperatures.  — Several 
experimenters,  but  especially  Despretz,  Pierre,  and  Kopp,  have 
determined  the  volume  of  the  same  quantity  of  water  at  differ- 
ent temperatures  between  — 15°  and  100° ;  and  then,  by  means 
of  interpolation  formulae,  calculated  the  volume  for  every  degree 
between  these  limits.  The  volumes  and  corresponding  specific 
gravities,  as  thus  calculated  by  Kopp,  are  given  in  Table  XVI. 
As  already  stated,  it  is  impossible  to  express  the  volume  of 
water  at  all  temperatures  by  any  single  formula;  but  the  fol- 
lowing formulas  will  give  the  volume  very  closely  over  an  in- 
terval of  twenty-five  degrees.  The  first  of  these  was  calculated 
by  Frankenheim  from  Pierre's  experiments,  the  rest  are  by 
Kopp. 

*  Comptes  Rendus,  Tom.  IV.  p.  435. 


HEAT.  527 

Between  — 15°  and  0°, 

V—  1  —  0.0000941 7 1  -f-  0.000001 449*2  —  0.0000005985  **. 

Between  0°  and  25°, 

F  =  1  —  0.000061045*  -f-  0.0000077183 *2  —  0.00000003734 1* 

Between  25°  and  50°, 

V—  1  —  0.000065415*  -f  0.0000077587  *2  —  0.000000035408 1*. 

Between  50°  and  75°, 

F  =  1  -f.  0.00005916*  +  0.0000031849*2  +  0.000000007 2848**. 

Between  75°  and  100°, 

V=  1  -f  0.00008645*  -f.  0.0000031892 *2  +  0.0000000024487 *3. 

(260.)  The  Coefficient  of  Expansion  of  Water.  —  We  Lave 
assumed  that  the  coefficient  of  expansion  of  a  substance  at  any 
given  temperature,  £,  is  the  small  fraction  of  its  volume  by  which 
one  cubic  centimetre  of  the  substance  will  increase  when  heated 
from  t°  to  (t  -f- 1)°  ;  and  this  assumption  is  sufficiently  correct  in 
the  case  of  most  substances,  for  we  may  regard  the  rate  of  expan- 
sion as  constant  through  one  degree.  The  coefficient  of  expan- 
sion of  water,  however,  increases  so  rapidly,  that  we  cannot 
without  error  regard  it  as  absolutely  the  same  even  for  one 
degree  ;  and  we  must  therefore  define  the  coefficient  of  water 
at  any  given  temperature,  £°,  as  the  small  fraction  of  its  volume 
by  which  one  cubic  centimetre  would  expand,  when  heated  from 
t°  to  (/  + 1)°>  tf  the  rate  of  expansion  were  the  same  during  the 
interval  that  it  is  at  t°. 

We  easily  obtain  from  [166],  for  the  value  of  the  coefficient  of 
expansion  at  any  given  temperature,  t,  the  value 

v 

[182.] 

in  which  F  is  the  volume  of  the  liquid  at  a  given  temperature,  £, 
and  F'  the  volume  at  a  temperature,  2',  a  few  degrees  higher. 
This  formula,  like  our  first  definition,  assumes  that  the  coefficient 
is  constant  between  t  and  f  degrees.  We  may  evidently,  how- 
ever, conform  the  formula  to  the  definition  just  given,  by  making 
the  interval  of  temperature  /'  —  t  infinitely  small.  It  may  then 
be  expressed  by  d  t,  and  the  corresponding  difference  of  volume, 


528  CHEMICAL  PHYSICS. 

or  V  --  F,  will  be  d  F.  Making  these  substitutions,  [182] 
becomes 

•l^fci^   '-r-TF- 

Since  now  we  can  easily  obtain  the  value  of  -7—  by  differen- 
tiating one  or  the  other  of  the  values  of  F  on  page  527,  we  can 
easily  calculate  the  coefficient  of  expansion  of  water  at  any  given 
temperature,  by  simply  dividing  this  differential  coefficient  by  the 
value  of  F  for  the  given  temperature,  calculated  by  means  of  the 
formulae  just  referred  to.  Such  calculations  would  show  that 
the  coefficient  of  expansion  of  water  varies  from  zero  at  the 
point  of  maximum  density  to  0.00076487  at  100°,  the  rate  of 
expansion  increasing  far  more  rapidly  than  that  of  any  other 
liquid  known. 

Expansion  of  Gases. 

(261.)  The  differences  between  the  amounts  of  expansion  of 
different  gases  for  the  same  increase  of  temperature  are  far  less 
than  with  either  liquids  or  solids  ;  indeed,  they  are  so  small,  that, 
previous  to  the  refined  investigations  of  Regnault  on  this  sub- 
ject, the  coefficient  of  expansion  of  all  gases  was  supposed  to  be 
absolutely  the  same.  The  annexed  table  gives  the  results  of 
Regnault' s  determinations  of  the  coefficients  of  expansion  of  a 
few  of  the  best-known  gases  ;  and  it  will  be  noticed  that  the 
coefficients  of  the  first  four,  which  have  not  yet  been  condensed 
to  liquids,  are  all  sensibly  the  same,  while  the  coefficients  of  the 
last  three,  all  condensible  gases,  are  considerably  greater,  and 
the  greater  in  proportion  to  the  readiness  with  which  they  may  be 
condensed. 

Coefficients  of  Expansion  of  Gases. 

Under  Under 

Constant  Volume.       Constant  Pressure. 

Air,        .        .        .        .        .  0.003665  0.003670 

Nitrogen,    ....  0.003668  0.003670 

Hydrogen,      ....  0.003667  0.003661 

Oxide  of  Carbon,        .        .  0.003667  0.003669 

Carbonic  Acid,        .        .         .  0.003688  0.003710 

Cyanogen,  ....  0.003829  0.003877 

Sulphurous  Acid,    .        .        .  0.003845  0.003903 


HEAT. 


529 


The  first  four  coefficients,  those  of  the  constituents  of  air  and 
water,  may  be  regarded  as  identical,  at  least  for  all  practical 
purposes  ;  and  if  considered  equal  to  0. 0036664- ,  the  expansion 
for  one  hundred  degrees  will  be  represented  by  the  vulgar  frac- 
tion ££,  which  can  be  easily  remembered.  In  like  manner,  the 
expansion  for  one  degree  may  be  represented  very  closely  by  the 
vulgar  fraction  ?f  3.  Hence  273  cTiu.3  of  any  permanent  gas  at 
0°  become  274  cTnf.8  at  1° ;  and  if  we  assume  that  the  expansion 
is  exactly  proportional  to  the  temperature,  they  will  become 
(273  +  t)  cTFri.3  at  t°.  Moreover,  representing  by  V  any  volume 
of  a  permanent  gas  at  0°,  we  shall  have  by  [166],  for  the  volume 
at  t°9  the  expression, 


F'=  F(l  +  0.003660- 


[184.] 


The  values  of  (1  +  0.00366  0  for  every  tenth  of  a  degree  from 
-^2°  to  40°,  with  their  corresponding  logarithms,  are  given  in 
Tables  XL  and  XII.  for  convenience  of  computation. 

The  coefficient  of  expansion  of  a  gas  may  be  estimated  in  two 
ways.  In  the  first  place,  we  may  measure  the  increase  of  volume 
which  the  gas  undergoes,  supposing  the  pressure  on  the  gas  to 
remain  constant  while  the  volume  expands ;  or,  in  the  second 
place,  keeping  the  volume  the  same,  we  can  measure  the  in- 
creased tension  which  the  gas  exerts  owing  to  the  increased 
temperature  ;  and  we  can  then  calculate  by  [98]  what  would 
have  been  the  increased  volume  had  the  gas  been  allowed  to 
expand.  The  difference  between  these  two  methods  will  be  better 
understood  by  experimental  illustration. 

In  Fig.  387,  B  is  a  glass  globe 
holding  from  1,000  to  800  cT^8 
of  perfectly  dry  gas,  whose  coeffi- 
cient of  expansion  is  to  be  meas- 
ured. This  globe  is  filled  by 
exhausting  the  air  by  means  of 
an  air-pump,  connected  by  a  flex- 
ible hose  with  the  tube  jo,  and 
then  allowing  the  gas  to  enter 
through  tubes  filled  with  pumice- 
stone,  moistened  with  sulphuric 
acid,  or  with  chloride  of  calcium,  Fi«- 387- 

two  substances  which  have  a  very  strong  attraction  for  water  (see 
45 


530  CHEMICAL   PHYSICS. 

Fig.  388).  The  exhaustion  is  repeated,  and  fresh  gas  admitted, 
twenty  or  thirty  times,  until  the  gas  in  the  globe  and  the  con- 
necting tubes  is  known  to  be  pure  and  dry.  The  connection 
between  the  globe  and  the  pump  is  now  closed  by  turning  a 
three-way  stopcock  at  #,  leaving,  however,  the  connection  be- 
tween the  globe  and  the  manometer-tube  a  /3  /  still  open.  The 
construction  of  this  manometer  has  already  been  described 
(168,  2).  When  the  apparatus  has  been  thus  filled  with  a 
gas,  the  coefficient  of  expansion  may  be  readily  determined  by 
either  of  the  two  methods  just  mentioned. 

First  Method.  We  begin  the  determination  by  surrounding 
the  globe,  supported  in  a  copper  boiler,  as  represented  in  the 
figure,  with  pounded  ice,  so  as  to  reduce  the  temperature  of  the 
enclosed  gas  to  0°.  We  then  regulate  the  quantity  of  mercury 
in  the  manometer  so  that  the  columns  in  the  two  tubes  shall 
stand  at  the  same  height,  as,  for  example,  a,  which  is  carefully 
noted.  This  is  readily  effected  by  either  drawing  out  mercury  at 
the  lower  stopcock,  or  by  pouring  it  in  at  the  mouth  of  the  open 
tube.  When  the  adjustment  is  perfect,  we  build  a  fire  under  the 
copper  boiler  and  surround  the  globe  with  steam,  by  which  the 
temperature  of  the  gas  is  soon  raised  to  100°.  The  increased 
elasticity  of  the  gas  due  to  the  increased  temperature  will  drive 
out  a  portion  into  the  manometer-tube,  forcing  down  the  mercury- 
column.  A  quantity  of  mercury  is  now  drawn  off  at  the  lower 
stopcock,  until  the  columns  in  the  two  tubes  again  stand  at  the 
same  level.  When  this  is  the  case,  the  gas  is  exposed  to  the 
same  pressure  as  before,  and  we  then  read  off  the  increased 
volume  by  means  of  graduations  on  the  tube  provided  for  the 
purpose. 

Let  us  represent  the  observed  increase  of  volume  in  this  experiment 
by  v,  and  let  us  assume  that  the  pressure  of  the  atmosphere,  as  indi- 
cated by  the  barometer,  remained  constant  at  76  c.  m.  during  the  ex- 
periment. If  now  we  represent  the  volume  of  air  in  the  globe  at  0°  by 
F,  it  is  evident  that,  if  heated  so  that  it  could  expand  freely,  this  volume 
would  become  at  100°,  V  (1  -f-  K 100) ;  an  expression  in  which  K  is  the 
coefficient  of  expansion  required.  In  the  apparatus  before  us,  however, 
the  excess  of  gas  due  to  the  expansion  escapes  into  the  tube  da  /?,  where 
it  is  exposed  to  a  much  lower  temperature.  Call  this  temperature,  which 
is  always  carefully  observed,  t°.  The  volume  of  this  small  amount  of  gas, 
had  its  temperature  been  maintained  at  100°,  would  evidently  have  been 
v  (1  -(-  K  [100  —  *]),  so  that  we  have  the  equation 


HEAT.  531 

K  100)  ='  F+  v  (1  +  K  [100  —  *])          [185.] 

It  must  be  remembered,  however,  that  the  glass  globe  expands  as  well  as 
the  gas,  and  therefore  contains  at  100°  a  larger  volume  of  gas  than  at  0°. 
This  increased  volume  can  be  readily  calculated  from  the  coefficient  of 
expansion  of  glass  (^T'),  and  is  V  (1  -)-  K'  100).  Substituting  this  value 
for  Fin  the  second  member  of  [185],  we  obtain 

V  (\-\-K  100)  =V  (\-\-K1 100)  +  v  (1  +  K  [100  •—<]); 

which  gives,  for  the  coefficient  of  expansion  of  gas  under  constant  pres- 
sure, the  value 

v  lOOVK'+v 

K -- -~  m~(v^)  +  rv* 

Second  Method.  In  order  to  determine  the  coefficient  of  ex- 
pansion by  the  second  method,  we  arrange  the  apparatus  exactly 
as  before,  so  that  the  mercury  stands  at  the  same  level  (a,  Fig. 
387)  in  both  tubes  of  the  manometer  when  the  globe  is  sur- 
rounded by  ice.  We  then,  as  before,  raise  the  temperature  of 
the  globe  to  100° ;  but  instead  of  allowing  the  gas  to  expand  into 
the  tube  d  a  a,  we  pour  mercury  into  the  tube  fl  y,  in  order  to 
balance  the  increased  tension  of  the  gas  and  retain  the  volume 
constant.  Lastly,  we  carefully  measure,  by  means  of  a  cathe- 
tometer,  the  difference  of  height  (a,  y)  of  the  mercury  columns 
in  the  two  tubes  of  the  manometer  ;  and,  having  observed  the 
temperature  of  the  apparatus,  reduce  the  observed  height  to 
what  it  would  have  been  at  0°.  Represent  this  height  by  7t0. 
Knowing  now  the  volume  of  the  globe  at  0°  (F),  the  height  of 
the  barometer  at  the  time  of  the  experiment  (-££>),  and  the  co- 
efficient of  expansion  of  glass  (A"'),  we  have  all  the  data  required 
for  calculating  the  coefficient  of  expansion  of  air. 

When  the  globe  was  at  0°,  the  gas  was  exposed  to  the  pressure  of  the 
atmosphere,  or  ff0 ;  but  after  the  globe  had  been  heated  to  100°,  the  pres- 
sure required  to  retain  the  volume  of  the  gas  the  same  as  before  was 
JfQ  _|_  hv  "We  can  now  easily  calculate  from  Mariotte's  law  [98]  what 
would  be  the  volume  of  this  gas  if  exposed  only  to  the  pressure  of  the 
atmosphere ;  in  other  words,  if  allowed  to  expand  freely.  It  will  be  found 
to  be 

F'  =  F^+— °-  [187.] 

//o 

But  by  [166]  the  increased  volume  of  the  gas  at  100°,  or  F',  is  also  equal 


532  CHEMICAL  PHYSICS. 

to  V  (1  +  K 100),  so  that  V(l  +  K  100)  =  V  H°  +  h° .     We   must 


remember,  however,  that  although  the  volume  of  the  gas  has  been  appar- 
ently kept  constant  during  the  experiment,  it  has  not  been  so  in  reality, 
owing  to  the  expansion  of  the  glass  globe.  In  consequence  of  this  expan- 
sion, the  volume  of  the  globe  at  100°  is  F(l  +  K1 100)  ;  and  this  value 
should  evidently  be  substituted  for  V  in  the  second  member  of  the  last 
equation.  Making  this  substitution,  we  obtain 


1  +  K 100  =  (1  +  K'  100)  -^jEr2 
whence 


™°.  [188.] 

-•  J.Q  •*•   V  V 

In  this  example,  as  in  the  last,  we  have  assumed  that  the  pressure  of 
the  atmosphere  was  constant  during  the  experiment.  When  this  is  not 
the  case,  certain  obvious  changes  must  be  made  in  the  formulae.  More- 
over, in  the  practical  application  of  these  methods,  certain  precautions 
must  be  taken,  which  will  be  found  described  at  length  in  Regnault's 
original  memoir*  on  the  subject,  as  well  as  the  peculiar  modifications  of 
the  apparatus  best  adapted  for  each  method. 

(262.)  General  Results  — Regnault  found  that  the  two  meth- 
ods just  described  for  determining  the  coefficient  of  expansion  of 
gases  yielded  slightly  different  results.  This  will  be  seen  by  re- 
curring to  the  table  on  page  528.  The  first  column  gives  the 
coefficient  as  determined  from  the  increased  elasticity,  the  volume 
remaining  constant  The  second  column  gives  the  coefficient  as 
determined  from  the  increased  volume,  the  pressure  remaining 
constant.  It  will  be  noticed  that  the  difference  between  the 
two  results,  although  very  small  with  the  permanent  gases,  is 
quite  large  with  those  that  can  be  easily  reduced  to  the  liquid 
state  ,  and  it  will  be  remembered  that  it  is  these  very  gases  which 
yield  most  readily  to  compression,  and  hence  deviate  most  mark- 
edly from  the  law  of  Mariotte.  Moreover,  the  fact  that,  with  the 
exception  of  hydrogen,  the  coefficients  under  constant  volume 
are  less  than  those  under  constant  pressure,  is  easily  explained. 
In  the  method  employed,  the  gases  are  exposed  to  a  greater 
pressure  at  100°  than  at  0°  By  this  pressure  they  are  con- 
densed more  than  we  assumed  by  applying  the  law  of  Mariotte 

*  Me'moires  de  I'Academie  de  Sciences  de  1'lnstitut,  Tom.  XXI. 


HEAT.  533 

in  our  calculation  as  if  it  were  exact,  and  consequently  the  effect 
of  the  increased  temperature  is  really  greater  than  appears.  In 
other  words,  the  mercury-column  h0  measures,  not  simply  the 
increased  tension  of  the  gas  caused  by  the  increased  temperature, 
but  the  difference  between  the  increased  tension  and  the  in- 
creased compressibility.  In  the  case  of  hydrogen,  which,  unlike 
all  other  gases,  is  compressed  less  than  the  law  of  Mariotte  re- 
quires, the  variation  is  in  the  opposite  direction.  (Compare 
page  296.) 

Regnault  also  discovered,  what  indeed  might  be  inferred  from 
the  facts  already  stated,  that  the  coefficients  of  expansion  of  all 
gases  except  hydrogen  increase  with  the  pressure  to  which  they 
are  exposed.  The  greater  the  pressure  on  a  mass  of  gas,  and 
hence  the  greater  its  density,  the  greater  is  the  amount  of  its 
expansion  for  the  same  difference  of  temperature ;  and,  on  the 
other  hand,  the  less  the  pressure  and  density,  the  smaller  the 
amount  of  expansion.  The  coefficient  of  expansion  in  any  case 
increases  with  the  pressure  in  proportion  as  the  compressibility 
of  the  gas  deviates  from  the  law  of  Mariotte,  and  hence  the  dif- 
ferences between  the  coefficients  of  different  gases  are  the  more 
decided  the  greater  the  pressure  to  which  the  gases  are  exposed. 
On  the  other  hand,  as  the  pressure  diminishes,  the  coefficients  of 
expansion  of  different  gases  approach  equality ;  and  it  is  probable, 
therefore,  that  all  gases  in  the  state  of  extreme  expansion  would 
have  the  same  coefficient.  (Compare  page  297.) 

It  appears,  therefore,  that  all  gases  have  the  same  coefficient  of 
expansion,  in  so  far  as  they  obey  the  law  of  Mariotte.  In  the 
case  of  those  gases  which  have  not  been  liquefied,  and  which  con- 
form very  closely  to  Mariotte's  law,  the  coefficients  of  expansion 
tinder  the  pressure  of  the  atmosphere  are  sensibly  equal,  and 
even  in  the  case  of  the  condensible  gases  the  differences  are 
very  small,  amounting  in  no  case  to  more  than  three  units  in  the 
fourth  decimal  figure.  We  may  therefore  say  that  the  coeffi- 
cient of  expansion  of  all  gases  under  the  pressure  of  the  atmos- 
phere is  equal  to  0.0036,  within  three  ten-thousandths. 

(263.)  Air- Thermometer.  —  We  have  seen  that  the  defects 
of  the  mercury-thermometer  arise  from  two  causes  ;  first,  the 
slowly  increasing  rate  of  expansion  of  mercury  as  the  tempera- 
ture rises,  and,  secondly,  the  irregular  and  uncertain  expansion 
of  the  glass  bulb.  Both  of  these  defects  may  be  avoided  by  using 
45* 


534 


CHEMICAL  PHYSICS. 


air  as  the  thermometric  material :  the  first,  because  the  expan- 
sion of  air  is  exactly  proportional  to  the  temperature  ;  and  the 
second,  because  the  expansion  of  air  is  so  much  greater  than  that 
of  glass  that  the  irregularities  in  the  expansion  of  the  latter 
may  be  overlooked.  It  is,  however,  by  no  means  so  easy  to  meas- 
ure the  volume  of  a  gas  as  that  of  a  liquid.  The  volume  of  a 
liquid  is  not  affected  by  the  changing  pressure  of  the  atmos- 
phere, while  that  of  a  gas  is  ;  so  that  while  a  small  increase  in 
the  volume  of  a  quantity  of  mercury  enclosed  in  a  common  ther- 
mometer can  be  measured  by  the  mere  inspection  of  the  divis- 
ions on  the  stem,  the  amount  of  expansion  of  a  quantity  of  air 
confined  in  a  glass  bulb,  although  much  larger,  can  only  be 
determined  with  certainty  by  a  tedious  process,  occupying  sev- 
eral hours.  Thus,  although  with  an  air-thermometer  we  can 
measure  temperatures  with  accuracy  to  the  hundredth  of  a  Centi- 
grade degree,  yet  it  requires  a  day  to  make  a  single  observation. 
The  air-thermometer  is,  therefore,  of  no  use,  except  in  the  few 
cases  which  require  the  very  highest  degree  of  scientific  precision. 
In  such  cases  it  is  an  invaluable  instrument ;  but  even  then,  as 
in  all  other  scientific  measurements,  the  greatest  attainable  accu- 
racy can  only  be  gained  at  the  cost  of  time,  labor,  and  skill. 


Fig.  388. 


(264.)  RegnauWs  Air-  Thermometer.  —  The  air-thermometer, 
which  is  used  only  in  delicate  measurements  of  temperature,  is 
represented  in  Figs.  388  and  389.  It  consists  of  a  cylindrical 
reservoir  of  glass,  B,  opening  into  a  capillary  tube  bent  at  right 


HEAT. 


535 


angles  and  drawn  out  to  a  fine  point.  In  order  to  estimate  tem- 
peratures with  this  instrument,  it  is  first  filled  by  means  of  an 
air-pump  and  drying-tubes,  as  shown  in  Fig.  388,  with  perfectly 
dry  air,  and  then  exposed  to  the  temperature  to  be  measured, 
which  we  will  call  T°.  When  an  equilibrium  of  temperature 
has  been  established  between  the  thermometer  and  the  heated 
substance,  the  fine  opening  is  closed 
with  a  blowpipe,  and  at  the  same  time 
the  height  of  the  barometer  is  noted, 
which  we  will  call  7J0.  The  air  in  the 
thermometer  is  now  expanded  to  the 
extent  corresponding  to  T°,  and  the  next 
step  is  to  ascertain  the  amount  of  this 
expansion,  since  we  can  easily  calculate 
from  this  the  temperature  T°.  For  this 
purpose,  we  place  the  thermometer  upon 
the  metallic  support  represented  in  Fig. 
389.  The  reservoir  of  the  thermometer 
rests  upon  three  brass  knobs,  and  is  kept 
in  its  place  by  means  of  a  binding  screw. 
The  tube  of  the  thermometer  passes 
through  a  hole  in  the  centre  of  the 
brass  stage  A,  and  the  end  dips  under 
mercury  contained  in  the  glass  dish  C. 

The  bent  end  of  the  tube  is  adjusted  opposite  to  an  iron  spoon,  a, 
filled  with  wax,  which  can  be  pushed  forward  on  its  support,  s, 
so  as  to  close  the  end  of  the  tube  while  under  mercury,  when 
necessary.  These  adjustments  having  been  completed,  the  tip 
end  of  the  tube  is  broken  off  with  a  pair  of  pliers,  when  the 
mercury  immediately  rushes  up  into  the  thermometer  and  par- 
tially fills  it.  The  thermometer  is  next  surrounded  with  pulver- 
ized ice,  which  is  piled  up  on  the  stage,  G ;  and  when  the  air  in 
the  reservoir  has  fallen  to  0°,  the  end  of  the  tube  a  is  carefully 
plugged  up  by  means  of  the  wax  in  the  iron  spoon,  and  at  the 
same  time  the  height  of  the  barometer  (#')  is  carefully  noted. 
The  ice  is  now  removed,  and  when  the  temperature  of  the  mer- 
cury in  the  thermometer  has  been  restored  to  that  of  the  air,  the 
height  of  the  mercury  in  the  thermometer  above  that  in  the 
reservoir  is  carefully  measured.  We  will  call  it  h ,  and  hence 
the  air  in  the  thermometer,  at  the  moment  the  tube  was  plugged 


Fig.  389. 


536  CHEMICAL  PHYSICS. 

with  wax,  must  have  been  exposed  to  the  pressure  of  H'  —  h. 
This  measurement  is  easily  made  by  means  of  a  cathetometer 
and  the  screw  g*,  in  the  manner  previously  explained  in  connec- 
tion with  Regnault's  barometer  (159). 

It  is  next  necessary,  in  order  to  determine  the  temperature  to  which 
the  thermometer  has  been  exposed,  to  ascertain,  first,  the  volume  of  air 
remaining  in  the  thermometer  after  contraction,  and,  secondly,  the  volume 
originally  contained  in  it.  For  this  purpose,  the  thermometer  is  removed 
from  its  support  and  weighed  ;  call  this  weight  W.  The  thermometer  is 
then  filled  completely  with  mercury  at  0°  and  weighed  ;  call  this  second 
weight  W.  Lastly,  it  is  completely  emptied,  and  the  glass  weighed  by 
itself;  call  this  last  weight  w.  We  have  now  all  the  data  for  calculating 
the  amount  of  expansion  of  the  air,  and  consequently  the  temperature 
required.  Before  commencing  the  calculation,  we  must  reduce  the  ob- 
served heights  of  the  barometer  (//and  H')  and  mercury  -column  (h)  to 
0°  by  the  method  given  in  (251).  We  will  call  these  corrected  heights 
HQ,  H'fr  hQ.  We  can  then  readily  calculate  the  following  quantities. 

W  —  w  =  weight  of  mercury  which  fills  the  thermometer  at  0°. 
~ari  _  ,j0 

—  -  --  =  capacity  of  thermometer  at  0°  when  d  =  Sp.  Gr.  of  mercury. 

-  ~  -  (1  +  K1  T)  =  capacity  of  thermometer  at  T70,  when  K1  =  co- 

efficient of  expansion  of  glass. 

W  —  w  =.  weight  of  mercury  which  entered  the  thermometer  on  break- 
ing the  tip,  the  temperature  of  the  thermometer  being  0°. 

--  —  volume  of  mercury  which  entered  the  thermometer  on  break- 
ing the  tip,  the  temperature  of  the  thermometer  being  0°. 

trr/  _  TTT 

—  -  —  =  volume  of  air  in  the  thermometer  at  the  moment  of  plugging 

with  wax,  exposed  to  a  pressure  H'0  —  A0  and  to  a  tem- 
perature of  0°. 

W  —  W    H  _  h 

-  «  -  •  —  ^  —  °  —  volume  which  same  air  would  have  under  76  c.m. 

S  76  and  0°. 

-rrrf  -TJTT          TT/  i 

-  r  —  —  •  —  !W  —  -  (\.-\-K  T)  •=.  volume  which  same  air  would  have 

under  Jf0c.  m.  and  T°. 

By  the  conditions  of  the  problem,  this  volume  of  air  just  filled  the  ther- 
mometer at  T°  and  under  barometric  pressure  ff0  ;  hence 

W'~W-  Zy*  (1  +KT)  =  ^^  (1  +  JT<  T)  =  the  capaci- 


ty  of  thermometer  at  T°  ; 


l+KT 

Put  W'  —  W 


HEAT.  537 

W'  —  W        ff'n  —  ha 


and  we  have 


",    and    A^=  0.00367;    [190.] 


'"  [191.] 


By  means  of  [189]  and  [190]  we  can  easily  calculate  the  temperature 
from  the  experimental  data.  The  coefficient  of  expansion  of  glass  is  the 
only  uncertain  element  which  enters  into  the  calculation.  When  the  ther- 
mometers are  made  of  the  common  crown-glass  of  Paris,  the  coefficients 
of  expansion  may  be  taken  from  the  table  on  page  497,  estimating  roughly 
the  required  temperature,  as  can  easily  be  done  by  means  of  a  common 
mercury-thermometer.  When,  however,  such  thermometers  cannot  be 
obtained,  it  is  best  to  have  a  number  made  from  the  same  pot  of  glass, 
and  ascertain  carefully  the  coefficient  of  expansion  of  this  glass  between 
0°  and  every  fifty  degrees  up  to  350°.  These  coefficients  can  afterwards 
be  used  in  all  experiments  with  the  same  set  of  thermometers. 

(265.)  By  substituting  T  for  100,  we  can  easily  obtain  from 
[186]  and  [188],  by  transposition,  the  value  of  Tin  terms  of  the 
coefficient  of  expansion  of  air;  and  since  this  coefficient  is  accu- 
rately known,  either  of  the  methods  of  (261)  may  be  used  for 
determining  temperature.  The  form  which  has  been  given  by 
Regnault  to  the  manometric  apparatus,  when  used  for  this  pur- 
pose, has  already  been  represented  in  Fig.  273.  The  glass  tube 
a  b  c,  which  serves  as  an  air-thermometer,  is  closed  by  a  stopcock 
r,  and  can  be  connected  to  the  manometer  by  a  brass  collar  of 
peculiar  construction,  as  before  described  (see  Figs.  274  and  275). 
The  air-thermometer  having  been  exposed  to  the  temperature  to 
be  measured,  the  stopcock  r  having  been  closed  at  the  moment  of 
observation,  and  the  height  of  the  barometer  noted,  we  can  easily 
determine  the  temperature  in  the  following  way. 

In  the  first  place,  mercury  is  poured  into  the  manometer  at  K  until  the 
tube  h  g  f  is  completely  filled,  and  when  the  mercury  begins  to  drop  from 
the  open  end  aty,  the  air-thermometer  is  connected.  The  thermometer  is 
now  surrounded  with  melting  ice  in  order  to  reduce  its  temperature  to  0°, 
and  before  the  stopcock  r  is  opened,  a  quantity  of  mercury  is  drawn  out  of 
the  manometer  at  7?,  in  order  to  make  a  great  difference  of  level  between 
the  two  columns.  On  opening  the  stopcock  r,  a  portion  of  the  air  in 
the  thermometer  passes  into  the  tube  g  h  ;  and  mercury  must  be  again 


538  CHEMICAL  PHYSICS. 

poured  into  the  tube  k  i,  until  the  surface  of  the  column  in  the  tube  g  h 
coincides  exactly  with  a  mark,  «,  on  the  side  of  the  tube.  The  determi- 
nation is  then  completed  by  measuring  with  a  cathetometer  the  difference 
of  level  of  the  two  mercury-columns,  noting  the  temperature  of  the  ma- 
nometer by  means  of  the  thermometer  Z,  and  observing  the  height  of  the 
barometer.  We  have  now  the  following  data  for  calculation,  the  heights 
of  the  mercury-columns  having  been  reduced  to  0°  :  — 

Jf'o  =  height  of  barometer  at  the  moment  of  observing  the  temperature. 
HO   =  height  of  barometer  at  the  moment  of  measuring  the  difference  of 
level. 

hQ    =  difference  of  level  as  measured  by  the  cathetometer. 

V    •=.  capacity  of  air-thermometer  at  0°. 

v     =  capacity  of  manometer-tube  between/  and  the  mark  «. 

t      =  temperature  of  the  manometer  at  the  time  of  the  experiment. 

T    =  required  temperature  to  which  the  thermometer  was  exposed. 

K    =  coefficient  of  expansion  of  glass. 

0.00367  =  coefficient  of  expansion  of  air. 

0.0012921  gram.  =  weight  of  one  cubic  centimetre  of  air  at  0°  and  76  c.  m. 

The  volume  of  air  in  the  air-thermometer  and  in  the  manometer-tube, 
when  the  value  h0  was  measured,  was  evidently  V-\-  v  ;  the  portion  V  at 
the  temperature  of  0°,  the  portion  v  at  t°,  and  the  whole  under  a  pres- 
sure ff0-t—hQ  [106].  Reducing  by  [166]  the  volume  v  to  what  it  would 
be  at  0°,  and  reducing  by  [107]  the  sum  of  the  volumes  at  0°  to  what 
this  total  volume  would  be  under  the  normal  pressure  of  the  atmosphere, 
we  easily  obtain  for  the  weight  of  this  mass  of  air, 

0.0012921   '  ^  '    -  A  '   ^fl— A« 


1_|_  0.003  67 1\       76 

But  we  know  that  this  same  mass  of  air  at  the  temperature  T  (that  is, 
at  the  moment  of  closing  the  stopcock  r),  and  under  the  pressure  H'Q  (the 
height  of  the  barometer  at  the  time),  occupied  just  the  volume  of  the  air- 
thermometer  at  that  temperature,  or  V  (\-\-K  T).  Reducing  this  volume 
to  what  it  would  be  at  0°  and  76  c.  m.,  and  multiplying  this  reduced 
volume  by  the  weight  of  one  cubic  centimetre  of  air,  we  obtain  a  second 
expression  for  the  weight  of  the  given  mass  of  air,  which,  in  the  following 
equation,  is  put  equal  to  the  first :  — 

0.0012921  ^1+o^7r  T  ^°  =  0.0012921 
or  reducing 

I+KT__       r       „__          _j I  H0-h0 

1  -f  0.0036  7.  T"  V         1-f  0.0036  7  ,t\       H'0 


HEAT.  539 

All  the  terms  of  the  second  member  of  this  equation  are  known  quantities 
except  Fand  v,  and  these  can  easily  be  obtained  in  the  following  way. 

In  the  first  place,  we  fill  the  manometer-tube  with  mercury,  as  before,  and 
then  slowly,  by  the  stopcock  JR,  draw  off  the  mercury  into  a  tared  vessel 
until  the  surface  of  the  column  coincides  with  the  mark  «.  The  weight 
of  this  mercury  divided  by  its  specific  gravity  [5G]  is  equal  to  v.  We 
then  attach  the  air-thermometer  (the  stopcock  r  being  open),  and  observe 
the  height  of  the  barometer,  ff0.  Since  the  mercury  is  at  the  same  level 
in  both  tubes  of  the  manometer,  the  confined  volume  of  air  (  V-\-  v)  is  of 
course  exposed  to  the  pressure  ffQ.  We  next  draw  off  more  mercury 
at  It  until  the  the  level  of  the  column  in  the  tube  h  g  sinks  to  a  second 
mark,  #.  The  weight  of  this  mass  of  mercury  divided  by  its  specific 
gravity  gives  the  volume  of  the  tube  between  a  and  #,  which  we  will  call 
v'.  Lastly,  we  measure  the  difference  of  level  of  the  mercury-columns  in 
the  two  tubes  of  the  manometer,  which  we  will  call  7/0.  At  this  moment 
the  volume  of  the  confined  air  is  V-\-  v  -(-  v1,  and,  assuming  that  the 
height  of  the  barometer  has  not  changed  during  the  short  interval  occu- 
pied by  the  experiment,  this  volume  is  exposed  to  the  pressure  HQ  —  h0. 
The  values  V-\-v  and  V  -\-v-\-v'  are  then  the  volumes  of  the  same 
mass  of  air  under  the  pressures  Ji0  and  Jf0  —  A0  respectively.  Hence, 
by  [98], 


I    4~  V  ~\-  V'  HQ 

and  from  this  equation  we  can  easily  deduce  the  value  of  V,  since  all  the 
other  terms  are  known. 


(266.)  Air-Pyrometer.  —  By  substituting  for  the  glass  ther- 
mometer (a  b  c,  Fig.  273)  a  thermometer  made  of  some  refrac- 
tory substance,  the  apparatus  described  in  the  last  section  may  be 
used  for  measuring  very  high  temperatures.  Pouillet*  employed 
for  the  purpose  a  small  globe  of  platinum  at  the  end  of  a  long 
and  narrow  tube  of  the  same  metal  ;  but  a  thermometer  made  of 
porcelain,  as  proposed  by  Regnault,  would  be  less  expensive,  and 
even  better  adapted  to  the  purpose.  In  the  use  of  platinum 
there  is  a  liability  to  error  arising  from  its  power  of  condensing 
gases  on  its  surface  at  the  ordinary  temperature. 

(267.)  The  True  Temperature.  —  It  is  generally  admitted  that 
the  expansion  of  a  given  mass  of  air  under  constant  pressure  is 
absolutely  proportional  to  the  quantity  of  heat  it  receives.  If  so, 

*  Comptes  Rendus,  Tom.  III.  p.  782. 


540  CHEMICAL  PHYSICS. 

the  temperatures  given  by  the  air-thermometer  are  the  true  tem- 
peratures ;  but  although  this  assumption  is  highly  probable,  it  is 
impossible,  in  the  present  state  of  our  knowledge,  fully  to  establish 
its  truth  by  experimental  proof.  Nevertheless,  the  temperatures 
given  by  the  air-thermometer  are  the  nearest  approach  we  can 
at  present  make  to  the  true  temperature,  and  it  is  important 
in  all  scientific  investigations  to  substitute  for  the  indications  of 
a  mercury-thermometer  the  corresponding  temperatures  of  the 
air-thermometer.  When  we  know  the  nature  of  the  glass  of  the 
mercury-thermometer,  we  can  readily  make  the  reduction  by 
means  of  Regnault's  table  on  page  435  ;  but  since  the  expansion 
of  glass  is  always  more  or  less  uncertain,  it  is  always  best  to  use 
the  air-thermometer  in  observing  high  temperatures  if  great  accu- 
racy is  required.  .^  \ 

(268.)  Effects  and  Applications  of  the  Expansion  of  Air.  — 
One  of  the  simplest  effects  of  the  expansion  of  air  is  seen  in  the 
action  of  a  stove  on  the  air  of  a  room.  The  particles  of  air  in 
contact  with  the  heated  iron  are  expanded,  and,  becoming  thus 
specifically  lighter,  rise  and  give  place  to  the  colder  particles 
which  flow  in  from  below.  Thus  a  circulation  is  established 
by  which  all  the  air  in  the  room  is  finally  brought  in  contact 
with  the  source  of  heat  and  warmed.  Were  the  air  visible,  the 
heated  air  would  be  seen  to  rise  from  the  stove,  spread  itself 
over  the  ceiling,  descend  along  the  walls,  and  flow  back  over  the 
floor  to  the  stove.  In  like  manner,  every  furnace-flue,  gas-light, 
or  candle,  and  every  human  body,  would  be  seen  to  be  the  centre 
of  an  ascending  column  of  heated  air  ;  indeed,  such  is  the  perfect 
freedom  of  motion  in  air,  that  a  single  lighted  candle  will  set  in 
motion  the  whole  atmosphere  of  a  quiet  apartment.  Similar  cur- 
rents are  established  whenever  a  door  is  opened  by  which  a  warm 
room  is  connected  with  a  cold  entry.  The  heated  and  lighter 
air  pours  out  from  the  room  at  the  top  of  the  door,  while  the 
colder  air  flows  in  over  the  door-sill.  The  flame  of  a  lighted 
candle  may  be  used  (as  represented  in  Fig.  390)  to  detect  the 
direction  of  the  currents.  A  current  of  air  may  always  be 
noticed  flowing  towards  the  sunny  side  of  a  building,  which 
supplies  the  current  rising  along  the  heated  wall.  But  by  far 
the  grandest  exhibition  of  this  aeriform  circulation  is  the  trade- 
winds.  These  are  caused  by  the  unequal  action  of  the  sun  on 
different  parts  of  the  earth's  surface.  At  the  equator,  the 


HEAT. 


541 


Fig  890 


strongly  heated  air  rises,  and  its  place  is  supplied  by  colder  air, 
which  flows  in  on  both  sides  from  the  temperate  zones ;  thus 
currents  are  established  which  would  blow  directly  north  and 
south,  were  it  not  that  the  rota- 
tion of  the  globe  causes  them  to 
deviate  from  this  direction,  while 
other  and  local  causes  come  in  to 
produce  the  irregularities  which 
are  observed. 

The  effect  of  a  glass  chimney 
on  the  flame  of  a  candle  is  an- 
other illustration  of  the  action  of 
heat  in  expanding  air.  By  the 
chimney,  the  heat  generated  by 
the  burning  combustible  is  con- 
fined within  the  glass  walls,  and 
consequently  the  air  surround- 
ing the  flame  becomes  more  in- 
tensely heated  than  it  would  be 

without  the  chimney.  Moreover,  the  heated  air  is  also  confined 
by  the  walls  of  the  chimney,  and  prevented  from  mixing  with  the 
atmosphere,  thus  forming  a  column  of  heated  air  whose  height  is 
equal  to  the  height  of  the  chimney.  This  column  of  air  will  evi- 
dently be  buoyed  up  by  a  force  equal  to  the  difference  between 
the  pressure  of  the  air  at  the  bottom  and  at  the  top  of  the  cylin- 
der, and  this  force  has  been  shown  (136  and  155)  to  be  equal  to 
the  weight  of  a  column  of  the  exterior  cold  air  of  the  same  area 
and  height.  Hence  the  heated  air  will  rise,  for  the  same  reason 
that  a  balloon  rises,  and  with  a  velocity  proportionate  to  the  ex- 
cess of  the  buoyancy  over  its  own  weight.  The  quantity  of  air 
passing  through  such  a  chimney  in  a  given  time  can  readily  be 
calculated,  when  the  area  of  the  section  of  the  chimney,  and  the 
difference  of  temperature  between  the  inner  and  exterior  air,  are 
known. 

The  draught  of  an  ordinary  brick  flue  is  caused  in  the  same 
way  as  that  in  the  glass  chimney  of  a  lamp.  The  weight  of  the 
column  of  heated  gas  C  D  (Fig.  391)  is  less  than  that  of  the 
column  of  exterior  air  A  B,  and  hence  there  results  an  excess  of 
upward  pressure  which  forces  the  products  of  combustion  up  the 
chimney  the  more  rapidly  the  greater  the  difference  of  weight 
46 


542 


CHEMICAL   PHYSICS. 


Fig  391. 


between  the  two  masses  of  gas.     A  good  draught  depends  on  the 
following  obvious  conditions: — 1.  The  size  of  the  flue  should  be 

proportional  to  the  amount  of  gas  it  is 
required  to  carry  ;  for  if  too  large, 
cold  currents  may  descend  in  the 
angles  of  the  flue,  while  a  heated  one 
ascends  in  the  axis.  2.  The  height 
of  the  chimney  should  be  as  great  as 
possible  ;  for  the  greater  the  height, 
the  greater  will  be  the  excess  of  the 
upward  pressure  on  which  the  draught 
depends.  3.  The  room  with  which 
the  flue  connects  should  not  be  so 
tight  that  air  cannot  enter  as  fast  as 
it  escapes  by  the  chimney.  4.  Any 
direct  communication  between  sepa- 
rate flues  in  adjoining  rooms  should 
be  avoided,  because,  if  one  flue  draws  better  than  the  other,  a 
downward  current  may  be  established  in  the  last. 

Still  another  application  of  the  ascensional  force  of  heated  air 
is  to  be  seen  in  the  hot-air  furnaces  which  are  so  universally  used 
in  this  country  for  heating  buildings.     They 
usually  consist  of  a  brick  chamber  placed  in 
the  cellar,  connected  by  the  cold-air  box  with 
the  exterior  air,  and  communicating  by  tin 
tubes  with  the   different   apartments    above. 
The  interior  of  this  brick  chamber  is  nearly 
filled  with  a  large  cast-iron  stove,  constructed 
of  various  patterns,  so  as  to  expose  a  large 
heating   surface   to   the    air   surrounding  it. 
This  heated  air  ascends,  in  virtue  of  its  buoy- 
ancy, through  the  tin  conducting-tubes,  and 
cold  air  is  pressed  in  from  the  outside  of  the  building  to  supply 
its  place.     A  furnace  of  this  kind  (Chilson's)  is  represented  in 
Fig.  392,  and  the  arrows  indicate  the  direction  of  the  currents 
of  air. 

The  ascensional  force  of  heated  air  is  not  only  applied  in 
warming  buildings,  but  it  is  also  used  for  producing  ventila- 
tion. One  of  the  best  arrangements  for  the  purpose,  which 
may  be  used  with  great  efficiency  in  connection  with  a  hot-air 


Fig.  392. 


HEAT. 


543 


furnace,  is  represented  in  Fig.  393.     The  smoke-flue  of  the  fur- 
nace, formed  by  a  cast-iron   pipe  A,  rises   in   the   centre  of  a 
large  brick  shaft  Br  with  which  the  different  rooms 
of  the  building  connect.     The  radiant  heat  of  this 
iron  flue  heats  the  air  in  the  shaft,  and  thus  causes 
a  powerful  ascending  current,  which  draws  in  the 
foul  air  from  the  room  at  the  openings  D  and  D  ; 
while  at  the  same  time  fresh  air  enters  the  room 
from  the  furnace  to  take  the  place  of  that  which 
is  thus  removed. 

It  is  evident,  from  what  has  already  been 
stated,  that  a  lump  of  ice  sustained  near  the  top 
of  a  room  would  cause  a  descending  current  of 
air,  and  thus  give  rise  to  a  circulation  in  the  at- 
mosphere of  the  apartment  similar  to  that  pro- 
duced by  a  stove.  This  principle  has  been  applied 
in  the  construction  of  refrigerators  for  preserving 
food  in  warm  weather.  One  of  these  (Winship's) 
is  represented  in  Figs.  394  and  395.  The  ice  is 
sustained  upon  a  shelf  (D  D)  in  the  upper  part 
of  a  chest,  the  hollow  walls  of  which  are  filled 
with  pulverized  charcoal,  a  very  poor  conductor  .of  heat.  The 
air  enters  at  a  register  (C),  and,  coming  in  contact  with  the 
ice,  is  cooled  and  falls  to  the  bottom  of  the  chest,  where  it  finds 


Fig.  393. 


Fig   394. 


Fig.  395. 


egress  at  E  between  the  hollow  walls,  and  finally  escapes  at  F. 
In  this  way  a  gentle  current  of  cold  air  is  steadily  maintained 
as  long  as  the  ice  lasts. 


544  CHEMICAL  PHYSICS. 

PROBLEMS. 

Expansion  of  Solids. 

311.  A  bar  of  iron  one  metre  long  at  0°  is  heated  to  15° ; 
increased  length  of  the  bar  ? 

312.  A  bar  of  railway  iron  is  3.425  metres  long  at  20°  ;  what  would 
be  its  length  at  —10°  ? 

313.  In  laying  the  iron  rails  of  a  railroad,  it  is  necessary  to  make  an 
allowance  for  the  expansion  of  the  metal  by  heat.     How  much  allowance 
is  necessary  on  a  distance  of  100  kilometres  ?     How  much  on  a  distance 
of  20  English  miles,  assuming  that  the  road  is  laid  at  a  temperature  of 
5°,  and  that  it  is  liable  to  be  exposed  to  a  temperature  of  20°  ? 

314.  The  length  of  one  of  the  tubes  of  the  Britannia  Bridge  over  the 
Menai  Strait  is  1,510  feet  1£  inches  at  0°;  what  would  be  its  length  at 
20°?     Determine  also  the  difference  of  length  between  — 10°  and  15°. 

315.  A  bar  of  metal  is  3.930  m.  long  at  0°  and  3.951  m.  long  at  the 
temperature  of  83D.     Calculate  the  coefficient  of  expansion. 

316.  A  bar  7  m.  long  made  of  a  metal  whose  coefficient  of  expansion  is 
TJ^  increases  in  length  from  the  same  increase  of  temperature  as  much 
as  a  bar  made  of  another  metal  9  m.  long.     Required  the  coefficient  of 
expansion  of  the  second  metal. 

317.  A  platinum  bar  2  m.  in  length  is  divided  at  one  of  its  extremities 
into  fourths  of  a  millimetre ;  a  copper  bar  1.950  m.  long  placed  over  the 
first  at  0°  differs  from  it  in  length  0.050  m.,  or  200  of  the  divisions  on 
the  platinum  bar.     Required  the  temperature  of  the  two  bars  at  which 
the  difference  would  be  equal  to  164  divisions  on  the  platinum  bar. 

318.  A  pendulum  made  of  brass  vibrates  seconds  at  0°  C.     How  many 
seconds  would  it  lose  each  day  if  the  temperature  were  20°. 

319.  It  is  required  to  make  a  compensating  pendulum  of  steel  and 
brass  rods,  whose  constant  length  shall  be  0.50  m.    What  disposition  must 
be  given  to  these  rods,  and  what  must  be  their  lengths,  in  order  to  effect 
the  compensation  ? 

320.  A  brass  tube  is  5.436  m.  long  at  20°.     How  long  will  it  be  at  0°? 

321.  A  plate  of  sheet-iron  has  at  0°  a  superficial  area  of  560  cTm.2« 
Required  its  area  at  15°. 

322.  The  iron  tire  of  a  wheel  is  1.123  m.  in  diameter  at  a  red  heat 
(1,200°).     What  will  be  its  diameter  when  cooled  to  10°  ? 

323.  An  iron  ball  has  a  diameter  of  15  c.  m.  at  0°.     What  will  be  its 
cubic  contents  at  100°? 

324.  A  glass  cylinder  has  a  capacity  of  100  £~in.8  at  15°.    What  will  be 
its  capacity  at  150°  ? 

325.  With  what  force  does  a  bar  of  copper  expand,  the  area  of  whose 
section  equals  1  H^.2,  if  heated  from  0°  to  15°  ? 


HEAT.  545 

326.  The  specific  gravity  of  a  solid  at  5°  was  found  to  be  7.788 ;  at 
20°  it  was  found  to  be  7.784.     Required  the  coefficient  of  expansion  of 
the  solid. 

Expansion  of  Liquids. 

327.  The  height  of  the  mercury-column  in  the  tube  A,  Fig.  379,  was 
found  to  be  54  c.  m.     The  difference  of  level  of  the  two  columns  A  and 
B  was  found  by  measurement  to  be  0.972  c.  m.     Required  the  coefficient 
of  absolute  expansion  of  mercury,  knowing  that  the  temperature  A  was  0°, 
and  that  of  B  100°. 

328.  Reduce  the  following  heights  of  the  barometer  observed  at  the 
annexed  temperatures  to  0°  :  — 


1.  77  c.  m.  t  =  20°  C. 

2.  74  "  t  =  10°. 

3.  75  "  t  =  25°. 

4.  73  "  t  =  -10°. 


5.  75.85  c.  m.  t  =  -13°. 55  C. 

6.  46.23  •'  t  —  15°.2. 

7.  78.65  "  t  =  14°.6. 

8.  75.21  "  t  =  -120.3. 


Calculate  the  reduced  height,  first,  on  the  assumption  that  the  scale  is  in- 
expansible  ;  secondly,  on  the  assumption  that  the  height  is  measured  with 
a  brass  cathetometer  graduated  at  0° ;  thirdly,  that  it  is  measured  on  a 
glass  scale  also  graduated  at  0°. 

329.  Reduce  the  following  barometric  observations  made  at  8°  to  the 
temperatures  indicated,  making  the  same  assumptions  as  in  the  last 
problem  :  — 


1.  76.9  c.  m.  t  =  30°. 

2.  76.8     "  t  =  29°. 

3.  76.7     "  t  =  28°. 


4.  76     c.  m.  t  =  -10°. 

5.  75.9     "  t  =    -9°. 

6.  75.8     "  t  =    -8°. 


330.  A  glass  cylinder  4  c.  m.  in  diameter  is  filled  at  0°  to  the  height  of 
0.5  m.  with  mercury.     How  high  is  the  centre  of  gravity  at  0°,  and  how 
high  at  30°  over  the  base  of  the  cylinder  ? 

331.  Required  the  volumes  of  the  following  liquids  at  the  temperatures 
indicated,  knowing  that  the  volume  at  0°  is  in  each  case  100  cTm.8  :  — 

Alcohol,      .        .        .    t  =  20°.         I        Oil  of  Turpentine,    .    t  =  100°. 
Ether,      .        .        .        t  =  15°.         |        Water,   .  t  =    50°. 

332.  Prepare  a  table  giving  the  volume  of  water  for  each  ten  degrees 
from  0°  to  100°,  the  volume  at  0°  being  taken  as  unity. 

333.  Construct  the  curves  of  expansion  of  alcohol,  ether,  and  oil  of  tur- 
pentine from  the  equations  on  page  518. 

334.  Construct  a  curve  of  expansion  for  water  corresponding  to  each 
equation  on  page  527. 

335.  A  glass  flask  whose  neck  has  been  drawn  out  to  a  point  contains 
at  0°  1,000  cTm.8  of  mercury.     Required   the  weight  of  mercury  which 
will  flow  from  the  flask  if  its  temperature  is  raised  to  100°. 

46* 


546  CHEMICAL  PHYSICS. 

336.  A  weight  thermometer,  Fig.  380,  contained  254.263  grammes  of 
mercury  at  0° ;  when  heated  to  100°,  3.864  grammes  of  the  mercury  es- 
caped.    What   is   the   apparent   coefficient   of  expansion   of  mercury  ? 
Assuming  that  the  coefficient  of  expansion  of  glass  is  0.00003,  what  is 
the  coefficient  of  absolute  expansion  ? 

337.  A  glass  thermometer-tube  was  carefully  calibrated  and  divided 
into  parts  of  equal  capacity.     The  weight  of  mercury  which  the  bulb  and 
tube  contained  below  the  6th  division  on  the  stem,  measured  at  0°,  was 
found  to  be  20.125  grammes.     After  introducing  an  additional  quantity  of 
mercury,  which  filled  25  divisions  of  the  stem  at  0°,  this  weight  was  in- 
creased to   20.156    grammes.     Subsequently,  in   order  to   measure   the 
apparent  expansion  of  mercury,  the  two  fixed  points  were  carefully  de- 
termined on  the  stem.     The  difference  between  the  two  was  found  to  be 
250  divisions.     Required  the  coefficients  both  of  absolute  and  of  apparent 
expansion,  using  for  the  coefficient  of  glass  the  value  given  in  the  last 
problem. 

338.  A  spherical  vessel  having  an  internal  diameter  equal  to  two  thirds 
of  a  metre  at  0°,  is  made  of  a  material  whose  coefficient  of  expansion  is 
equal  to  3315 TT-     Required  the  weight  of  mercury  which  the  vessel  will 
hold  at  0"  and  at  25°. 

339.  A  cylinder  of  brass  immersed  in  water  is  suspended  from  the  pan 
of  a  hydrostatic  balance,  and  counterpoised  at  4D.     The  temperature  is 
then  raised  to  9°,  and  it  is  required  to  determine  the  weight  necessary  to 
restore  the  equilibrium.     The  circumference  of  the  cylinder  is  0.135  m. ; 
its  height,  0.12  m. 

340.  A  spherical  glass  vessel,  whose  diameter  is  equal  to  0.28  m.,  is 
filled  with  mercury  at  70°.     This  mercury  is  turned  into  a  quantity  of 
water  which  half  fills  a  cylindrical  vessel  0.40  m.  high  and  0.40  m.  in 
diameter.     Required  the  temperature  of  the  mixture,  neglecting  the  tem- 
perature of  the  glass. 

341.  Determine  the  coefficient  of  expansion  of  platinum  from  the  fol- 
lowing data:—  Grammes 

"Weight  of  the  platinum  bar, 198.0 

"  "       glass  bulb  and  platinum  bar  enclosed,          ....         240.5 

"  "  "          "  "          when  filled  with  mercury  at  0°,  .    390.1 

"  "       mercury  expelled  on  heating  the  tube  to  100°,     .       >«..  ;  .  ,         7.97 

This  problem  can  be  most  readily  solved  by  first  calculating  the  values  of 

HL,  Jl,  and  — IT— >  an(*  afterwards  substituting  these  values  in  [180]. 

Expansion  of  Gases. 

342.  To  what  temperature  must  an  open  vessel  be  heated  before  one 
half  of  the  air  which  it  contains  at  0D  is  driven  out  ?     The  pressure  is  as- 
sumed to  be  constant. 


HEAT.  547 

343.  An  open  vessel  is  heated  to  1,000°.    What  portion  of  the  air  which 
the  vessel  contained  at  0°  remains  in  it  at  this  temperature  ?     The  pres- 
sure is  assumed  to  be  constant. 

344.  A  closed  glass  vessel,  which  at  0°  was  filled  with  air  having  a 
tension  of  76  c.  m.,  is   heated   to  500°.     Determine  the  tension  of  the 
heated  air. 

345.  Required  the  temperature  at  which  one  litre  of  air  would  weigh 
one  gramme,  the  pressure  being  76  c.  m. 

346.  An  iron  bomb-shell  was  filled  with  nitrogen  gas  at  0°,  and  after 
having  been  hermetically  sealed  was  heated  white-hot  (1,300°  C.).     Re- 
quired the  tension  of  the  heated  gas. 

347.  Reduce  the  following  volumes  of  gas,  measured  at  the  tempera- 
tures and  pressures  annexed,  to  0°  and  76  c.  m. :  — 

1.  10    ^T.3    H=  74  c.  m.    t  =  10°. 

2.  7.5    "        H=  73    "        t  =  12°. 

3.  10       "        H=  80    "        t  =  10°. 


4.     12C7S.3    J7=38c.  m.      *  =    30°. 


5.  1  1     "        H  =  50     "         t  =    20°. 

6.  9     "        #=60     "          *  =  -10°. 


348.  It  is  required  to  determine  the  temperature  to  which  an  air-ther- 
mometer was  exposed  from  the  following  data  :  — 

Weight  of  the  glass  thermometer, w     =    25.364  grammes. 

"          "      thermometer  filled  with  mercury  at  0°,     .          W   =  705.164      " 
"          "  "  partially  filled  with  mercury  at  0°,   W    =251.964      " 

Height  of  the  barometer  reduced  to  0°,  .        .        .        .        H 'o  =    75.64    c.  m. 
"          "      mercury-column  in  thermometer,  .         .         .    ho     =    13.54       " 
"          "      barometer  at  the  time  of  closing  thermometer,    Ho   =    76.22       " 

Ans.  232°.7. 

349.  It  is  required  to  determine  the  temperature  to  which  the  air-ther- 
mometer of  Fig.  273  was  exposed  from  the  following  data :  — 

Height  of  barometer  at  the  moment  of  observing  the  temperature,    H'o  =  76.22  c.  m. 

"  "  "  "  measuring  difference  of  level,  H0  =  76.54  " 
Difference  of  level  as  measured  by  a  cathetometer,  .  .  .  Ao  =  40.34  " 
Volume  of  the  air-thermometer  at  0°, V  =  254  cTnT3 

"          "      manometer-tube  between  /  and  o,          .        .        .    v      =    20       " 

Temperature  of  the  manometer, t      =    10°. 

Ans.  265°. 

350.  It  is  required  to  determine  the  volume  of  the  air-thermometer 
from  the  following  data :  — 

Weight  of  mercury  above  mark  o,        ....      81 .600  grammes. 
"        between  a  and  #,        .        .        .        272.000 

Height  of  barometer, 76         c.  m. 

Difference  of  level  of  the  two  columns,     .        .        .          39.4        " 

351.  A  glass  tube,  the  area  of  whose  section  is  T^  of  a  square  cen- 
timetre, is  connected,  as  in  Fig.  355,  with  a  glass  bulb  whose  capacity 
equals  0.75  cTm".8     At  the  temperature  of  — 40°  and  under  a  pressure  of 
76  c.  m.  the  small  thread  of  liquid,  A,  stands  at  the  lowest  part  of  the 
tube.     It  is  required  to  determine  how  long  the  tube  must  be,  in  order 
that  we  may  measure  with  the  instrument  a  temperature  of  120°. 


548 


CHEMICAL  PHYSICS. 


CHANGE  OF  STATE  OF  BODIES. 

1.   Solids  to  Liquids. 

(269.)  Melting-Point.  —  If  we  heat  a  solid,  the  first  effect  of 
heat  is,  as  we  have  seen,  to  expand  it ;  the  second  effect  is  to 
change  its  mechanical  condition,  —  to  melt  it.  The  temperature 
at  which  solids  melt  differs  very  greatly  for  different  substances  ; 
but  it  is  always  constant  for  the  same  substance.  Moreover,  the 
temperature  remains  absolutely  constant  during  the  whole  period 
of  melting.  This  temperature  is  termed  the  melting-point. 

Melting-Points. 


Mercury  .... 
Oil  of  Turpentine 
Ice           .... 
Lard    .... 
Phosphorus      •         •         • 

—39° 
—10 
0 
+33 
43 

Sulphur     .... 
Alloy  (l  Tin,  1  Bismuth)    . 
"       (3  Tin,  2  Lead)     . 
"      (8  Tin,  1  Bismuth)   . 
Tin   

109° 
141 
167 

200 
230 

Spermaceti           .         .         « 
Potassium 
Wax  (not  bleached)     . 
Stearic  Acid     . 
Sodium        »         . 
Fusible  metal  (5  Pb,  3  Sn,  8  Bi) 
Iodine          .         .         .         , 

49 
58 
61 
70 
90 
100 
107 

Bismuth 
Lead          .... 
Zinc        .... 
Antimony 
Silver,  pure,   . 
"       alloyed  with  T\y  gold, 

256 
322 
360 
432 
999 
1048 

(270.)  Vitreous  Fusion.  —  Most  solids,  when  heated  to  their 
melting-point,  change  at  once  into  perfect  liquids ;  but  some, 
such  as  platinum,  iron,  glass,  phosphoric  acid,  the  resins,  wax,  and 
many  others,  pass  through  an  intermediate  pasty  condition  before 
they  attain  complete  fluidity.  In  such  cases  the  melting-point  is 
not  fixed,  although,  so  far  as  we  can  judge,  a  definite  tempera- 
ture corresponds  to  each  stage  of  the  change.  The  term  vitreous 
fusion  has  been  applied  to  this  gradual  change  of  state,  because 
it  is  a  characteristic  property  of  all  vitreous  substances  ;  and  it  is 
when  in  this  intermediate  pasty  state  that  glass  is  worked  and 
iron  or  platinum  forged. 

(271.)  Freezing-Point.  —  If  a  substance  in  the  liquid  form  is 
cooled  below  the  temperature  at  which  it  melts,  it  again  becomes 
solid,  and  as  a  general  rule  the  freezing-point  is  the  same  as  the 
melting-point.  But  in  many  cases  we  can  cool  a  liquid  several 


HEAT.  649 


degrees  below  its  melting-point  without  its  solidifying  ;  thus,  by 
keeping  water  perfectly  still,  we  can  succeed  in  cooling  it  to 
— 15°,  or  even  to  — 17°,  before  it  freezes.  If,  however,  when  in 
this  condition,  we  drop  into  the  water  an  angular  body,  like  a 
piece  of  sand,  or  gently  jolt  the  vessel  containing  it,  congelation 
begins  at  once,  and  the  temperature  suddenly  rises  to  0°.  It  has 
already  been  stated  (258)  that  water  continues  to  expand  when 
cooled  below  0°,  while  ice  under  the  same  circumstances  con- 
tracts. Despretz  has  followed  its  expansion  to  — 20°. 

This  singular  phenomenon  seems  to  be  caused  by  the  inertia 
of  the  particles  of  the  liquid,  and  is  exhibited  to  a  still  greater 
degree  in  viscid  liquids,  like  the  fats,  where,  on  account  of  the 
imperfect  fluidity,  the  inertia  is  greater.  Such  liquids  uniformly 
do  not  begin  to  freeze  until  they  are  cooled  several  degrees  below 
the  melting-point ;  but  as  soon  as  the  change  commences,  the 
temperature  at  once  rises  to  this  point. 

It  has  been  noticed  that  the  phenomenon  just  described  is  most 
readily  produced  when  the  liquid  is  enclosed  in  a  capillary  tube, 
and  this  circumstance  has  been  thought  to  explain  the  fact  that 
plants  and  many  of  the  lower  animals  frequently  seem  to  resist  the 
action  of  frost  without  any  apparently  adequate  protection  ;  for, 
as  is  well  known,  their  liquid  juices  circulate  through  exceedingly 
minute  capillary  vessels. 

(272.)  Effect  of  Sails  on  the  Freezing-Point  of  Water.  —  The 
freezing-point  of  water  is  depressed  by  the  presence  of  salts  in 
solution.  Thus  sea-water  freezes  at  about  — 3°,  and  a  saturated 
solution  of  common  salt  must  be  cooled  as  low  as  — 20°  before 
freezing.  The  freezing-points  of  various  saline  solutions  at  dif- 
ferent degrees  of  concentration  have  been  given  by  Despretz  in  a 
memoir  already  referred  to  (258).  In  all  these  cases  pure  ice  is 
formed  by  the  freezing,  and  a  more  saturated  solution  of  the  salt 
is  left.  The  change  may  in  fact  be  regarded  as  a  process  of  crys- 
tallization, in  which  the  water  crystallizes  out,  leaving  the  salt 
behind.  In  like  manner,  alcohol,  which  when  mixed  with  water 
very  greatly  reduces  the  freezing-point,  is  entirely  eliminated 
from  it  in  the  process  of  freezing.  Hence  weak  alcoholic  liquids 
like  wine  or  beer  may  be  concentrated  by  exposing  them  to  cold 
and  removing  the  layers  of  ice  as  they  form. 

To  the  same  class  of  phenomena  belongs  the  fact,  that  the 
melting-point  of  several  alloys  is  lower  than  that  of  either  of  the 


550  CHEMICAL  PHYSICS. 

metals  of  which  they  consist.  The  most  remarkable  example  of 
this  kind  is  Rose's  fusible  metal,  consisting  of  two  parts  bismuth, 
one  part  tin,  and  one  part  lead,  which  melts  between  95°  and 
98°,  although  the  melting-points  of  its  constituents  are  all  be- 
tween 235°  and  334°.  The  following  table,  which  gives  the  melt- 
ing-points of  several  alloys  of  tin  and  lead,  furnishes  another 
example  of  the  same  fact.  The  lowest  melting-point  corre- 
sponds to  an  alloy  of  three  equivalents  of  tin  and  one  equivalent 
of  lead.  Compounds  of  two  equivalents  of  sulphur  and  three 
equivalents  of  phosphorus,  of  two  equivalents  of  bismuth  and 
three  equivalents  of  tin,  show  similar  relations. 

Percentage  Composition.  Melting-Point. 

Tin.  Lead. 

100  0  235 

73.7  26.3  194 

69.3  30.7  189 

63.0  37.0  186 

53.2  46.8  196 

36.2  63.8  241 

15.9  84.1  289 

0  100  334 

(273.)  Effect  of  Pressure  on  the  Melting-Point.  —  Since  the 
effect  of  an  external  pressure  must  be  to  resist  the  expansive 
force  of  heat,  we  might  naturally  expect  that  it  would  tend  to 
raise  the  melting-point.  That  this  is  indeed  the  fact  is  shown 
by  the  following  table,  which  gives  the  results  of  experiments 
made  by  Mr.  Hopkins*  on  this  subject. 

Pressure  in 
Atmospheres. 

1 

520 
793 

On  the  other  hand,  it  has  been  shown  by  Professor  Thompson 
that  the  effect  of  pressure  on  water  is  exactly  opposite  to  that 
just  described.  He  found  that  a  pressure  of  8.1  and  16.8' atmos- 
pheres caused  a  depression  of  the  freezing-point  of  0°.059  and 
0°.129.  But  it  will  be  shown  in  the  next  section,  that,  while  the 

*  Silliman's  American  Journal,  Second  Series,  Vol.  XIX.  p.  140. 


Spermaceti. 

51.1 

Melting-Point. 
Wax.                 Sulphur. 

64°.7             107!2 

Stearine. 

60.0 

74.7 

135.2 

68.3 

80.2 

80.2 

140.5 

73.8 

HEAT.  551 

volume  of  the  substances  on  which  Mr.  Hopkins  experimented  in- 
creases by  melting,  that  of  water  diminishes.  We  should,  there- 
fore, expect  an  opposite  result  in  the  two  cases  ;  in  fact,  not 
only  the  general  effect  of  the  pressure,  but  also  the  amount  to 
which  the  melting-point  of  ice  is  depressed  by  it,  are  in  accord- 
ance with  the  theory.  Indeed,  the  phenomenon  was  predicted  by 
Professor  Thompson*  on  purely  theoretical  grounds,  and  the 
experimental  results  since  obtained  have  agreed  very  closely  with 
his  predictions. 

(274.)    Change  of  Volume.  —  At    the    moment    of    melting 
there  is  a  sudden  change  of  volume,  which  is  usually  an  ex- 
pansion ;   but  in  the  case  of  water  and  a  few  metals  the  effect 
is  a  condensation.     This  subject  has  been  carefully  investigated 
by  Kopp,f    who   used   in   his   experiments   the  simple  appara- 
tus  represented   in   Fig.  396.      The   small    test-tube 
a  a,  containing  the  substance  to   be   examined,  was 
placed  within  a  somewhat  larger  tube  of  the  same 
shape  ;  and  this,  having  been  filled  with  water  or  some 
other  suitable  liquid,  was  closed  by  a  cork  provided 
with  a  capillary  glass  tube  divided  into  parts  of  equal 
capacity.      It  is  evident  that  any  -change  of  volume 
of  the  solid  in   the  tube  a  a  could   be  measured  by 
the  rise  or  fall  of  the  enclosed  liquid  in  the  capillary 
tube.     In  practice,  the  apparatus  was  heated  at  the 
side  of  a  thermometer  in  an  oil-bath,  so  arranged  that 
the  temperature  could  be  kept  constant  for  a  few  min- 
utes at  any  point,  and  at  each  stationary  point  the 
temperature  and  the  height  of  the  liquid  in  the  capil- 
lary tube  were  observed.     The  weight  of  the  substance 
and  of  the  liquid  used  (commonly  water)  having  been 
previously  determined,  and  the  rate  of  expansion  of 
glass  and  of  the  liquid  being  known,  and  also  the  vol- 
ume of  the  tube  between  any  two  divisions,  it  was 
easy  to  calculate  the  volume  of  the  substance  at  eacli       Fig  398. 
observed  temperature,  and  of  course  to  measure  the 
change  of  volume  which  took  place  at  melting.      Some  of  the 
results  obtained   by  Kopp   are   represented   in  Figs.   397,  398, 
399,  and  400.     Here,  as  in  Figs.  381  and  386,  the   abscissas  of 

*  Philosophical  Magazine,  1850,  Vol.  XXXVII.  p.  123. 
t  Annalcn  der  Chemie  und  Pharmacie,  Bund  XCIII.  *•  5. 


552 


CHEMICAL   PHYSICS. 


the  curves  indicate  degrees  of  temperature,  and  the  ordinates  tho 
corresponding  volumes  of  the  substance,  the  volume  at  0°  being 
taken  as  unity.  Solid  phosphorus  (Fig.  397),  it  will  bo  noticed, 


Fig.  397. 


Fig.  398. 


expands  very  regularly,  like  other  solids,  until  it  reaches  44°,  its 
melting-point,  when  a  sudden  expansion,  amounting  to  about 
0.035  of  the  original  volume,  takes  place.  After  melting,  the 
expansion  continues,  with  tolerable  regularity,  as  before.  Ice,  on 
the  other  hand  (Fig.  398),  which,  so  long  as  it  remains  solid,  is 
expanded  by  heat,  suddenly  contracts  in  melting,  —  the  con- 
traction amounting  to  about  0.1  of  the  volume  of  the  water  at 

0°.  After  melting,  the  water 
expands  according  to  the 
laws  before  stated,  but  the 
total  amount  of  expansion 
between  the  freezing  and 
boiling  points  is  less  than 
one  half  as  great  as  the  con- 
traction in  melting.  Hence 
ice  will  float  on  water,  even 
when  at  the  boiling-point. 
The  expansion  of  water  in 
freezing  takes  place  with  ir- 
resistible force.  Thick  iron 

Fig  ggg  bomb-shells  have  been  burst 

by  exposing  them  to   great 
cold  when  filled  with  water  and  tightly  plugged. 

The  law  of  the  expansion  of  wax  while  melting  is  shown  by 
the  curve  in  Fig.  399.  Since  wax  does  not  change  suddenly  into 
a  liquid,  but  passes  through  an  intermediate  pasty  condition,  we 
should  not  expect  to  find  a  point  of  sudden  expansion.  As  tne 


HEAT. 


553 


curve  indicates,  the  expansion  is  very  rapid  during  the  melting, 
and  vastly  more  rapid  than  the  expansion  above  64°,  the  point 
at  which  the  wax  becomes  perfectly  liquid. 

Fig.  400  represents  the  curve  of  stearine,  which  is  exceedingly 
irregular.  The  substance 
has  in  fact  two  melting- 
points.  It  melts  first  at 
50°,  and  this  change  is  at 
tended  with  a  sudden  con- 
densation. But  as  the  tern 
pcrature  rises  higher,  the 
substance  again  thickens, 
owing  undoubtedly  to  a 
change  in  its  molecular 
condition  ;  and  this  new 
condition  of  stearine  melts 
at  GO0,  when  the  change 
is  attended  with  a  sudden  rig.  400. 

expansion. 

Besides  water,  the  only  substances  known  to  expand  in  so- 
lidifying, which  do  not  contain  water  as  a  chief  constituent,  are 
cast-iron,  bismuth,  antimony,  and  a  few  alloys,  such  as  type- 
metal,  brass,  and  bronze.  These  metals  and  alloys  all  give 
sharp  casts,  because  the  expansion,  which  takes  place  when 
the  metal  sets,  forces  it  into  the  minute  cavities  of  the  mould  ; 
and  on  this  fact  depend  many  of  their  useful  applications  in 
founding. 

(275.)  The  melting  of  solids,  like  their  expansion,  may  be 
explained  by  the  expansive  force  exerted  by  heat.  When  this 
expansive  force  becomes  equal  to  the  cohesive  force,  we  evi- 
dently have  a  condition  of  matter  in  which  the  particles  are  in 
perfect  equilibrium  between  two  forces,  and  are  therefore  free 
to  move  at  the  slightest  impulse  ;  in  a  word,  we  have  the  condi- 
tion of  liquidity.  We  may  define,  then,  a  liquid  as  that  condition 
of  matter  in  which  the  cohesive  force  is  balanced  by  the  expan- 
sive force  of  heat.  With  a  few  exceptions,  all  solids  which  can 
bear  the  requisite  change  of  temperature  without  undergoing 
chemical  change,  may  be  melted.  Many  substances  which  are 
generally  regarded  as  infusible  —  such,  for  example,  as  platinum, 
flint,  and  siliceous  minerals  —  readily  melt  before  the  compound 
47 


554  CHEMICAL  PHYSICS. 

blowpipe,  or  between  the  poles  of  a  powerful  galvanic  battery. 
Carbon  is,  indeed,  almost  the  only  substance  which  has  not 
yielded  to  these  high  temperatures  ;  and  it  is  probable  that  even 
this  will  be  melted  when  the  means  of  obtaining  still  higher  tem- 
peratures shall  be  Discovered.*  There  are,  however,  a  great 
number  of  substances,  especially  organic  compounds,  which 
cannot  be  melted,  because  they  are  decomposed  by  the  action 
of  heat.  Thus  wood,  when  heated,  is  decomposed  into  certain 
gases  and  acid  vapors,  which  escape,  and.  into  carbon,  which  is 
left  behind.  In  like  manner  carbonate  of  lime  (chalk),  when 
heated,  is  decomposed  into  carbonic  acid  gas  and  lime  at  a  tem- 
perature below  its  point  of  fusion.  If,  however,  we  prevent  the 
gas  from  escaping,  by  confining  the  carbonate  of  lime  in  a  gun- 
barrel  hermetically  closed,  it  can  be  melted  in  a  furnace  fire. 

As,  with  very  few  exceptions,  all  solids  may  be  melted,  we 
have  every  reason  to  infer  that  all  liquids  might  be  frozen  if  a 
sufficient  degree  of  cold  could  be  attained.  There  are,  however, 
several  liquids  which  have  never  yet  been  frozen.  Such,  for 
example,  are  sulphide  of  carbon,  alcohol,  and  several  others  of 
organic  origin  ;  but  even  alcohol  becomes  very  thick  and  oily 
when  exposed  to  the  intense  cold  produced  by  a  mixture  of  solid 
carbonic  acid  and  ether. 

(276.)  Determination  of  the  Melting-Point.  —  The  melting- 
point  is  an  important  physical  property  of  a  substance,  and  the 
chemist  has  frequent  occasion  to  determine  it.  The  simplest 
method  is  to  heat  the  solid  in  a  convenient  vessel  until  it  begins 
to  melt,  and  then  test  the  temperature  with  a  thermometer  before 
it  is  fully  melted.  It  is  always  well,  however,  also  to  reverse  the 
experiment,  and,  by  cooling  down  the  liquid,  test  the  temperature 
while  it  is  freezing.  But  if  there  is  a  difference  between  the  two 
temperatures,  the  melting-point  should  be  taken  as  the  physical 
constant  rather  than  the  freezing-point,  for  the  reasons  already 
stated  (271). 

The  apparatus  represented  in  Fig.  401  will  be  frequently  found 
very  convenient  for  determining  the  melting  or  freezing  .point  of 
many  organic  substances,  especially  when  only  a  small  quantity 

*  Both  Silliman  and  Despretz  have  obtained  evidence  of  the  partial  fusion  and  vola- 
tilization of  carbon,  when  exposed  to  the  action  of  a  galvanic  battery  of  great  intensity. 
For  a  description  of  the  best  means  of  producing  intense  furnace  heat,  see  a  memoir 
by  Deville,  Annales  de  Chimie  et  do  Physique,  3e  Serie,  Tom.  XL VI.  p.  182. 


HEAT. 


555 


Fig.  401. 


is  available  for  the  experiment.     It  consists  of  a  water  or  oil  bath, 
made  with  two  beaker  glasses  (one  supported  within  the  other,  as 
represented  in  the  figure),  so  that  the  conduction  of  heat  from  the 
lamp  to  the  inner  vessel  may  be  as  uni- 
form as  possible.    A  thermometer  in  the 
inner  glass  gives  the  temperature  of  the 
bath  at  each  instant,  and  the  substance 
under  experiment,  enclosed  in  a  capilla- 
ry glass  tube,  is  immersed  in  the  bath  at 
the  side  of  the  thermometer.     By  slowly 
heating  and  then  cooling  the  bath,  it  is 
easy  to  catch  the  exact  point  at  which 
the   solid   melts  and  the   liquid  again 
freezes  ;  and  the  experiment  can  read- 
ily be  repeated  a  great  number  of  times. 

(277.)  Heat  of  Fusion.  —  It  has  al- 
ready been  stated,  that  while  a  solid 
is  melting  the  temperature  remains  the 
same.  This  fact  can  be  easily  verified 
by  watching  a  thermometer  immersed  in  a  tumbler  filled  with 
melting  ice,  when  it  will  be  found  that  the  thermometer  will 
stand  at  0°  until  the  whole  of  the  ice  has  disappeared.  During 
all  this  time,  which  may  be  several  hours,  heat  has  been  continu- 
ally entering  the  water  from  the  air,  and  the  question  naturally 
arises,  What  has  become  of  this  heat  ?  The  answer  is,  that  it 
has  been  used  up  in  melting  the  ice. 

In  order  to  study  this  phenomenon  more  closely,  let  us  take 
two  vessels,  the  first  containing  one  kilogramme  of  ice-cold  water, 
and  the  second,  one  kilogramme  of  coarsely  pulverized  ice.  A 
thermometer  placed  in  each  vessel  will  indicate  that  both  the 
ice  and  the  water  have  exactly  the  same  temperature,  viz.  0°. 
Let  us  now  expose  both  to  such  a  source  of  heat,  that  the  same 
amount  of  heat  must  enter  each  vessel  during  the  same  time. 
It  will  be  found  that  the  thermometer  in  the  first  will  remain 
stationary  while  the  ice  is  melting  ;  but  the  thermometer  in  the 
second  will  gradually  rise.  If  at  the  moment  the  last  particle  of 
ice  has  melted  we  examine  the  two  thermometers,  we  shall  find 
that  the  one  in  the  first  vessel  marks  still  0°,  while  that  in  the 
second  has  risen  to  79°.  From  the  definition  of  the  unit  of  heat 
(231),  it  follows  that  79  units  of  heat  must  have  entered  both 


556  CHEMICAL  PHYSICS. 

vessels.  This  heat  has  not  raised  the  temperature  of  the  first, 
because  it  has  all  been  consumed  in  melting  the  ice.  The  differ- 
ence, then,  between  one  kilogramme  of  ice  at  0°  and  one  kilo- 
gramme of  water  at  the  same  temperature  is  79  units  of  heat. 

The  same  truth  may  be  illustrated  in  another  way.  If  we  take 
one  kilogramme  of  water  at  79°,  and  one  kilogramme  of  ice  at  0°, 
and  mix  the  two  together,  we  shall  find,  on  testing  the  water  with 
a  thermometer  after  the  ice  has  melted,  that  its  temperature  is  0°. 
What  then  has  become  of  the  79  units  of  heat  that  the  kilo- 
gramme of  water  contained  ?  It  is  evident  that  they  have  disap- 
peared in  the  melting  of  the  ice.  What  is  true  of  ice  and  water 
is  also  true  of  other  substances.  All  solids,  in  melting,  absorb  a 
large  amount  of  heat,  without  any  corresponding  change  of  tem- 
perature. The  heat  which  is  thus  absorbed  is  sometimes  called 
the  heat  of  fusion-,  but  more  frequently  the  latent  heat  of  the 
liquid,  because  it  is  not  sensible  to  the  thermometer.  The  heat 
of  fusion  of  a  few  solids  is  given  in  the  following  table :  — 

Melting-  Heat  absorbed  by  1  kilo- 

Point,  gramme  in  melting. 

Ice,      .      .  -,'**•      .  .         .         0°.0  71J.25  units. 

Phosphorus,      k        *  *           44°.2  5.03  " 

Sulphur,       .     ..,  ,,,>.        .     115°.2  9.37  « 

Lead,        .     <>.,».   .  .         326°.2  5.37  " 

Bismuth,       .         .     j  .         .     266°.8  12.64  " 

Tin,          .      '  V  ,     .  .         237°.7  14.25  " 

Silver,           .         /  I.       .     999°.  21.07  " 

Zinc,         .         .        .  .         415°.3  28.13  " 

The  principle  under  discussion  is  well  illustrated  by  the  so- 
called  free z ing*  mixtures.  The  most  common  of  these  is  a  mix- 
ture of  equal  parts  of  snow  or  pounded  ice  and  salt,  which  pro- 
duces a  degree  of  cold  of  about  — 16°.  The  salt  causes  the  ice  to 
melt  and  the  water  dissolves  the  salt,  so  that  both  become  liquid, 
and  in  consequence  a  large  amount  of  heat  is  absorbed.  This 
mixture  is  used,  as  is  well  known,  for  freezing  ice-creams.  A 
much  more  powerful  freezing  mixture  is  formed  by  mixing 
together  three  parts  of  crystallized  chloride  of  calcium,  previ- 
ously cooled  to  0°,  and  two  parts  of  snow.  A  degree  of  cold 
may  be  thus  produced  equal  to  — 45°,  and  sufficient  to  freeze 
mercury. 

The  solution  of  most  salts  in  water  is  attended  with  the  ab- 


HEAT. 


557 


sorption  of  heat,  because  the  salt,  in  dissolving,  changes  from  a 
solid  to  a  liquid  condition.  Nitre,  for  example,  cools  the  water 
in  which  it  is  dissolved  eight  or  ten  degrees.  One  part  of  chlo- 
ride of  potassium  dissolved  in  four  parts  of  water  also  cools  the 
water  about  the  same  amount.  The  depression  of  temperature 
is  frequently  more  considerable  when  we  dissolve  the  salt  in  an 
acid  liquid  instead  of  pure  water.  A  very  convenient  method  of 
freezing  water  without  the  use  of  ice  consists  in  mixing  together 
finely  pulverized  Glauber's  salt  and  the  common  muriatic  acid 
of  commerce.  The  salt  dissolves  to  a  greater  extent  in  the  acid 
than  in  water,  and  a  depression  of  temperature  results  which 
may  amount  to  28°.  An  apparatus  (Fig.  402)  is  constructed  at 
Paris  for  freezing  water  by  this  process,  and  it  is  found  to  require 


Fig.  402. 

about  six  kilogrammes  of  Glauber's  salt  and  five  kilogrammes 
of  muriatic  acid  to  freeze  five  kilogrammes  of  water.  The  freez- 
ing mixture  is  placed  in  the  cylindrical  chamber  C,  while  the 
hollow  walls  of  this  chamber,  as  well  as  the  interior  cylinder  -4, 
are  filled  with  the  water  to  be  frozen.  The  crank  at  the  top  of 
the  apparatus  serves  to  turn  the  cylinder  A  and  the  vanes  at- 
tached to  it,  by  which  means  the  acid  and  salt  are  kept  constantly 
mixed  and  the  surfaces  of  contact  renewed.  After  the  ke  forms, 
the  freezing  mixture  is  drawn  off  into  the  lower  chamber  V9 
where  it  may  be  further  used  for  cooling  bottles  of  wine. 
47* 


558  CHEMICAL  PHYSICS. 

As  the  change  of  state  from  solid  to  liquid  is  attended  with  the 
absorption  of  a  definite  amount  of  heat,  we  should  naturally 
expect  that,  when  the  fluid  changes  hack  again  to  a  solid,  the 
same  amount  of  heat  would  be  evolved.  That  this  is  really  the 
case,  may  be  proved  by  reversing  the  experiments  just  described. 

If  we  take  two  vessels,  the  first  containing  one  kilogramme  of 
water  at  79°,  and  the  second,  one  kilogramme  of  water  at  zero, 
and  expose  them  to  the  air  during  a  cold  winter  day,  so  that 
equal  amounts  of  heat  shall  escape  from  both  during  any  given 
time,  we  shall  find  that  the  temperature  of  the  water  in  the  first 
vessel  will  immediately  fall,  while  that  of  the  water  in  the  sec- 
ond vessel  will  remain  stationary.  In  the  mean  time,  however, 
the  water  in  the  second  vessel  will  begin  to  freeze  ;  but  so  long 
as  the  water  remains  liquid,  the  temperature  will  continue  sta- 
tionary at  zero.  If  at  the  moment  the  last  particle  of  water  has 
frozen,  and  before  the  temperature  begins  to  fall,  we  observe  the 
temperature  of  the  water  in  the  first  vessel,  we  shall  find  that 
the  thermometer  stands  exactly  at  zero.  Evidently,  then,  79 
units  of  heat  have  escaped  from  the  water  in  the  first  vessel. 
The  same  amount  also  must  have  escaped  from  the  water  in  the 
second  vessel.  Why,  then,  has  it  not  changed  the  temperature  ? 
Simply  because  it  is  the  heat  of  fusion,  which  has  been  given  up 
by  the  water  in  changing  into  ice. 

In  like  manner,  as  the  solution  of  a  salt  in  water  is  attended 
with  absorption  of  heat,  so  the  separation  of  a  salt  from  its 
state  of  solution  (the  process  of  crystallization)  is  attended  with 
evolution  of  heat.  As  a  general  rule,  however,  the  crystalli- 
zation is  so  slow,  that  the  heat  escapes  as  fast  as  it  is  liberated, 
and  therefore  does  not  raise  sensibly  the  temperature  of  the  mass. 
"We  can,  however,  so  arrange  the  experiment  as  to  make  it  very 
perceptible.  We  prepare  for  this  purpose  a  supersaturated  solu- 
tion of  Glauber's  salt,  as  described  in  (198),  and  when  the  so- 
lution is  cold  make  it  crystallize  suddenly  by  uncorking  the  flask. 
On  grasping  the  flask  with  the  hand  as  soon  as  the  crystallization 
has  been  completed,  it  will  be  found  that  its  temperature  has 
risen  very  perceptibly,  thus  proving  that  crystallization  is  at- 
tended with  liberation  of  heat. 

As  a  last  illustration  of  the  principle  under  discussion,  we  may 
cite  the  well-known  process  of  slaking  lime  in  the  preparation 
of  mortar.  If  we  add  to  one  kilogramme  of  quicklime  one  half 


HEAT.  559 

a  kilogramme  of  water,  the  lime  rapidly  combines  with  the  water 
and  falls  into  a  loose  white  powder,  a  portion  of  the  water  at  the 
same  time  escaping  as  steam.  The  water  is  thus  changed,  by 
entering  into  combination  with  the  lime,  from  the  liquid  to  the 
solid  state  ;  and,  as  we  might  anticipate,  a  great  amount  of  heat 
is  suddenly  evolved.  The  elevation  of  temperature  which  is 
thus  caused  is  sometimes  sufficiently  high  to  inflame  gunpowder. 
The  heat  which  is  liberated  in  this  process  is  not,  however, 
wholly  caused  by  the  solidifying  of  the  water.  A  portion  of  it 
results  from  the  chemical  combination  between  the  lime  and  the 
water,  in  accordance  with  the  general  law  that  chemical  combi- 
nations are  attended  with  the  evolution  of  heat. 

The  quantity  of  heat  which  becomes  latent  during  the  fusion 
of  solids  is  ascertained  by  pouring  a  known  weight  of  the  melted 
solid,  at  its  melting-point,  into  a  mass  of  water  whose  weight  and 
temperature  are  known.  The  temperature  of  the  water  will  evi- 
dently be  increased  by  the  addition  of  the  amount  of  heat  which 
the  liquid  gives  out  in  solidifying,  plus  the  amount  which  the 
solid  gives  out  in  cooling  from  the  melting-point  to  the  increased 
temperature  of  the  liquid.  This  last  quantity  may  be  easily  cal- 
culated when  the  specific  heat  of  the  solid  is  known.  From  the 
increased  temperature  and  weight  of  the  water,  we  can  also  easily 
calculate  the  amount  of  heat  which  the  water  has  gained ;  and  then 
the  difference  between  these  two  quantities  will  be  the  amount  of 
heat  which  the  liquid  gave  out  in  solidifying, — in  other  words,  the 
heat  of  fusion.  The  method  may  be  made  clear  by  an  example. 

In  order  to  determine  the  latent  heat  of  melted  tin,  25 
grammes  of  the  liquid  metal  at  its  melting-point  (238°)  were 
poured  into  1,500  grammes  of  water  at  15°.  After  an  equilib- 
rium of  temperature  was  established,  a  thermometer  dipping  in 
the  water  indicated  15°. 45.  Hence  it  followed  that  the  water 
had  gained  in  temperature  15°.45  —  15°  =  0°.45,  and  must 
therefore  have  absorbed  0.45  X  1.5  =  0.675  units  of  heat  (231). 
On  the  other  hand,  the  tin  had  lost  in  temperature  238°  — 15°.45 
=  222°.55  ;  and,  since  the  specific  heat  of  tin  is  equal  to  0.0562 
(page  466),  it  must  have  given  out,  in  cooling  from  the  melting- 
point  after  solidifying,  222.55  X  0.025  X  0.0562  =  0.313  units  of 
heat.  Subtracting  this  quantity  from  0.675,  we  find  that  the 
amount  of  lueat  given  out,  in  solidifying,  by  25  grammes  of  tin, 
is  equal  to  0.362  units  ;  and  a  simple  calculation  will  show  that 


560  CHEMICAL  PHYSICS. 

one  kilogramme  of  the  melted  metal  would  give  out,  under  the 
same  circumstances,  14.48  units  of  heat,  —  a  quantity  which,  by 
definition,  is  the  heat  of  fusion  of  the  substance.  This  result 
corresponds  with  the  number  given  in  the  table  on  page  556. 

A  general  formula  for  such  calculations  may  be  readily  derived. 
Using  the  notation  of  (233),  and  also  representing  the  specific 
heat  of  the  substance  by  JV,  and  the  required  heat  of  fusion  by 
x,  we  shall  have 

TT(0  — 0  =  w  .  N  .  (T—  ff)  +  wx\ 

that  is,  the  heat  which  the  water  lias  gained,  W '  (0  —  0>  is 
equal  to  the  heat  which  the  solid  has  lost  in  cooling  from  its 
melting-point,  iv  .  JV(T— - 0),  plus  the  heat  which  the  liquid 
lost  in  solidifying,  w  x.  From  this  equation  we  get  the  value 


w 


Here,  as  in  determining  the  specific  heat  of  a  substance,  it  is 
necessary  to  take  into  account  the  heat  absorbed  by  the  vessel  in 
which  the  experiment  is  conducted,  and  also  the  heat  lost  by 
radiation  and  from  other  causes.  In  order  to  insure  that  the 
temperature  of  the  liquid  is  at  its  melting-point  when  poured  into 
the  water,  it  is  best  to  pour  it  from  a  vessel  which  still  contains 
some  of  the  unmelted  solid,  since  so  long  as  any  of  the  solid 
remains  unmelted  the  temperature  of  the  mass  is  constant  at 
the  melting-point.  In  other  respects,  the  experiment  may  be 
conducted  precisely  as  in  determining  the  specific  heat  of  a  sub- 
stance by  the  method  of  mixture  (233),  so  that  further  details 
are  unnecessary. 

(278.)  Person's  Law.  —  It  has  already  been  stated  (234)  that 
the  specific  heat  of  the  same  substance  is  greater  in  the  liquid 
than  in  the  solid  state,  and  by  referring  to  the  table  on  page  475 
it  will  be  seen  that  the  difference,  which  is  very  considerable  in 
the  case  of  non-metallic  substances,  is  very  slight  in  the  case  of 
metals.  Moreover,  it  has  also  been  stated  that  a  liquid  may 
sometimes  be  cooled  several  degrees  below  the  normal  freezing- 
point  without  solidifying ;  and  it  is  a  possible,  although  not  a 
probable  supposition,  that  under  certain  circumstances  a  liquid 
might  be  reduced  to  the  lowest  possible  temperature  without 


HEAT.  561 

undergoing  this  change.  Let  us  now  assume  that  at  N  degrees 
below  zero  we  should  reach  the  lowest  possible  temperature,  or 
absolute  zero,  a  condition  in  which  bodies  would  contain  abso- 
lutely no  heat,  and  let  us  suppose  that  we  start  at  this  tempera- 
ture with  one  kilogramme  of  any  given  substance  in  the  solid 
condition,  and  one  kilogramme  of  the  same  substance  in  the 
liquid  condition.  Also  let  us  represent  by  C  the  specific  heat 
of  the  liquid,  by  C'  the  specific  heat  of  the  solid,  and  by  T°  the 
normal  freezing  or  melting  point  of  the  substance.  If  then  we 
assume  —  as  we  may  without  any  great  probable  error  —  that  the 
specific  heat  does  not  vary  between  the  absolute  zero  and  T°,  it 
follows  (232)  that  (-ZV+  T)  C  units  of  heat  would  be  required 
to  raise  the  temperature  of  the  one  kilogramme  of  the  substance 
in  the  liquid  condition  from  the  absolute  zero  to  the  melting- 
point,  and  that  (^V+  T)  C'  units  of  heat  would  be  required  to 
raise  the  temperature  of  the  one  kilogramme  of  the  substance 
in  the  solid  condition  to  the  same  extent.  Furthermore,  it  is 
evident  that  the  first  of  these  expressions  represents  the  actual 
quantity  of  heat  which  one  kilogramme  of  the  substance  at  the 
melting-point  contains  in  the  liquid  state  ;  and  the  second,  the 
quantity  of  heat  which  one  kilogramme  of  the  same  substance 
contains  at  the  same  temperature  in  the  solid  state.  The  differ- 
ence between  these  quantities  is,  then,  the  number  of  units  of 
heat  which  would  be  required  to  convert  one  kilogramme  of  the 
substance  at  the  melting-point  from  the  solid  to  the  liquid  state ; 
or,  in  other  words,  the  heat  of  fusion.  Representing  the  heat  of 
fusion  by  L,  we  have  L  =  (.2V+  T)  C  —  (JV+  T)  C',  which 
may  be  written 

L=(7\T+T)  (C—  C').  [195.] 

If,  then,  the  theory  on  which  this  formula  is  based  is  cor- 
rect, it  follows  that  the  heat  of  fusion  of  a  substance  is  equal  to 
the  difference  in  the  specific  heat  in  the  two  states  of  aggrega- 
tion, multiplied  by  the  number  of  degrees  above  the  absolute 
zero  at  which  the  substance  melts.  By  giving  to  N  the  value 
•of  160°,  Person  found  that  the  heat  of  fusion  of  many  non- 
metallic  substances  calculated  by  the  above  formula  agreed  al- 
most precisely  with  the  results  of  direct  experiment,  as  is  shown 
by  the  following  table :  — 


562 


CHEMICAL   PHYSICS. 


Specific  Heat  in 

Latent  Heat. 

Name  of 

Melting- 

Substance. 

Point. 

i 

Solid  State. 

Liquid  State. 

Observed. 

Calculated. 

0 

Water,      .    ;    .^ 

0 

0.504 

1.0000 

79.25 

79.20 

Phosphorus,  . 

44.2 

0.1788 

0.2045 

5.034 

5.243 

Sulphur,    . 

115 

0.20259 

0.234 

9.868 

9.350 

Nitrate  of  Soda, 

310.3 

0.27S21 

0.413 

62.975 

63.4 

Nitrate  of  Potassa, 

339 

0.23875 

0.33186 

47.371 

46.462 

The  agreement  between  the  observed  and  calculated  results  is 
certainly  remarkably  close,  and  sustains  so  far  the  theory  on 
which  the  formula  is  based,  and  the  necessary  inference  from  it, 
that  the  absolute  zero  is  at  160°  below  the  Centigrade  zero. 
Whether,  however,  we  accept  the  theory  or  not,  it  is  evident  that 
the  formula  [195]  is  the  expression  of  an  empirical  law  with 
which  the  observed  facts  very  closely  agree. 

(279.)  This  law  of  Person,  however,  only  holds  true  in  regard 
to  non-metallic  substances.  In  the  case  of  the  metals,  where  the 
difference  in  the  specific  heat  in  the  two  states  of  aggregation  is 
exceedingly  small,  it  entirely  fails.  The  cause  of  this  failure 
Person  explains  as  follows. 

The  amount  of  heat  absorbed  by  a  solid  in  melting  is  not  solely 
the  quantity  necessary  to  supply  the  excess  of  specific  heat  in  the 
liquid  over  that  in  the  solid  state  ;  because,  in  addition,  a  certain 
quantity  of  heat  is  required  to  overcome  the  cohesive  force  by 
which  the  particles  of  the  solid  are  held  together  (275).  In  the 
case  of  non-metallic  substances,  where  the  tenacity  is  compara- 
tively slight,  the  quantity  of  heat  required  to  overcome  the  cohe- 
sion is  so  small  that  it  may  generally  be  neglected ;  and  the  heat 
absorbed  in  fusion  very  nearly  corresponds  to  the  increased  spe- 
cific heat  in  the  liquid  state.  In  the  case  of  the  metals,  on  the 
contrary,  the  amount  of  heat  required  by  the  increase  in  the 
specific  heat  is  very  small,  and  almost  the  entire  heat  of  fusion 
is  used  iji  overcoming  the  very  great  tenacity  of  these  substances. 
Hence,  Person  argues  that  the  amounts  of  heat  required  to  melt 
one  kilogramme  of  each  of  the  different  metals  must  be  propor- 
tional to  the  work  to  be  done  ;  in  other  words,  to  the  power  which 
must  be  used  in  overcoming  the  cohesion  between  the  particles 
comprised  in  the  unit  of  weight.  This  power  would  be  measured 
by  the  coefficient  of  elasticity,  were  it  not  that  in  determining  this 


HEAT.  563 

constant  (101)  we  do  not  have  regard  to  equal  weights.  It  is 
evidently,  however,  a  function  of  this  coefficient,  and  Person 

(2    \ 
1  +  — —  ) ,   in  which  K 
A/  d  / 

is  the  coefficient  of  elasticity,  and  8  the  specific  gravity  of  the 
metal.  Representing  also  by  K'  the  coefficient  of  elasticity  of 
a  second  metal,  and  by  L  and  L'  the  corresponding  heat  of  fusion, 
we  obtain  the  proportion 


This  formula  is  the  expression  of  a  second  law  which  may  be 
thus  stated  :  The  heat  of  fusion  of  metals  is  sensibly  propor- 
tional to  their  coefficients  of  elasticity  corrected  for  the  differ- 
ence of  density. 

If  we  substitute,  in  [196],  for  L',  K',  and  #',  the  known  values 
for  zinc,  taken  as  a  standard  of  comparison,  we  obtain  for  the 
heat  of  fusion  of  any  other  metal  the  value, 

L  =  0.001669  K  (l  +  -L)  ;  [197.] 

v       \/  <j/ 

and  the  heat  of  fusion,  calculated  by  this  formula,  agrees  very 
well  with  the  observed  result.  As  the  value  of  L  [195]  is  based 
on  the  assumption,  that  the  heat  required  to  overcome  the  te- 
nacity of  the  solid  may  be  neglected,  so  [197]  is  founded  on  the 
assumption  that  the  specific  heat  of  a  metal  is  the  same  in  the 
liquid  as  in  the  solid  state.  Evidently,  however,  the  true  value  of 
L,  in  any  case,  should  include  both  terms,  —  that  depending 
on  the  specific  heat,  as  well  as  that  depending  on  the  tenacity. 
Hence  we  obtain  Person's  general  formula  for  the  heat  of  fusion 
of  all  solids, 

L  =  (160  +  T)  ( (7—  C')  +  0.001669  K  (l  +  -~)  .     [198.] 

In  the  case  of  the  metals  the  first  term  may  be  neglected,  and  in 
the  case  of  non-metallic  substances  the  same  is  true  of  the  sec- 
ond term.  There  are  substances,  however,  for  which  both  terms 
have  definite  values  ;  but  we  have  not  the  experimental  data  in 
regard  to  them  which  would  enable  us  to  test  the  formula. 


564  CHEMICAL  PHYSICS. 

We  may  then  admit  that  the  heat  of  fusion  consists  of  two 
parts,  one  of  which  is  used  in  overcoming  the  force  of  cohesion, 
the  other  furnishing  the  additional  specific  heat  required  in  the 
liquid  state. 

We  have  been  able  to  give  in  this  section  only  a  very  imperfect 
abstract  of  Person's  remarkable  investigations  on  this  subject, 
and  we  must  refer  the  student  for  further  information  to  the 
original  memoirs.* 

(280.)  Absolute  Zero.  —  If  Person's  theory  is  correct,  the 
absolute  zero,  as  we  have  seen,  is  situated  160  degrees  below  the 
Centigrade  zero.  This  theory  is  not  a  little  confirmed  by  the 
remarkable  results  obtained  by  Pouillet,f  with  an  instrument 
called  an  actinometer,  in  regard  to  the  temperatures  of  the  celes- 
tial space.  If  we  eliminate  the  effects  of  the  rays  of  the  sun,  it  is 
evident  that  the  temperature  of  the  space  around  the  earth  must 
be  very  near  the  absolute  zero ;  for  this  space  is  traversed  only  by 
the  rays  of  the  stars,  which,  coming  from  such  immense  distances, 
are  exceedingly  feeble ;  and  Pouillet  has  concluded,  from  his 
experiments  and  from  various  terrestrial  phenomena,  that  this 
temperature  must  be  between  the  limits  of  — 175°  and  — 115°,  at 
the  same  time  fixing  on  — 142°  as  the  most  probable  value.  On 
the  other  hand,  Clement  and  De'sormes  fixed  on  — 273°  as  the 
absolute  zero,  on  the  ground  that,  since  the  permanent  gases 
expand  for  each  degree  of  temperature  ^fg-  of  their  volume  at 
0°,  the  amount  of  contraction  when  the  temperature  was  reduced 
to  — 273°  would  be  equal  to  the  initial  volume,  and  the  gases 
would  cease  to  exist.  Moreover,  since  a  gas  heated  from  0° 
to  273°  doubles  its  volume,  they  thought  it  evident  that  the 
quantity  of  heat  added  must  be  equal  to  that  contained  in  the 
primitive  volume. 

Even  if  matter  can  exist  without  heat,  which  there  is  great  rea- 
son to  doubt,  it  is  impossible  to  predict  what  would  be  its  condition 
under  such  circumstances.  It  is  supposed  by  some,  who  hold 
the  atomic  theory,  that  the  molecules  of  matter  would  be  brought 
into  absolute  contact,  and  that  phenomena  of  a  new  and  unex- 
pected nature  would  appear.  The  violent  explosion  experienced 
by  Chenot,  while  submitting  silver  in  powder  to  a  pressure  of 

*  Annales  de  Chiraie  et  de  Physique,  3"  Se'rie,  Tom.  XXI.,  XXIV.,  XXVII. 
t  Comptes  Rendus,  Tom.  VIL  p.  56. 


HEAT.  565 

three  hundred  atmospheres  in  an  hydraulic  press,  is  frequently 
cited  in  this  connection.  But  these  are  mere  assumptions, 
for  we  are  as  yet  far  from  having  realized  experimentally  an 
absolute  zero  of  heat.  The  lowest  temperature  ever  observed 
in  the  arctic  region  is  — 57°,  and  the  lowest  we  can  artificial- 
ly produce  is  — 140° ;  at  these  temperatures  several  liquids  still 
retain  their  fluid  condition,  which  could  hardly  be  the  case  if 
we  had  removed  the  greater  part  of  the  heat  which  they  con- 
tain. 

Change  of  State.  —  Liquids  to  Gases. 

(281.)  Boiling-Point.  —  It  has  been  shown,  that,  when  a  solid 
is  heated  to  such  a  temperature  that  the  expansive  force  of  heat 
between  its  particles  is  equal  to  the  cohesive  force,  it  melts.  If 
the  liquid  be  now  heated  above  its  melting-point,  the  expansive 
force  will  become  greater  than  the  cohesive  force,  and  by  con- 
tinuing to  raise  the  temperature  we  shall  finally  attain  to  a  point 
where  the  excess  of  expansive  force  is  equal  to  the  atmospheric 
pressure.  Then  we  have  the  condition  of  a  gas,  and  a  phe- 
nomenon presents  itself  which  we  term  boiling.  Bubbles  of  gas 
form  beneath  the  surface  of  the  fluid,  and  rise  tumultuously 
through  its  mass. 

This  phenomenon  can  best  be  studied  by  heating  water  in  a 
glass  flask  over  the  flame  of  a  spirit>lamp.  The  first  action  of  the 
heat  is  to  expand  the  portion  of  the  liquid  immediately  in  contact 
with  the  bottom  of  the  vessel,  which,  becoming  specifically  lighter, 
rises  and  gives  place  to  colder  water,  which  is  heated  and  rises  in 
its  turn  ;  and  thus  a  circulation  is  established  by  which  each  par- 
ticle of  liquid  is  brought,  in  its  turn,  in  contact  with  the  heated 
surface.  As  the  temperature  of  the  mass  rises,  the  air  which  is 
dissolved  in  the  water  separates  in  bubbles  on  the  inner  surface 
of  the  flask  (compare  page  396),  and  these,  when  they  have  at- 
tained sufficient  size,  disengage  themselves  and  escape  through 
the  liquid.  They  are  followed  by  bubbles  of  steam,  which  form 
on  the  heated  surface  of  the  flask,  where,  in  consequence  of  the 
close  proximity  of  the  source  of  heat,  the  temperature  is  higher 
than  that  of  the  mass  of  the  liquid  ;  but  as  the  bubbles  rise 
through  the  cooler  water  above,  they  are  condensed,  and  the 
shock  produced  by  the  sudden  collapse  gives  rise  to  a  peculiar 
48 


566 


CHEMICAL  PHYSICS. 


noise,  an  instance  of  which  appears  in  the  singing  of  a  tea-kettle. 
After  the  whole  mass  of  water  has  been  heated  to  100°,  the  bub- 
bles of  steam  are  no  longer  condensed,  but  rise  to  the  surface 
and  break,  allowing  the  steam  to  escape ;  and  as  the  tension  of 
this  steam  is  equal  to  the  pressure  of  the  air,  it  drives  out  the 
air  from  the  upper  part  of  the  flask,  and  takes  its  place. 

What  is  so  familiar  in  the  case  of  water,  is  equally  true  of 
other  liquids.  There  is  for  each  a  temperature  at  which  the 
expansive  force  of  heat  becomes  equal  to  the  pressure  of  the 
air,  and  at  which  this  phenomenon  of  boiling  invariably  appears. 
This  temperature,  which  is  constant  for  the  same  substance  under 
the  same  atmospheric  pressure,  is  called  the  boiling-point.  As 
the  boiling-point  varies  with  the  atmospheric  pressure,  it  is  neces- 
sary, in  describing  the  boiling-point  of  a  substance,  to  state  the 
pressure  under  which  it  was  observed.  In  the  following  table, 
the  boiling-points  of  some  of  the  best-known  liquids  are  given  for 
the  mean  pressure  of  76  c.  m. :  — 


Soiling-Points  under  the  Pressure  of  76  c.m. 


v 

Protoxide  of  Nitrogen,  .  — 105 
Carbonic  Acid,  .  .  — 78 

Cyanogen,  .  .  .  — 22 
Sulphurous  Acid, .  .  — 10 

Chloride  of  Ethyle,  .  .  +11 
Common  Ether,  ...  35 
Sulphide  of  Carbon,  .  47 

Bromine,  ....  63 
Chloroform,  ...  63 


Alcohol,       .         .         .  .78 

Water,     ....  100 

Nitric  Acid  (1.42),       .  .     120 

Oil  of  Turpentine,    .  .         157 

Phosphorus,          .         .  .290 

Sulphuric  Acid  (1.843),  .         325 

Mercury,      .         .         .  .     350 

Sulphur,            .         ,  .         440 


The  influence  of  pressure  upon  the  boiling-point  of  liquids  may 
be  illustrated  by  a  great  variety  of  experiments.  If  we  place  a 
glass  of  lukewarm  water  under  the  receiver  of  an  air-pump  and 
exhaust  the  air,  the  water  will  at  once  begin  to  boil  violently. 
The  same  experiment  may  be  tried  even  more  simply  in  the  fol- 
lowing way. 

Take  a  glass  flask,  to  which  a  cork  has  been  carefully  fitted, 
fill  it  about  one  half  full  of  water,  and  heat  the  water  to  boiling 
by  means  of  a  spirit-lamp.  When  the  water  is  boiling  rapidly, 
and  the  upper  part  of  the  flask  is  filled  with  steam,  remove  the 
lamp  and  quickly  insert  the  cork.  If  now  the  flask  is  inverted 


HEAT. 


567 


and  cold  water  poured  upon  it,  as  represented  in  Fig.  403,  the 
boiling  will  be  renewed,  and  continue  for  some  time. 

This  apparent  paradox  of  boiling  water  by  cold  is  thus  ex- 
plained.     The   cold  water  condenses   the   steam,  producing   a 
vacuum  in  the  upper  part  of  the  flask,  and,  the  pressure  of  the 
atmosphere  being  thus  removed,  the  water 
continues  to  boil  at  a  greatly  diminished 
temperature.     In  the  experiment  of  Leslie, 
hereafter  to  be  described,  water  is  made  to 
boil  at  its  freezing-point.     Common  ether 
boils   under  the   receiver  of  an   air-pump, 
from  which  the  air  lias  been  partially  ex- 
hausted, with  explosive  violence,  even  at 
the    lowest    natural    temperatures.     Such 
experiments   as  these   may   be   multiplied 
indefinitely. 

The  ordinary  variations  of  atmospheric 
pressure  exert  a  very  sensible  influence  on 
the  boiling-point  of  water.  The  extreme 
heights  of  the  barometer  observed  at  Paris 
for  the  last  thirty  years  have  been  71.9c.m. 
and  78.1  c.  m.  Under  the  first  pressure, 
water  boils  at  98°. 5,  under  the  second,  at  100°. 8  ;  so  that  the 
boiling-point  is  liable  to  a  variation  of  about  two  degrees  at  that 
place.  Hence  the  importance  of  regarding  the  height  of  the 
barometer  in  determining  the  boiling-point  on  the  scale  of  the 
thermometer  (218).  Much  greater  variations  in  the  boiling- 
point  than  these  arise  from  differences  of  pressure  at  different 
elevations  on  the  earth's  surface.  At  the  city  of  Quito,  which  is 
at  an  elevation  of  2,908  metres  above  the  level  of  the  sea,  and 
where  the  mean  barometric  pressure  is  equal  to  52.7  c.  m.,  water 
boils  at  90°.l.  At  the  city  of  Mexico,  at  an  elevation  of  2,277 
metres  and  under  a  pressure  of  57.2  c.  m.,  it  boils  at  92°. 3. 
Boiling  water  is  not,  therefore,  equally  hot  at  all  places  of  the 
earth.  At  high  elevations,  as  at  Quito,  for  example,  its  tempera- 
ture is  much  too  low  for  cooking  many  substances  'which  can  be 
cooked  at  one  hundred  degrees. 

It  follows  from  the  facts  already  stated,  that  a  difference  of 
pressure  of  0.25  c.  m.  will  cause  a  difference  in  the  boiling-point 
of  water  of  one  tenth  of  a  degree  ;  so  that  from  the  boiling-point 


Fig.  403. 


568 


CHEMICAL  PHYSICS. 


of  water,  determined  with  accuracy,  we  can  ascertain  the  pres- 
sure of  the  atmosphere  at  the  time.  An  instrument  has  been 
constructed  for  this  purpose,  consisting  essentially  of  a  very  deli- 
cate thermometer,  made  with  an  enlargement  in  the 
centre  of  the  stem,  as  represented  in  Fig.  348.  Its 
scale  is  limited  to  five  or  six  degrees  around  the 
freezing-point  and  eight  or  ten  degrees  around  the 
boiling-point,  and  each  degree  is  subdivided  into 
one  hundred  parts.  This  instrument  is  much  more 
portable  than  a  barometer,  but  on  account  of  the 
shifting  of  the  zero  point,  to  which  even  the  most 
carefully  constructed  thermometers  are  liable,  it  is 
much  inferior  to  it  in  accuracy.  A  metallic  vessel 
and  a  lamp  for  boiling  the  water  accompany  the  in- 
strument (Fig.  404). 

(282.)  Variations  of  the  Boiling-Point.  —  The 
boiling-point  of  liquids  is  influenced  by  other  cir- 
cumstances, whose  action  is  not  so  readily  explained 
as  that  of  the  atmospheric  pressure.  Thus  a  sub- 
stance dissolved  in  a  fluid  more  volatile  than  itself 
increases  the  boiling-point  in  proportion  to  the 
amount  dissolved.  Water,  for  example,  which  boils 
at  100°  when  pure,  boils  only  at  a  considerably 
higher  temperature  when  it  contains  salt  in  solution,  viz. :  — 


i\ 


Fig.  404. 


"Water  saturated  with  Common  Salt, 

"  «  "     Nitrate  of  Potash,     . 

"  "  "     Carbonate  of  Potash, 

"  «     Nitrate  of  Lime, 

"  «  «     Chloride  of  Calcium, 


Boiling- Point. 

.     109° 

116 
.     135 

151 

179 


Substances,  however,  held  simply  in  suspension,  like  shavings  of 
wood  or  earthy  particles,  do  not  alter  the  boiling-point. 

Again,  Gay-Lussac  observed  that  water  boiled  in  a  glass  vessel 
at  a  higher  temperature  than  in  a  metallic  vessel ;  and,  more  re- 
cently, Marcet  has  established,  first,  that  water  boils  in  a  glass 
vessel  coated  with  sulphur  or  gum-lac  at  a  temperature  a  little 
less  than  in  a  metallic  vessel ;  secondly,  that  in  a  glass  vessel  the 
boiling-point  of  water  is  1°  or  1°.25  higher  than  in  a  metallic 
vessel  ;  thirdly,  that  after  sulphuric  acid  has  been  boiled  in  a 


HEAT.  569 

glass  flask,  the  boiling-point  is  increased  to  a  much  greater  extent 
than  before,  this  increase  sometimes  amounting  to  five  or  six 
degrees.  By  throwing  into  the  water,  in  either  of  these  cases, 
pieces  of  metal,  the  boiling-point  is  at  once  reduced  to  100°. 
The  same  variation  of  the  boiling-point  in  glass  vessels  takes 
place  with  other  liquids  as  well  as  water,  and  with  some  of  them 
to  a  much  greater  extent.  It  is  only  in  metallic  vessels  that  the 
boiling-point  is  regular. 

It  follows  from  what  has  been  said,  that  in  any  case  the  expan- 
sive force  of  the  vapor  formed  during  boiling  is  equal  to  the 
pressure  to  which  the  liquid  is  exposed,  and  it  is  also  true,  that 
the  temperature  of  the  vapor  is  the  same  as  that  of  the  boiling 
liquid.  Two  thermometers,  the  bulb  of  one  dipping  under  the 
surface  of  a  boiling  liquid,  and  the  other  immersed  in  the  vapor 
just  above  it,  will,  therefore,  always  indicate  the  same  temper- 
ature, unless  the  boiling-point  has  been  unnaturally  increased  by 
one  of  the  causes  just  mentioned. 

(283.)  Determination  of  the  Boiling-Point.  —  The  causes 
mentioned  in  the  last  section,  which  influence  the  temperature 
of  the  boiling  liquid,  do  not  affect  at  all,  or  affect  very  slightly, 
the  temperature  of  the  vapor  which  rises  from  it.  This  at  once 
adjusts  itself  to  the  pressure  of  the  atmosphere,  and  is  always 
constant  for  the  same  liquid  under  the  same  pressure.  Hence 
the  temperature  of  the  vapor  is  more 
fixed  than  that  of  the  liquid,  and  it  is 
for  this  reason  that,  in  graduating  a 
mercury-thermometer,  the  tube  is  ex- 
posed to  the  steam  from  boiling  water, 
and  not  dipped  into  the  liquid  itself. 
So  also,  in  determining  the  boiling-point 
of  other  liquids,  it  is  always  best  to 
measure  the  temperature  of  the  vapor, 
and  not  that  of  the  liquid,  taking  care 
that  the  pressure  of  the  atmosphere  is 
transmitted  freely  to  its  surface  while 
boiling.  The  arrangement  represented 
in  Fig.  405  is  very  well  suited  to  this 
purpose,  the  size  of  the  glass  boiler 
being  adapted  to  the  circumstances  of 
the  case.  When  the  liquid  under  experiment  is  very  costly,  all 
48* 


570  CHEMICAL  PHYSICS. 

loss  can  be  avoided  by  connecting  the  exit-tube  with  a  Liebig's 
condenser  (see  Fig.  416). 

(284.)  Formation  of  Vapor  of  Low  or  High  Tension.  —  The 
vapors  or  gases  which  are  formed  during  the  boiling  of  liquids 
have  always  the  same  tension  as  the  atmospheric  air,  and  are 
therefore  able  to  retain  their  gaseous  condition  when  exposed  to 
its  pressure.  It  is  the  formation  of  vapors  of  this  kind  that  we 
have  considered  in  the  preceding  sections.  Liquids,  however, 
yield  vapors  both  of  a  lower  and  of  a  higher  tension  than  that  of 
the  atmosphere,  and  we  propose  next  to  consider  the  conditions 
and  laws  under  which  these  are  formed. 

In  order  to  make  the  conditions  as  simple  as  possible,  let  us 
suppose  a  vessel  having  the  capacity  of  one  cubic  metre,  and  let 
us  dispose  in  it  a  barometer  and  thermometer,  so  that  we  can 
observe  the  tension  and  temperature  of  the  confined  gas.  More- 
over, let  us  pour  into  it  a  few  kilogrammes  of  water  and  perfectly 
exhaust  the  air.  If  now  we  expose  this  vessel  to  various  tem- 
peratures, it  will  be  found,  first,  that  for  every  giveli  temperature 
a  certain  fixed  weight  of  water  will  evaporate,  and,  secondly,  that 
the  vapor  thus  formed  will  have  a  certain  definite  tension  which 
is  invariable  for  that  temperature.  If  we  increase  the  tempera- 
ture, the  weight  of  the  vapor  formed  will  be  greater,  and  the 
tension  greater.  If  we  diminish  it,  the  weight  will  be  less  and 
the  tension  less,  provided  always  that  some  liquid  water  remains 
in  the  vessel.  The  table  on  the  opposite  page  gives  for  each 
temperature,  first,  the  weight  of  vapor  in  grammes  which  the 
cubic  metre  will  contain,  and,  secondly,  the  tension  of  the  vapor. 

By  inspecting  this  table,  several  remarkable  facts  will  be  dis- 
covered. It  will  be  seen,  in  the  first  place,  that  a  very  sensible 
amount  of  water  will  evaporate  even  at  a  temperature  of  ten 
degrees  below  the  freezing-point,  when,  of  course,  the  water  in 
the  vessel  is  in  the  state  of  ice.  In  the  second  place,  it  will  be 
noticed  that  the  tension  of  the  vapor  is  less  than  the  pressure 
of  the  atmosphere  for  all  temperatures  under  100°,  and  greater 
than  the  pressure  of  the  atmosphere  for  all  temperatures  above 
100°  ;  so  that  for  all  temperatures  under  100°  the  pressure  ex- 
erted by  the  vapor  on  the  inner  surface  of  the  vessel  is  less  than 
the  atmospheric  pressure  on  the  outside,  while  for  all  tempera- 
tures over  100°  it  is  greater.  In  the  third  place,  it  will  be 
noticed  that  at  100°  the  tension  is  exactly  equal  to  76  c.  m.,  the 


HEAT. 


571 


Tension  of  the  Vapor  of  Water,  according  to  Regnault. 


Tempera- 
ture. 

Tension  in 
Centimetres. 

Weight  of 
1  Cubic  Metre. 

Tempera- 
ture. 

Tension  in 
Centimetres. 

Weight  of 
1  Cubic  Metre. 

0 

—10 

0.2078 

2.284 

-+-33 

3.7410 

35.336 

9 

02261 

2.476 

34 

3.9565 

37.249 

8 

0.2456 

2.679 

35 

4.1827 

39.252 

7 

0.2666 

2.897 

40 

5.4906 

50.700 

6 

0.2890 

3.129 

45 

7.1391 

64.884 

5 

0.3131 

3.377 

50 

9.1982 

82.302 

4 

0.3387 

3.640 

55 

11.7478 

103.51 

3 

0.3662 

3.920 

60 

14.8791 

129.13 

2 

0.3955 

4.219 

65 

18.6945 

159.84 

—1 

0.4267 

4.535 

70 

23.3093 

196.38 

0 

0.4600 

4.871 

75 

28.8517 

239.59 

-f-1 

0.4940 

5.212 

80 

35.4643 

290.31 

2 

0.5302 

5.574 

85 

43.3041 

349.53 

3 

0.5687 

5.957 

90 

52.5450 

418.27 

4 

0.6097 

6.363 

95 

63.3778 

497.64 

5 

0.6534 

6.795 

100 

76.  =  1  At. 

588.73 

6 

0.6998 

7.251 

120.6 

2  Atmosph. 

1115.8 

7 

0.7492 

7.735 

133.9 

3       « 

1618.9 

8 

0.8017 

8.247 

144.0 

4       « 

2106.1 

9 

0.8574 

8.789 

152.2 

5       « 

2581.9 

10 

0.9165 

9.362 

159.2 

6       « 

3048.0 

11 

0.9792 

9.967 

165.3 

7       « 

3506.5 

12 

.0457 

10.606 

170.8 

8       « 

3957.7 

13 

.1062 

11.181 

175.8 

9       « 

4402.6 

14 

.1906 

11.992 

180.3 

10       « 

4843.3 

15 

.2699 

12.746 

184.5 

11       « 

5278.6 

16 

.3536 

13.539 

188.4 

12       « 

5709.8 

17 

.4421 

14.375 

192.1 

13       « 

6136.4 

18 

.5357 

15.255 

195.5 

14       « 

6560.4 

19 

.6346 

16.182 

198.8 

15       « 

6979.6 

20 

.7391 

17.157 

201.9 

16       " 

7396.4 

21 

.8495 

18.184 

204.9 

17       " 

7809.3 

22 

.9659 

19.263 

207.7 

18       « 

8220.3 

23 

2.0888 

20.398 

210.4 

19             4t 

86286 

24 

2.2184 

21.590 

213.0 

20       « 

9034.0 

25 

2.3550 

22.843 

215.5 

21       « 

9437.4 

26 

2.4988 

24.156 

217.9 

22       « 

9838.1 

27 

2.6505 

25.538 

220.3 

23       « 

10235.5 

28 

2.8101 

26.985 

222.5 

24       « 

10632.9 

29 

2.9782 

28.504 

224.7 

25       « 

11026.6 

30 

3.1548 

30.095 

226.8 

26       « 

11419.6 

31 

3.3405 

31.762 

228.9 

27       « 

11809.2 

32 

3.5359 

33.509 

230.9 

28       ts 

12198.3 

572  CHEMICAL  PHYSICS. 

pressure  of  the  atmosphere.  This  is  the  boiling-point  of  water, 
the  temperature  at  which  bubbles  of  steam  can  form  beneath  the 
surface  and  rise  to  the  top  without  being  condensed.  Lastly,  it 
will  be  noticed  that  above  100°  the  tension  of  the  vapor  increases 
very  rapidly  with  the  temperature  ;  so  that  at  121°. 4  it  is  equal 
to  2  atmospheres,  or  twice  the  pressure  of  the  atmosphere,  and  at 
201°. 9  to  16  atmospheres.  Steam  of  greater  tension  than  the 
atmospheric  pressure  is  called  high-pressure  steam,  and  it  is  this 
condition  of  steam  which  is  found  above  the  water  in  a  steam- 
boiler,  and  which  is  used  with  so  much  effect  in  the  steam- 
engine. 

(285.)  Daltotfs  Apparatus. — The  experiment  described  above, 
for  determining  the  tension  and  weight  of  a  cubic  metre  of  the 
vapor  of  water  at  different  temperatures,  was  merely  devised  for 
simplicity  of  illustration.  In  order  to  obtain  even"  approximate 
results,  it  is  necessary  to  experiment  in  a  different  manner  and 
on  a  very  much  smaller  scale.  The  tension  of  the  vapor  of  water 
between  0°  and  100°  can  be  measured  quite  accurately  by  means 
of  a  common  barometer-tube.  If  the  tube  is  filled  with  mercury 
and  inverted,  as  described  in  (157),  the  column  of  mercury  will 
stand  in  the  tube  at  the  height  of  76  c.  m.,  more  or  less,  above 
the  mercury  in  the  basin,  according  to  the  varying  pressure  of 
the  air.  Suppose,  now,  that  we  fill  the  tube  again  with  mercury, 
only  adding  at  the  top  a  few  drops  of  water,  and  invert  it  as 
before.  The  water  will  of  course  rise  to  the  surface  of  the  mer- 
cury, and  a  portion  of  it,  varying  with  the  temperature,  will 
evaporate  into  the  vacuum  above.  This  vapor  will  exert  a  certain 
pressure,  and  depress  the  mercury-column  ;  the  amount  of  the  de- 
pression will  be  equal  to  the  difference  between  the  present  height 
of  the  column  and  that  of  the  barometer  at  the  beginning  of  the 
experiment.  Moreover,  it  will  be  exactly  the  same  as  the  height 
to  which  the  vapor  would  raise  the  mercury  of  a  barometer,  if  im- 
mersed in  it,  and  will  therefore  be  the  measure  of  the  tension. 

The  apparatus  used  by  Dalton  in  his  determinations  of  the 
tension  of  the  vapor  of  water,  and  based  on  the  principles  just 
explained,  is  represented  in  Fig.  406.  It  consists  of  two  barom- 
eter-tubes dipping  into  the  same  basin  of  mercury.  The  first  of 
these  tubes,  7?,  is  a  perfect  barometer.  The  second,  J.,  is  a  ba- 
rometer with  a  small  amount  of  water  above  the  mercury-column. 
These  two  tubes  are  enclosed  hi  a  tall  glass  cylinder,  standing  in 


HEAT. 


573 


the  basin  of  mercury  and  filled  with  water,  whose  temperature 
can  be  regulated  by  means  of  the  furnace  below.  This  tempera- 
ture, observed  by  means  of  the  ther- 
mometer T  conveniently  disposed,  is 
of  course  the  common  temperature  of 
the  two  barometers  and  of  the  vapor  at 
the  top  of  the  second.  In  order,  then, 
to  determine  the  elastic  force  of  this 
vapor,  it  is  only  necessary  to  meas- 
ure the  difference  of  height  of  the 
two  columns,  since  this  height  re- 
duced to  0°  is  the  measure  of  its 
tension. 

The  apparatus  of  Dalton  can  be 
used  so  long  as  the  elastic  force  of 
the  vapor  does  not  exceed  the  pres- 
sure of  the  atmosphere.  When  the 
tension  is  equal  to  76  c.  m.,  the  sur- 
face of  the  mercury-column  will  be 
depressed  to  the  level  of  the  mercury 
in  the  basin,  and  the  experiment  is 
at  an  end.  In  order  to  continue  the 
determination  above  this  point,  we 
can  use  a  siphon- 
tube,  inverted  and 

closed  at  the  shorter  end,  as  represented  in  Fig. 
407.  The  tube  is  filled  with  mercury,  with 
the  exception  of  a  small  amount  of  water 
above  the  mercury  in  the  shorter  branch,  and 
heated  in  an  oil-bath.  The  tension  of  the 
vapor  is  evidently  equal,  at  each  moment,  to 
the  pressure  of  the  atmosphere  increased  by 
the  weight  of  the  column  C  D. 

On  account  of  the  difficulty  of  preserving  a 
constant  and  uniform  temperature  throughout 
the  whole  height  of  the  cylinder  of  water,  the 
method  of  Dalton  is  not  calculated  to  give 
accurate  results,  although  in  a  modified  form 
it  was  used  by  Regnault  with  great  success  for 
rig.  407.  temperatures  between  0°  and  60°.  The  two 


Fig  406. 


574 


CHEMICAL  PHYSICS. 


forms  of  apparatus  just  described  may,  however,  be  used  for 
illustration  with  advantage  ;  only  in  this  case  it  is  as  well  to 
substitute  for  the  water  some  more  volatile  liquid. 

(286.)  Marcet's  Globe.  —  The  tension  of  the  vapor  of  water 
above  100°  may  be  roughly  estimated  by  means  of  the  apparatus 
represented  in  Fig.  408.  It  consists  of  a  stout 
brass  globe  containing  water,  and  serving  as  a 
boiler.  Through  a  tight  packing-box  passes 
a  glass  manometer-tube  of  about  a  metre  in 
length,  whose  lower  end  opens  under  mercury 
resting  on  the  bottom  of  the  brass  boiler.  The 
globe  has  also  two  other  openings ;  one  of  these 
may  be  closed  by  a  stopcock,  and  through  the 
other  passes  the  tube  of  a  thermometer,  having 
its  bulb  within  the  globe.  On  commencing  the 
experiment,  the  water  is  boiled  for  some  time 
in  order  to  expel  all  the  air,  and  the  stopcock  is 
then  closed.  At  this  moment  the  temperature 
of  the  steam  is  100°,  and  the  tension  76  c.  m. 
more  or  less,  according  to  the  pressure  of  the 
air.  As  soon,  however,  as  the  steam  is  pre- 
vented from  escaping  freely,  the  temperature 
of  the  globe  will  begin  to  rise,  and  at  the  same 
time  the  tension  of  the  confined  steam  will 
increase,  raising  the  mercury  in  the  manome- 
ter-tube. For  any  temperature  indicated  by 
the  thermometer,  the  corresponding  tension 
of  the  vapor  will  be  found  by  adding  to  the 
height  of  the  barometer  for  the  time  being  the  height  of  the 
mercury  in  the  tube,  measured  by  a  scale  provided  for  the  pur- 
pose. This  apparatus,  like  the  last,  is  only  calculated  for  illus- 
tration, and  yields  but  approximate  results. 

(287.)  Apparatus  of  Gay-Lussac.  —  For  measuring  the  ten- 
sion of  the  vapor  of  water  below  zero,  Gay-Lussac  employed  the 
apparatus  represented  in  Fig.  409.  It  consists,  like  the  appara- 
tus of  Dalton,  of  two  barometer-tubes  filled  with  mercury,  the 
open  ends  dipping  under  mercury  in  the  same  basin ;  one  of 
these,  A,  which  is  straight,  and  perfectly  freed  from  air  and  mois- 
ture by  boiling  the  mercury  in  the  tube,  serves  to  measure  the 
pressure  of  the  air ;  the  other  contains  a  few  drops  of  water  above 


Fig.  408. 


HEAT. 


575 


the  mercury-column,  and  its  closed  end  is  bent  so  that  it  can  be 
surrounded  by  a  freezing  mixture,  as  represented  in  the  figure. 
A  thermometer,  t,  indicates  the  temperature  of  the  vapor  above 
the  mercury-column,  and  the  tension  of 
this  vapor,  corresponding  to  each  temper- 
ature, is  readily  determined  by  measur- 
ing with  a  cathetometcr  the  difference  of 
level  of  the  mercury  in  the  two  tubes  A 
and  C.  It  will  be  noticed  at  once,  that 
only  a  portion  of  the  vapor  in  the  tube  C 
is  exposed  to  the  freezing  mixture  ;  but 
it  is  an  established  principle  of  hygrom- 
etry,  that,  when  the  temperatures  of  two 
vessels  communicating-  with  each  other 
are  unequal,  the  tension  of  the  vapor  is 
the  same  in  both,  and  is  always  that 
which  corresponds  to  the  lowest  temper- 
ature.  The  application  of  this  principle 
in  the  above  method  is  evident. 

(288.)  Apparatus  of  Regnault. — The 
accurate  determination  of  the  tension  of 
the  vapor  of  water  at  high  temperatures 
is  attended  with  great  difficulties  ;  but 
on  account  of  the  importance  of  the  sub- 
ject, arising  from  its  connection  with  the  Fig  409. 
steam-engine,  no  subject  has  been  the 

object  of  more  careful  scientific  investigation.  It  was  first  care- 
fully investigated,  in  1830,  by  a  commission  of  the  French  Acad- 
emy, consisting  of  Arago  and  Dulong  ;  and  more  recently  it  has 
been  reinvestigated  by  Regnault  with  his  usual  perseverance  and 
skill.  The  results  of  his  investigations  were  published  in  the 
twenty-first  volume  of  the  Memoires  de  /' Academic  des  Sciences, 
to  which  we  have  so  frequently  had  occasion  to  refer  in  these 
pages.  Indeed,  the  determinations  made  by  Regnault  of  the 
compressibility  of  gases  (165),  of  their  coefficients  of  expansion 
(261),  and  of  the  coefficients  of  expansion  of  mercury  and  glass 
(250  and  254),  were  merely  preliminaries  to  this  main  investi- 
gation. 

For  temperatures  below  60°,  Regnault  made  use  of  the  same 
method  as  Dal  ton,  but  modified  his  apparatus  so  as  to  avoid  the 


576 


CHEMICAL   PHYSICS. 


cause  of  error  mentioned  in  (285).  The  apparatus,  as  thus 
modified,  is  represented  in  Fig.  410.  The  open  ends  of  the  two 
barometer-tubes  t  and  f  dip  into  the  same  basin  of  mercury, 

which  is  furnished  with  an  adjusting- 
screw,  O,  similar  to  that  described  in 
(159).  The  upper  ends  of  these  tubes 
are  enclosed  within  a  cylindrical  vessel, 
F,  made  of  sheet-metal,  and  provided 
with  a  glass  front,  through  which  the 
height  of  the  mercury-columns  may 
be  observed.  The  tubes  pass  through 
tubulatures  in  the  bottom  of  the  vessel, 
and  are  secured  in  their  places  by 
india-rubber  connectors.  The  vessel 
V  is  filled  with  water,  and  its  tempera- 
ture is  readily  kept  constant  and  uni- 
form, at  any  point  below  60°,  by  means 
of  a  spirit-lamp  and  by  constant  agita- 
tion. 

In  one  series  of  experiments,  Reg- 
nault  employed  two  simple  barometer- 
tubes,  one  filled  with  perfectly  dry 
mercury,  and  the  other  containing,  in 

addition,  a  small  quantity  of  water  above  the  mercury-column. 
For  each  temperature  of  the  bath  as  indicated  by  the  thermom- 
eter, T,  he  determined  the  difference  of  level  of  the  mercury  in 
the  two  barometer-tubes.  This  height  reduced  to  0°  was  evi- 
dently the  measure  of  the  tension  of  the  vapor. 

In  another  series  of  experiments,  he  connected  with  the  upper 
end  of  the  barometer-tube  t,  by  means  of  a  copper  connector,  a 
glass  globe,  B,  having  a  capacity  of  about  500  c.  m.3.  A  branch 
of  this  connector,  e  i,  served  also  to  connect  the  globe  with 
an  air-pump,  through  a  U  tube,  n,  filled  with  pieces  of  pumice- 
stone  moistened  with  sulphuric  acid ;  but  before  finally  adjusting 
the  apparatus,  a  small  glass  bulb,  completely  filled  with  water 
and  hermetically  sealed,  was  introduced  into  the  glass  globe. 
After  the  adjustments  were  completed,  the  interior  of  the  globe 
was  first  perfectly  dried  by  exhausting  the  air,  and  allowing  it  to 
re-enter  a  great  number  of  times  through  the  tubes  e,  t,  n.  It 
was  then  exhausted  for  the  last  time  as  perfectly  as  possible,  and 


Fig.  410. 


HEAT.  5  <  < 

the  tube  i  hermetically  sealed  by  the  flame  of  a  blowpipe.  The 
globe  was  next  surrounded  by  melting  ice,  and  the  tension  of  the 
small  amount  of  air  left  in  it  carefully  determined  by  measuring 
with  a  cathetometer  the  difference  of  level  of  the  mercury  in  the 
two  barometers.  The  ice  having  been  removed,  some  pieces  of 
burning  charcoal  were  now  brought  near  the  bottom  of  the  globe, 
so  as  to  break  the  glass  biilb  within  and  liberate  the  water,  which 
at  once  evaporated,  and  filled  the  globe  and  the  upper  part  of  the 
barometer-tube  t  with  vapor.  It  only  remained  then  to  fill  the 
vessel  F  with  water,  and  to  heat  the  bath  to  different  tempera- 
tures, when  the  depression  of  the  column  of  mercury,  measured 
in  the  usual  way,  gave  the  tension  of  the  vapor  corresponding  to 
each  temperature. 

It  has  been  already  stated,  that  the  use  of  the  apparatus  just 
described  is  limited  to  temperatures  below  60°.  In  order  to  de- 
termine the  tension  of  the  vapor  of  water  at  higher  temperatures, 
Regnault  resorted  to  an  entirely  different  method.  We  have 
before  seen  (282)  that  the  temperature  of  the  vapor  rising  from 
a  boiling  liquid  is  the  same  as  that  of  the  liquid,  and  that  its 
tension  is  always  equal  to  the  pressure  to  which  the  liquid  is 
exposed.  By  boiling  water,  then,  under  different  pressures,  and 
determining  the  temperature  at  which  it  boils,  we  shall  have  at 
once  the  tension  of  the  vapor  corresponding  to  each  tempera- 
ture. The  apparatus  represented  in  Fig.  411  was  used  by 
Regnault  for  this  purpose.  It  consists  of  a  copper  boiler,  (7, 
connected  by  the  tube  A  B  with  a  large  globe,  My  and  further 
connected  by  the  flexible  hose  H  H'  with  an  air-pump,  by  which 
the  pressure  on  the  surface  of  the  water  in  the  boiler  may  be 
varied  at  pleasure.  This  steam,  as  it  rises  from  the  boiler,  is 
condensed  in  the  tube  A  B,  which  is  kept  surrounded  by  cold 
water  for  the  purpose,  and  the  temperature  of  the  globe  M  is 
also  retained  at  a  constant  point  in  a  similar  way.  The  pressure 
under  which  the  water  boils  is  accurately  measured  by  the  ma- 
nometer O,  and  the  temperature  at  which  it  boils,  when  under 
this  pressure,  is  determined  with  equal  accuracy  by  means  of 
four  thermometers,  whose  indications  serve  to  correct  each  other. 
They  are  inserted  into  iron  tubes  closed  at  the  bottom  and  filled 
with  mercury,  which  pass  hermetically  through  the  top  of  the 
boiler  and  descend  to  different  depths  in  the  steam  and  water  it 
contains. 

49 


578 


CHEMICAL  PHYSICS. 


The  method  of  using  the  apparatus  will  be  made  clear  by  an 
example.  Let  us  suppose,  then,  that  we  wish  to  measure  the 
tension  of  the  vapor  of  water  at  temperatures  between  150°  and 
100°.  We  should,  in  the  first  place,  connect  the  hose  HH1  with 
a  condensing-pump,  and  force  air  into  the  globe  and  boiler  until 


Fig.  411. 

the  manometer  indicated  a  pressure  in  the  interior  of  about  four 
atmospheres.  We  should  then,  by  means  of  a  charcoal-furnace, 
boil  the  water  in  the  vessel  (7,  taking  care  so  to  regulate  the  heat 
that  the  steam  will  condense  in  the  tube  A  B  as  fast  as  it  forms 
in  the  boiler.  When  this  is  the  case,  the  height  of  the  ma- 
nometer will  remain  constant  during  the  whole  course  of  the 
experiment,  provided,  of  course,  that  the  pressure  of  the  atmos- 
phere does  not  vary.  The  tension  of  the  steam  forming  in  the 
boiler  can  now  easily  be  determined,  for  it  must  evidently  be 
equal  to  the  height  of  the  barometer  added  to  the  difference  of 
level  of  the  two  mercury-columns  of  the  manometer.  The  tem- 
perature of  the  steam  corresponding  to  this  tension  is  then  ascer- 
tained, by  merely  inspecting  the  thermometers  connected  with 
the  copper  boiler.  Let  us  suppose  that  the  difference  of  level  of 


HEAT.  570 

the  mercury-column  of  the  manometer  when  reduced  to  0°  is 
found  to  be  254.524  c.  m.,  and  that  the  height  of  the  barometer 
at  the  time,  also  reduced  to  0°,  is  76.209  c.  m.  The  tension  of 
the  steam  is  then  equal  to  830.733  c.  m.  On  inspecting  the  four 
thermometers,  they  were  found  to  indicate  respectively  147°.50, 
147°.49,  147°.54,  and  147°.35,  the  mean  of  the  four  being  equal 
to  147°. 48,  which  we  take  as  the  true  temperature.  Hence  it 
follows  that  at  147°. 48  the  tension  of  the  vapor  of  water  is  equal 
to  330.733  c.  m. 

Having  determined,  as  just  described,  the  tension  of  the  vapor 
of  water  at  one  temperature,  we  should  next  diminish  the  pres- 
sure on  the  surface  of  the  water  in  the  boiler,  by  allowing  a 
portion  of  the  air  to  escape  from  the  globe.  The  boiling-point 
of  the  water  would  at  once  fall,  and  we  should  then  measure  the 
tension  and  temperature  corresponding  to  the  new  conditions; 
and  by  repeating  this  process  several  times,  we  should  be  enabled 
to  fix  the  tension  and  corresponding  temperature  at  several  points 
between  150°  and  100°. 

The  apparatus  just  described  was  constructed  by  Regnault 
chiefly  to  test  the  method  on  which  it  is  based,  and  to  discover 
the  causes  of  error  to  which  the  method  is  liable.  The  appa- 
ratus actually  used  in  the  determination  of  the  tension  of  the 
vapor  of  water  at  temperatures  above  100°,  although  on  precisely 
the  same  principle,  was  constructed  on  a  very  much  greater  scale, 
and  capable  of  sustaining  a  very  great  pressure.  The  copper  boiler 
had  a  capacity  of  about  70  litres,  and  its  walls,  5  millimetres 
thick,  were  strengthened  by  bands  of  iron.  The  glass  globe  M  of 
Fig.  411  was  replaced  by  a  very  strong  copper  chamber,  having  a 
capacity  of  280  litres,  and  this  was  connected  with  the  boiler  by 
a  tube  arranged  exactly  as  in  the  smaller  apparatus.  The  upper 
part  of  the  chamber  was  also  connected,  on  the  one  side  with  a 
pump  for  condensing  air,  and  on  the  other  with  a  manometer. 
This  manometer  was  the  same  as  that  used  by  Regnault  in  his 
experiments  on  the  compressibility  of  gases,  to  which  we  have 
already  referred  in  connection  with  that  subject  (page  296). 
We  have  not  space,  however,  to  enter  into  a  detailed  descrip- 
tion of  the  apparatus.  This  will  be  found  in  Regnault's  original 
memoir.  Suffice  it  to  say,  that  every  precaution  was  taken  to 
secure  accuracy  which  physical  science  could  suggest,  both  in 
the  apparatus  and  in  the  method  of  experimenting.  Regnault 


580 


CHEMICAL  PHYSICS. 


was  able  to  experiment  with  this  apparatus  up  to  a  pressure  of 
twenty-eight  atmospheres.  Unfortunately,  at  thirty  atmospheres 
one  of  the  bolts  which  fastened  the  iron  bands  broke,  in  con- 
sequence of  the  distention  of  the  boiler,  and  it  was  thought 
imprudent  to  continue  the  experiments. 

(289.)  Discussion  of  the  Results.  —  By  the  methods  described 
in  the  last  section,  Regnault  determined  the  tension  of  the  vapor 
of  water  at  different  temperatures  between  — 32°  and  230°.  The 
intervals  of  temperature  between  the  numerous  determinations 
were  necessarily  very  irregular,  the  precise  temperature  in  each 
case  depending  on  accidental  circumstances.  This  is  shown  by 
the  following  table,  which  gives  the  results  of  a  few  only  of  the 
observations  made  by  Regnault :  — 


Temp.       Tension. 

—  32°.84       0.028 
—12.53       0.161 
0.00       0.454 
-f-20.51       1.781 

Temp.      Tension. 
*42°.61         6.322 
58  62       13.905 
*76.49       30.671 
*99.92       75.790 

Temp.        Tension. 
*1  25^71       177.895 
153.90       394.486 
*1  67.40       555.483 
185.67       857.242 

Temp.         Tension. 
*194°42       1034.427 
212.20       1486.818 
221.33       1779.011 
230.50       2112.700 

From  these  results,  however,  we  can  easily  determine  the  tension 
corresponding  to  any  other  temperature  between  the  limits  of 
observation  by  either  one  of  two  methods. 

The  first  method  is  to  make  a  geometrical  construction  of  the 
results  of  the  experiments  similar  to  that  which  is  given  in  Fig. 
412.  In  this  figure,  the  abscissas  of  the  curve  abed  are  the 
degrees  of  temperature  ;  the  ordinates  are  the  corresponding 
tensions  in  atmospheres.  The  curve  is  constructed  through  the 
points  indicated  on  the  figure  by  dots,  and  these  were  fixed  by 
the  observations  marked  with  a  star  in  the  above  table.  By 
means  of  this  curve  we  can  evidently  ascertain  at  once  the  ten- 
sion at  any  intermediate  temperature,  and  prepare  a  table  similar 
to  that  on  page  571.  The  scale  of  Fig.  412  is,  however,  alto- 
gether too  small  to  furnish  even  approximate  results  ;  but  on 
the  plate  accompanying  Regnault' s  memoir  the  same  curve  will 
be  found  drawn  on  a  scale  which  is  suitable  for  the  purpose. 
The  curve,  even  as  drawn  in  our  figure,  will,  however,  convey 
to  the  mind  a  far  better  conception  of  the  rapidity  with  which 
the  tension  of  the  vapor  of  water  increases  with  the  temperature, 
than  could  be  given  by  a  column  of  numbers. 

The  second  method  of  determining  the  tension  at  temperatures 


HEAT.  581 

intermediate  between  those  at  which  it  has  been  actually  observed, 
consists  in  using  empirical  formulae  similar  in  principle  to  those 
which  we  have  previously  em- 
ployed to  express  the  solubility 
of  salts  in  water,  or  the  rate  of 
expansion  of  liquids  at  different 
temperatures.  At  least  thirty 
such  formulae  have  been  proposed 
at  different  times  for  the  purpose, 
which  agree,  with  more  or  less 
accuracy,  with  different  sets  of  ob- 
servations. The  determinations 
of  Regnault  agree  very  nearly 
with  the  following  exponential 
formula  proposed  by  Biot :  — 


A          £?  s*x          t~i  (3x 
=  A—tiCL   -  -C//P, 

in  which 

The  five  constants  of  this  for- 
mula were  calculated  by  Reg- 
n  a  u  1 1 
from  5 
observ- 
ed val- 
ues of  t 
and  $, 
taken 
at  in- 
terval s 

of  sixty  Fig.  412. 

degrees 
between  —20°  and  220°,  and  were  found  to  be 

A  =  6.2640348 
log  B  =  0.1397743 
log  O  =  0.6924351 
log  «  =  9.9940493 
log  /?  =  9.9983438 

By  means  of  this  formula  we  can  calculate  the  tension  of  the 


582  CHEMICAL  PHYSICS. 

vapor  of  water  at  any  temperature  within  the  limits  of  the  obser- 
vations, with  as  great  accuracy  as  that  of  the  experimental  data 
on  which  the  formula  is  based ;  but,  like  other  empirical  formulae, 
it  cannot  be  relied  upon  if  the  temperature  much  exceeds  these 
limits  on  either  side.  In  calculating  the  table  on  page  571, 
Regnault  used  the  formula  and  constants  just  given  for  all  tem- 
peratures between  100°  and  230°,  but  for  lower  temperatures  he 
found  it  best  to  use  two  similar  formulae  with  different  constants. 

(290.)  Formation  of  Vapors  of  different  Liquids.  —  The  laws 
of  the  formation  of  the  vapor  of  water,  which  have  been  enun- 
ciated in  the  last  few  sections,  also  hold  true  for  the  vapors  of 
other  liquids.  If  instead  of  water  we  should  introduce  into 
the  vessel  of  one  cubic  metre  capacity  assumed  in  (284)  a  small 
amount  of  alcohol,  ether,  sulphide  of  carbon,  or  any  other 
liquid,  it  would  be  found  that  for  any  given  temperature  a  cer- 
tain fixed  weight  of  each  of  these  liquids  would  evaporate,  and 
that  the  vapor  formed  would  have  a  certain  fixed  tension.  If  the 
temperature  were  increased,  more  liquid  would  evaporate  into 
the  cubic  metre,  and  the  atmosphere  of  vapor  formed  would  have 
a  greater  tension  ;  and  if  the  temperature  were  diminished,  both 
the  weight  of  the  cubic  metre  of  vapor  and  its  tension  would  be 
less.  Furthermore,  the  tension  of  the  vapor  at  different  temper- 
atures could  be  determined  by  the  same  methods  used  in  the  case 
of  water,  and  we  could  make  for  each  liquid  a  table  similar  to 
that  on  page  571.  Regnault*  has  furnished  us  with  such  a  table 
for  five  of  the  most  familiar  liquids.  This  table,  which  gives, 
however,  only  the  tensions  of  the  vapors,  will  be  found  on  the 
opposite  page.  The  weight  of  one  cubic  metre  of  each  vapor 
can  readily  be  calculated  for  each  temperature  by  means  of  the 
formulae  which  will  be  developed  in  the  next  chapter. 

It  has  already  been  stated  (282),  that  at  the  boiling-point  the 
tension  of  the  vapor  of  any  liquid  is  exactly  equal  to  the  pressure 
of  the  atmosphere,  and  Dalton  supposed  that  at  temperatures 
equally  distant  from  their  respective  boiling-points  the  vapors  of 
all  liquids  were  approximatively  equal  in  tension.  If  this  principle 
(which  is  usually  known  under  the  name  of  Dalton's  law)  were 
true,  we  could  easily  calculate  from  the  tension  of  the  vapor  of 
water  that  of  any  other  liquid.  Suppose,  for  example,  it  was  re- 
quired to  find  the  tension  of  the  vapor  of  ether  at  50°,  which  is  15° 

*  Comptes  Renclus,  Tom.  XXXIX.  p.  301. 


HEAT. 


£83 


Tempera- 
ture. 

Alcohol* 

Ether. 

Sulphide  of 
Carbon. 

Chloroform. 

Oil  of 
Turpentine. 

c 

—21 

0.312 

20 

0.334 

6.92 

16 

.    .    . 

.    .    • 

5.88 

—10 

0.650 

11.32 

7.90 

0 

1.273 

18.23 

12.73 

.     .     • 

0.21 

+10 

2.408 

28.65 

19.93 

13.04 

0.23 

20 

4.40 

43.48 

29.82 

19.02 

0.43 

30 

7.84 

63.70 

43.46 

27.61 

0.70 

40 

13.41 

91.36 

61.75 

36.40 

1.12 

50 

22.03 

126.80 

85.27 

52.43 

1.72 

60 

35.00 

173.03 

116.26 

73.80 

4.69 

70 

53.92 

230.95 

154.90 

97.62 

4.19 

80 

81.28 

294.72 

203.05 

136.78 

6.12 

90 

119.04 

389.90 

262.31 

181.15 

9.10 

100 

168.50 

492.04 

332.13 

235.46 

13.49 

110 

235.13 

624.90 

413.63 

302.04 

18.73 

116 

.    .    . 

707.62 

.    .    . 

.    .    . 

.    .    . 

120 

320.78 

.    .    . 

512.16 

381.80 

25.70 

130 

433.12 

... 

626.06 

472.10 

34.70 

\      136 

.    .    . 

.    .    . 

702.92 

.    .    . 

.    .    . 

140 

563.77 

.    .    . 

.    .    . 

.    .    . 

46.23 

150 

725.78 

.    .    . 

.    .    . 

.    .    . 

60.45 

152 

761.73 

.    •    . 

.    •    . 

.    .    . 

.    .    . 

160 

•    •    • 

... 

•    •    . 

.    .    . 

77.72 

170 

.    .    • 

.    •    . 

.    .    . 

.    .    . 

98.90 

180 

.    .    . 

.    .    . 

.    .    . 

.    .    . 

122.50 

190 

.    .    . 

.    .    . 

.    .    . 

.    .    • 

151.47 

200 

.    .    . 

.    .    . 

.    .    . 

.    .    . 

186.56 

210 

.    .    . 

.    .    . 

.    .    . 

.    .    . 

225.12 

220 

.    .    . 

.    .    . 

.    .    . 

.    .    . 

269.03 

222 

.    .    . 

.    .    . 

.    .    . 

.    .    . 

277.85 

above  its  boiling-point.  According  to  the  above  principle,  this 
tension  is  the  same  as  that  of  the  vapor  of  water  at  115°,  or  126.9 
c.  m.,  a  number  which  differs  but  very  slightly  from  that  deter- 
mined by  actual  experiment,  and  given  in  the  foregoing  table.  It 
has  been  shown,  however,  by  the  investigations  of  Regnault,  that 
Dalton's  law  is  not  absolutely  rigorous,  and  at  large  distances 
from  the  boiling-point  is  so  far  from  coinciding  with  the  facts, 
that  it  cannot  be  relied  upon  except  for  furnishing  the  first  rough 
approximation  to  the  actual  tension  of  a  volatile  liquid. 

It  follows  at  once  from  the  law  of  Dalton,  that  at  any  given 
temperature  different  liquids  may  have  very  unequal  tensions, 


584 


CHEMICAL  PHYSICS. 


ABCDE 


Fig.  413. 


and,  moreover,  that  in  any  one  case 
the  tension  must  be  the  greater  the 
lower  the  boiling-point  and  hence  the 
more  volatile  the  liquid.  These  facts 
may  be  illustrated  by  means  of  the 
apparatus  represented  in  Fig.  413. 
It  consists  of  four  barometer-tubes, 
all  dipping  into  the  same  basin  of 
mercury.  The  first  at  the  left  is  a 
perfect  barometer,  and  therefore  in- 
dicates the  pressure  of  the  air  ;  but 
the  others  contain  a  few  drops  of 
some  volatile  liquid  above  the  mer- 
cury-column. The  tension  of  the  va- 
por of  these  liquids  is  measured,  of 
course,  by  the  depression  of  the  mer- 
cury; this  will  be  found  to  be  greater 
in  proportion  as  the  boiling-point  is  lower. 

(291.)  Maximum  Tension  of  Vapors.  —  The  vapor  of  any 
liquid  which  forms  in  a  confined  space  and  in  the  presence  of 
an  excess  of  the  liquid,  has  always  the  greatest  tension  which 
the  vapor  can  have  at  the  given  temperature.  To  recur,  for  ex- 
ample, to  our  previous  illustration :  at  the  temperature  of  20°, 
there  would  form  in  the  vessel  described  in  (284)  a  cubic  metre 
of  vapor  weighing  17.155,  and  having  a  tension  equal  to  1.739 
c.  m.,  provided  only  an  excess  of  water  were  present.  Now  this 
is  the  greatest  tension  which  the  vapor  of  water  can  have  at  20°. 
If  by  mechanical  means,  as  by  sinking  a  piston  in  a"  cylinder,  we 
attempt  to  increase  the  elasticity  of  the  vapor  without  changing 
the  temperature,  we  find  that  it  is  at  once  condensed  to  liquid 
water,  and  that  its  tension  remains  constant  at  1.739  c.  m.  until 
all  the  vapor  has  disappeared.  On  now  raising  the  piston,  the 
space  will  be  filled  again  with  vapor ;  but  so  long  as  a  drop  of 
water  remains  in  the  cylinder,  the  tension  of  this  vapor  will 
still  be  equal  to  1.739  c.  m.  If,  however,  after  all  the  water  has 
evaporated,  we  still  continue  to  enlarge  the  capacity  of  the  cylin- 
der, then  the  vapor  will  act  like  a  gas,  and  its  tension  will  dimin- 
ish, in  accordance  with  the  law  of  Mariotte  ;  compare  (156. 3)  and 
(163).  In  the  above  illustration  we  have  assumed  that  the  tem- 
perature of  the  vessel  was  constant  at  20° ;  but  the  same  principle 


HEAT. 


585 


is  equally  true  at  all  temperatmes  and  for  all  liquids,  and  all  the 
tensions  given  in  the  tables  on  pages  571  and  583  are  the  maxi- 
mum tensions  possible  at  the  respective  temperatures. 

This  principle  may  be  illustrated  experimentally  by  means  of 
the  apparatus  represented  in  Fig.  414.  It  consists  of  a  barom- 
eter-tube and  a  deep  mercury  cistern,  in  which 
the  tube  can  be  entirely  immersed.  In  order 
to  mount  the  apparatus,  the  tube  is,  in  the 
first  place,  nearly  filled  with  mercury,  which 
is  boiled  to  expel  the  air,  and  then  the  rest  of 
the  tube  filled  with  ether.  On  inverting  the 
tube  and  plunging  the  open  end  under  the 
mercury  of  the  cistern  in  the  usual  way,  the 
ether  rises  to  the  top  of  the  tube,  and  a  part 
remains  liquid,  while  the  rest  forms  a  va- 
por which,  at  the  ordinary  temperature  of 
the  air,  depresses  the  mercury-column  about 
36  c.  m.  ;  so  that  the  mercury  stands  in  the 
tube  at  40  c.  m.,  instead  of  76  c.  m.,  above 
the  level  of  the  mercury  in  the  cistern.  The 
tension  of  ether  vapor  at  the  ordinary  temper- 
ature is  consequently  36  c.  m.  If  now  we 
attempt  to  increase  the  tension  of  this  vapor, 
and  consequently  diminish  its  volume,  by  sink- 
ing the  tube  in  the  cistern  (Fig.  414),  we 
shall  find  that  a  portion  of  the  vapor  will  con- 
dense ;  but  the  mercury-column  will  remain 
at  the  same  height  in  the  tube,  proving  that 
the  vapor  which  is  still  uncondensed  has  the 
same  elasticity  as  before.  On  continuing  to 
depress  the  tube,  it  will  be  found  that  the 
height  of  the  mercury-column,  and  conse- 
quently the  tension  of  the  vapor,  will  remain  Fig.4u. 
absolutely  the  same  until  the  last  bubble  has 
been  condensed.  This  proves  that  36  c.  m.  is  the  maximum 
tension  which  the  vapor  of  ether  can  be  made  to  assume  at  the 
ordinary  temperature  of  the  air. 

(292.)  Gases  and  Vapors. — The  principles  of  the  last  section 
furnish  a  convenient  ground  of  distinction  between  gases  and 
vapors.  It  is  usual  to  apply  the  term  vapor  to  such  aeriform 


586  CHEMICAL  PHYSICS. 

substances  as  are  easily  condensed,  either  by  pressure  or  by  cold, 
into  liquids,  and  which,  under  the  ordinary  conditions  of  atmos- 
pheric temperature  and  pressure,  exist  in  the  liquid  state.  This 
definition,  however,  is  purely  artificial,  and  makes  no  essential 
distinction  between  a  gas  and  a  vapor ;  and  we  therefore  prefer 
to  distinguish  by  the  word  vapor  the  peculiar  condition  of  aeri- 
form matter  when  it  is  at  the  point  of  maximum  tension.  Ac- 
cording to  this  definition,  a  vapor  is  a  condition  of  aeriform  mat- 
ter which  obeys  the  law  of  Mariotte  when  its  volume  is  increased, 
but  which,  if  the  volume  be  diminished,  is  in  part  changed  into 
a  liquid  ;  a  gas,  on  the  other  hand,  is  a  condition  of  aeriform 
matter  which  obeys  the  law,  whether  its  volume  be  increased  or 
diminished.  We  may  also  define  a  vapor  as  that  condition  in 
which  a  gas  exists  the  moment  before  its  change  of  state. 

This  distinction  between  a  gas  and  a  vapor  will  be  made  clearer 
by  pursuing  still  further  the  illustration  of  the  last  section.  Let 
us  suppose  that  we  have  a  cylindrical  vessel  exposed  to  the  tem- 
perature of  130°,  and  filled  with  steam  having  a  tension  equal  to 
98.956  c.  m.  By  referring  to  Table  IX.  of  the  Appendix,  it  will 
be  seen  that  the  maximum  tension  of  the  vapor  of  water  at  130° 
is  203.028.  Now,  if  there  were  in  the  vessel  a  supply  of  water, 
the  liquid  would  continue  to  give  off  vapor  until  this  tension  was 
attained.  But  we  will  assume  that  there  is  no  liquid  water  pres- 
ent, and  that  the  cylinder  is  filled  with  expanded  steam.  Under 
these  circumstances,  the  steam  must  retain  the  tension  of  98.956 
c.  m.  so  long  as  both  the  temperature  and  the  volume  remain 
unchanged. 

If  now,  keeping  the  temperature  constant,  we  increase  the  ca- 
pacity of  the  cylinder  by  raising  the  piston,  the  steam  will  expand, 
and  its  tension  will  diminish  in  accordance  with  Mariotte' s  law. 
When  the  volume  is  doubled,  the  tension  will  be  found  to  be 
49.478  c.  m. ;  when  quadrupled,  the  tension  will  be  reduced  to 
24.739  c.  m. ;  and  in  any  case  we  can  find  the  tension  corre- 
sponding to  the  increased  volume  by  the  proportion  * 

V  :    V  =  %':$.  [200.] 

*  This  equation  is  merely  [98],  substituting  {$  and  fy'  for  H  and  H1.  The  stu- 
dent must  be  careful  to  bear  in  mind  that  the  tension  of  a  gas  is  always  equal  to  the 
pressure  to  which  it  is  exposed  (149).  We  here  leave  out  of  the  account  any  deviation 
from  Mariotte's  law,  which,  nevertheless,  may  be  very  considerable  as  the  point  of  con- 
densation is  approached  (165  and  166). 


HEAT.  587 

Moreover,  when  the  volume  has  been  only  so  far  increased  that 
the  tension  of  the  steam  has  been  reduced  to  76  c.  m.,  it  is  then 
in  the  same  condition  as  that  in  which  a  gas  (like  sulphurous 
acid,  for  example)  exists  at  the  ordinary  temperature.  It  will 
sustain  the  pressure  of  the  atmosphere,  and,  were  the  tempera- 
ture of  the  laboratory  as  high  as  130°,  it  might  be  collected  over 
a  mercury  trough  and  transferred  from  one  jar  to  another,  like 
any  other  gas. 

Again,  if,  still  keeping  the  temperature  constant  at  130°,  we 
now  lessen  the  capacity  of  the  cylinder  by  sinking  the  piston, 
the  tension  of  the  confined  steam  will  be  increased  up  to  a  cer- 
tain point  in  accordance  with  Mariotte's  law ;  in  other  words, 
it  will  manifest  all  the  characters  of  a  gas,  and  its  tension  at 
any  degree  of  condensation  may  be  calculated  by  the  same  for- 
mula as  before.  If,  however,  we  continue  to  sink  the  piston 
until  the  volume  of  the  steam  is  reduced  to  a  little  less  than  one 
half  of  its  original  volume,  and  the  tension  increased  to  203.028 
c.  m.,  we  shall  reach  a  point  at  which  the  steam  suddenly  ceases 
altogether  to  obey  the  law  of  Mariotte  ;  and  if  we  sink  the  piston 
still  further,  the  tension  will  not  increase  in  the  slightest,  but  a 
portion  of  the  steam  will  be  changed  into  water,  and  this  change 
will  proceed  until  the  piston  reaches  the  bottom  of  the  cylinder, 
the  tension  all  the  time  remaining  constant  at  203.028  c.  m.  It 
is  to  this  peculiar  condition  of  aeriform  matter  that  we  give  the 
name  of  vapor. 

Returning  now  to  the  initial  condition  of  the  cylinder,  when  it 
is  filled  with  steam  at  the  tension  of  98.956  c.  m.,  let  us  vary  the 
temperature,  while  we  keep  the  volume  absolutely  constant.  If 
we  increase  the  temperature,  we  shall  increase  the  tension  of  the 
confined  steam,  according  to  the  same  law  by  which  the  tension 
of  a  confined  mass  of  air  would  be  increased  under  the  same 
circumstances.  If,  on  the  other  hand,  we  lessen  the  tempera- 
ture, we  shall  diminish  the  tension  of  the  confined  steam,  accord- 
ing to  the  same  law  as  before,  until  we  reach  a  temperature  at 
which  the  tension  of  the  steam  is  the  maximum  tension  for  that 
temperature.  Then,  on  still  further  cooling  the  cylinder,  a  por- 
tion of  the  steam  will  change  into  water,  and  the  tension  of  the 
remaining  vapor  will  be  found  to  be  the  maximum  tension  corre- 
sponding to  the  reduced  temperature. 

If  we  know  the  tension  of  a  confined  mass  of  gas  at  any  given 


588  CHEMICAL  PHYSICS. 

temperature,  we  can  always  readily  calculate  its  tension  for  any 
other  temperature,  assuming,  as  we  have  above,  that  the  volume 
does  not  change.  Let  V  represent  the  volume  of  a  gas  which 
has  a  tension  §  at  t°.  The  volume  of  this  mass  of  gas  at  J'°,  if 
allowed  to  expand  freely,  the  tension  remaining-  constant,  would 
be,  by  [184],  F(l  +  0.00366  [*'  —  *]).  If  now  this  increased 
volume  is  reduced  by  pressure  again  to  F,  the  tension  (which 
was  before  $)  will  of  course  be  increased,  and  we  shall  evidently 
have  the  same  condition  as  if  the  gas  had  not  been  allowed  to 
expand.  But  we  have,  by  [200], 

V  (1  +  0.00366  [*'  —  *])  :  F  =  §'  :  4} , 
and  hence  we  obtain  for  the  value  of  the  increased  tension, 

§'  =  fj  (1  +  0.00366  [*'  —  *]).  [201.] 

Applying  now  this  formula  in  the  example  under  discussion, 
we  should  find  that  the  steam,  whose  tension  was  equal  to 
98.956  c,  m.  at  130°,  would  have  at  105°  a  tension  of 

$  ==  98.956  -*-(!  +  0.00366  X  25)  =  90.641  c.  m.  ; 

and  on  referring  to  the  table,  it  will  be  seen  that  this  is  the 
maximum  tension  which  steam  can  have  at  105°.  Hence  at  this 
point  the  steam  assumes  the  condition  of  vapor.  By  the  same 
formula,  it  will  appear  that  at  104°  the  tension  of  the  steam  would 
be  90.334  c.  m.,  but  by  the  table  87.541  c.  m.  is  the  maximum 
tension  possible  at  104° ;  as  much  vapor  will,  therefore,  be  con- 
densed to  water  as  is  necessary  to  reduce  the  tension  to  this 
amount.  The  same  will  be  true,  to  a  still  greater  degree,  at 
any  lower  temperature. 

(293.)  Distillation.  —  It  has  now  been  shown,  first,  that  the 
tension  of  the  vapor  which  rises  from  a  boiling  liquid  is  always 
equal  to  the  pressure  of  the  atmosphere ;  secondly,  that  this  ten- 
sion is  the  maximum  tension  possible  for  the  temperature,  so  that 
if  the  volume  is  reduced  by  mechanical  means  the  tension  is  not 
increased,  but  a  portion  of  the  vapor  is  condensed  to  the  liquid 
state.  From  these  two  facts  it  follows,  as  a  necessary  conse- 
quence, that  a  vapor  will  be  condensed  to  a  liquid  by  the  pres- 
sure of  the  atmosphere,  if  its  temperature  falls  below  the  boiling- 
point  of  this  liquid  (except  under  the  conditions  hereafter  to  be 
considered,  when  the  vapor  is  diffused  through  the  atmosphere 


HEAT. 


589 


The  process  of  distillation,  which  is  used  in  the  arts  for  the 
purpose  of  separating  a  volatile  substance  from  one  that  is  fixed 
or  less  volatile,  is  a  direct  illustration  of  this  principle.  The 
simplest  apparatus  for  the  purpose  is  represented  in  Fig.  415. 


Fig  415 

The  liquid  is  boiled  in  a  glass  retort,  and  the  vapor  which  is  thus 
formed  is  conducted  into  a  receiver,  where  it  is  cooled  below  the 
boiling-point,  and  again  reduced  to  the  liquid  state.  Since  glass 
vessels  when  exposed  to  a  naked  fire  are  liable  to  break,  the  body 
of  the  retort  is  usually  protected  by  placing  it  within  an  iron  pot 
and  surrounding  it  with  saiid.  Such  ail  arrangement  is  termed 


Fig.  416. 


a  sand-bath,  or,  when  water  is  used  in  the  place  of  sand,  a  water- 
bath.     Another  form  of  distillatory  apparatus  is  represented  in 
Fig.  416.     Here  the  neck  of  the  retort  is  connected  with  what  is 
50 


590 


CHEMICAL   PHYSICS. 


usually  termed  a  Liebig-'s  condenser.  It  consists  of  a  tube 
of  glass,  which  is  kept  cold  by  a  current  of  water  circulating 
through  a  copper  cylinder,  which  surrounds  it.  In  the  corn- 


Fig.  417. 

mon  still,  Fig.  41T,  a  large  copper  boiler  supplies  the  place  of 
the  retort,  and  the  vapor  is  condensed  in  a  spiral  tube  of  cop- 
per, called  a  worm,  which  is  kept  immersed  in  a  tank  of  cold 
water. 

Since  the  boiling-point  of  a  liquid  is  reduced  in  proportion  as 
the  atmospheric  pressure  is  removed,  it  is  sometimes  advantageous 

to  conduct  the  process 
of  distillation  in  a  par- 
tial vacuum.  This  is 
especially  the  case  with 
some  organic  substances 
which  have  a  high  boil- 
ing-point and  are  de- 
composed by  heat.  The 
apparatus  represented 
in  Fig.  418  is  adapted- 

for  this  purpose.     The  retort  A  is  connected  by  an  hermetically 
sealed  joint  with  the  receiver  B,  and  this  again,  through  the  tube 


HEAT. 


591 


r,  with  an  air-pump,  by  which  the  pressure  on  the  surface  of  the 
liquid  in  the  retort  may  be  very  greatly  reduced.  The  same 
principle  is  applied  in  the  sugar  refineries  in  order  to  concen- 
trate syrups  at  a  low  temperature  (vacuum-pans). 

(294.)  Steam-Bath.  —  The  fact,  that  the  temperature  of  boil- 
ing water  and  of  the  steam  rising  from  it  is  constant  at  100°, 
is  frequently  applied  in  the  laboratory  when  it  is  important  to 
maintain  a  moderate  and  constant  degree  of  heat  for  a  length 
of  time.  The  arrangement  which  is  usually  adopted  for  evapo- 
rating liquids  at  100°  is  represented  in  Fig.  419.  The  porcelain 
evaporating-dish  rests  on  the  rim  of  a  hemispherical  vessel  of 
copper,  in  which  water  is  kept  constantly  boiling  by  means  of  a 
spirit>lamp. 


Fig.  419. 


Fig.  420. 


For  drying  precipitates,  or  for  expelling  the  water  of  crystalli- 
zation from  a  salt,  the  chemist  frequently  uses  a  steam-bath  like 
the  one  represented  in  Fig.  420.  This  is  simply  a  copper  oven 
with  double  sides,  which  is  maintained  at  100°  by  boiling  the 
water  which  partially  fills  the  cavity  between  the  inner  and  outer 
lining  of  the  oven. 

(295.)  Papirfs  Digester.  —  Water,  when  enclosed  in  a  strong 
vessel,  can  be  heated,  as  we  have  seen,  to  a  temperature  very 
much  above  100° ;  and  this  fact  is  advantageously  applied  in 
Papin's  Digester,  which  is  very  useful  in  the  laboratory  when  it 
is  required  to  expose  substances  to  the  action  of  water  at  a  tem- 
perature between  100°  and  200°  for  a  length  of  time.  It  consists 


592 


CHEMICAL   PHYSICS. 


generally  of  a  thick  cylindrical  vessel  of  brass,  Z>,  Fig.  421, 
closed  by  a  thick  cover  of  the  same  material,  which  is  kept  in 
its  place  by  the  screw  B  S.  A  safety-valve,  o  p  A,  serves  to 

regulate  the  pressure,  and  thus 
the  temperature  of  the  water, 
as  well  as  to  insure  the  safety 
of  the  apparatus.  The  details 
of  the  construction  of  the  safety- 
valve  are  given  in  Fig.  440.  This 
digester  can  also  be  used  with 
great  advantage  to  produce  chem- 
ical reactions  which  could  not  be 
readily  obtained  under  the  pres- 
sure of  the  air.  For  this  pur- 
pose, the  substances  are  sealed 
up  together  in  glass  tubes,  and 
exposed  to  the  temperature  of  the 
overheated  water,  and  any  inte- 
rior pressure  resulting  from  the 
evolution  of  gas  in  the  tube  is 
more  or  less  balanced  by  the  ex- 
terior pressure  of  the  confined  steam. 

(296.)  Condensation  of  Gases.  —  There  are  many  substances 
which  boil  at  so  low  a  temperature  that  they  retain,  at  the  ordi- 
nary temperature  of  the  atmosphere  and  under  the  usual  pressure, 
the  condition  of  a  gas.  The  boiling-points  of  a  number  of  such 
substances  are  given  in  the  following  table  :  — 


421. 


Sulphurous  Acid,       •»;'.;  *;  — 10 
Cyanogen,      .         .      4  *.        — 20 

Ammonia,  •;       »  .     — 36 

Arsenide  of  Hydrogen,  .          — 58 


Sulphide  of  Hydrogen,     .  —73 

Hydrochloric  Acid,     .«•>-.  — 80 

Carbonic  Acid,       •<         .  —80 

Protoxide  of  Nitrogen,  — 87.2 


All  these  substances  manifest,  at  the  ordinary  temperature  of 
the  air,  the  same  physical  properties  which  steam  would  manifest 
at  130°,  as  described  in  (292)  ;  and  if  in  either  case  the  temper- 
ature of  the  gas  is  reduced  below  the  boiling-point,  then  the 
tension  of  the  vapor  will  be  reduced  to  less  than  76  c.  m.,  and 
the  gas  will  be  condensed  to  a  liquid  by  the  pressure  of  the  air, 
exactly  as  in  the  process  of  distillation. 


HEAT. 


593 


This  fact  is  illustrated  by  the  common  method  of  preparing 
liquid  sulphurous  acid.  This  gas,  which  is  generated  by  heating 
together  metallic  mercury 
and  strong  sulphuric  acid 
in  a  glass  retort  (Fig.  422), 
is  passed  into  a  U  tube 
surrounded  by  a  mixture 
of  ice  and  salt,  where  it 
collects  as  a  liquid.  Had 
we  the  means  of  pro- 
ducing readily  a  sufficient 
degree  of  cold,  we  might 
easily  condense  to  liquids 
the  other  gases  in  the  same  way. 

For  any  given  temperature,  the  vapor  of  each  of  the  substances 
included  in  the  above  table  has,  like  the  vapor  of  water,  a  definite 
maximum  tension,  which  it  cannot  exceed  ;  and  if  we  had  the 
requisite  data,  we  could  make  out  for  each  one  a  table  of  maxi- 
mum tensions  at  different  temperatures  similar  to  the  tables  on 
pages  571  and  583.  Bunsen  has  furnished  us  with  such  a  table 
for  the  first  three  substances. 


Fig.  422. 


Temperature. 

-37 

20 

15 

10 

—5 

0 

+5 
10 
15 
20 
25 


Sulphurous  Acid. 
Tension  in  c.  in. 


78 
111 
148 
191 
239 
293 
354 
420 


Cyanogen. 
Tension  in  c. : 


80 
110 
141 
173 
207 
244 
283 
333 
380 


Ammonia. 
Tension  in  c.  m. 

74.9 


304 
361 
426 
498 
578 
667.4 


Moreover,  what  was  shown  in  (292)  to  be  true  in  regard  to 
steam  at  130°  is  equally  true  of  these  gases  at  the  ordinary  tem- 
perature of  the  air.  If,  for  example,  we  suppose  the  cylinder,  so 
often  referred  to,  to  be  filled  with  sulphurous  acid  gas,  and 
maintained  at  a  constant  temperature  of  15°,  we  should  find,  on 
pressing  down  the  piston,  that  the  tension  would  increase  as  the 
50* 


594 


CHEMICAL   PHYSICS. 


volume  diminished,  until  it  became  equal  to  293  c.  m. ;  but  on 
still  further  reducing  the  volume,  the  gas  would  liquefy.  The 
same  would  be  true  of  cyanogen  when  the  tension  became  equal 
to  333  c.  m.,  and  of  ammonia  when  it  became  equal  to  578  c.  m., 
assuming,  of  course,  that  the  temperature  of  the  cylinder  is 
maintained  constant  at  15°.  If  the  temperature  is  diminished, 
the  gases  cannot  acquire  so  great  a  tension  ;  if  it  is  raised,  the 
tension  may  be  greatly  increased. 

These  facts  may  be  very  elegantly  illustrated  by  means  of  the 
apparatus  represented  in  Fig.  423.     It  consists  of  an  iron  cistern, 

A,  filled  with  mercury,  and  closed 
on  all  sides  with  the  exception  of 
five  circular  apertures  through  the 
top.  Into  four  of  these  may  be 
screwed  the  iron  tubes  a,  6,  c,  and 
d,  which  reach  to  the  bottom  of 
the  cistern.  These  tubes  are  pro- 
vided with  a  broad  shoulder,  and 
are  screwed  down  upon  lead  wash- 
ers with  a  wrench,  so  as  to  enable 
the  joint  to  resist  a  pressure  of 
ten  or  twelve  atmospheres  with- 
out yielding.  Into  the  open  ends 
of  these  iron  tubes  the  glass  tubes 
1,  2, 3,  and  4  are  cemented.  They 
are  about  one  centimetre  in  diam- 
eter and  closed  at  the  top.  When 
the  apparatus  is  in  use,  one  of  the 

tubes  may  be  filled  with  air,  and  the  other  three  with  ammonia, 
cyanogen,  and  sulphurous  acid,  respectively.  By  the  fifth  aper- 
ture, e,  the  interior  of  the  mercury-cistern  connects  with  the 
force-pump  P,  through  the  tube  g ;  and  by  this  water  may  be 
forced  in  upon  the  surface  of  the  mercury.  The  pressure  thus 
exerted  will  cause  the  mercury  to  rise  in  the  several  tubes,  and 
as  the  volumes  of  the  confined  gases  are  diminished,  it  will  be 
noticed  that  their  tension  rapidly  increases.  This  tension,  which 
is  evidently  the  same  in  all  four  tubes,  is  measured  by  the  tube 
containing  air,  which  serves  as  a  manometer  (168.  3).  If  the 
temperature  of  the  apparatus  is  kept  constant  at  15°,  the  tension 
will  increase  until  it  is  equal  to  293  c.  m. ;  then  the  sulphurous 


Fig.  423. 


HEAT. 


595 


acid  will  begin  to  liquefy,  and  the  tension  will  remain  equal  to 
293  c.  m.  until  all  this  gas  has  disappeared.  It  will  then  again 
increase  until  it  reaches  333  c.  m.,  when  the  cyanogen  will 
liquefy ;  and,  finally,  after  this  gas  has  also  been  reduced  to  a 
liquid,  the  tension  will  increase  again  until  it  becomes  equal  to 
578  c.  m.,  when,  last  of  all,  the  ammonia  will  liquefy.  If  now 
we  remove  the  pressure  by  opening  the  stopcock,  which  vents  the 
water  from  the  cistern,  the  liquids  will  be  seen,  one  after  the 
other,  to  boil  violently,  and  return  to  the  condition  of  gas. 

Since  the  tension  of  a  gas  is  always  equal  to  the  pressure  to 
which  it  is  exposed,  it  follows  that  any  gas  will  be  condensed  to 
a  liquid  if  it  is  exposed  to  a  pressure  which  is  greater  than  its 
maximum  tension  at  the  given  temperature.  The  maximum 
tensions  of  a  number  of  gases  at  0°  are  approximatively  as  fol- 
lows :  — 


Maximum  Tension  at  0°  C. 


Atmospheres. 

Sulphurous  Acid, 

1.53 

Cyanogen, 

2.37 

lodohydric  Acid, 

3.97 

Ammonia,      . 

4.40 

Arsenide  of  Hydrogen, 

8.80? 

Chlorine,  .         .         » 
Sulphide  of  Hydrogen, 
Chlorohydric  Acid,    . 
Protoxide  of  Nitrogen, 
Carbonic  Acid,  .         • 


Atmospheres. 

.     8.95 

10 
.  26.2 

32 
.  38.5 


And  if,  in  either  case,  the  temperature  being  at  0°,  the  gas  is 
exposed  to  a  greater  pressure  than  the  tension  indicated  in  the 
table,  it  will  be  condensed  to  a  liquid.  If  the  temperature  is 
higher,  the  pressure  required  in  each  case  will  be  greater.  If  the 
temperature  is  lower,  the  pressure  required  will  be  less  ;  and  if 
in  either  case  the  temperature  is  reduced  below  the  boiling-point 
of  the  substance,  the  gas  will  be  condensed,  as  we  have  seen,  by 
the  pressure  of  the  air  alone.  It  is  evident  that,  in  condensing 
gases  to  liquids,  a  great  advantage  is  gained  by  reducing  the 
temperature  as  low  as  the  circumstances  will  permit,  and  hence 
it  is  usual  to  employ  both  pressure  and  cold  for  the  purpose. 
Several  of  the  processes  in  use  are  as  follows. 

The  simplest  method  of  condensing  gases  consists  in  generat- 
ing a  large  volume  of  the  gas  from  the  proper  chemical  materials 
ift  a  confined  space.  This  method  was  used  by  Faraday  in  his 
original  experiments  on  this  subject.  He  generated  the  gas  in 


596 


CHEMICAL   PHYSICS. 


Fig.  424. 


one  end  of  a  strong  glass  tube,  bent  at  the  middle,  as  represented 
in  Fig.  424,  and  hermetically  sealed.  The  gas  accumulating  in 
the  confined  space  exerted  a  great  pressure 
against  the  sides  of  the  tube,  and  when  this 
pressure  became  equal  to  the  maximum  ten- 
sion, a  portion  of  the  gas  was  condensed  to  a 
liquid.  This  collected  in  the  other  end  of  the 
tube,  which  was  immersed  in  a  freezing-mixture  to  facilitate  the 
process.  With  this  simple  apparatus  Faraday  succeeded  in 
liquefying  sulphurous  acid,  cyanogen,  chlorine,  ammonia,  sul- 
phide of  hydrogen,  carbonic  acid,  muriatic  acid,  and  nitrous 
oxide  gases. 

The  principle  of  Faraday's  condensing  tubes  was  afterwards 
applied  by  Thilorier  to  condensing  carbonic  acid  gas  on  a  large 


Fig.  425. 

scale.  The  apparatus  which  he  devised  for  the  purpose  is  repre- 
sented in  Fig.  425.  It  consists  of  two  cylindrical  vessels  of  iron, 
made  exceedingly  strong,  and  of  the  capacity  of  about  eight  litres 
each.  They  are  closed  by  valve  stopcocks  of  peculiar  construc- 
tion, which  screw  into  the  necks  of  the  two  vessels  and  can  be  re- 
moved at  pleasure.  By  means  of  the  copper  connecting-tube  F, 
which  can  be  attached  by  couplers  to  the  discharging  orifice  of  the 
valves  D  and  N9  the  two  cylinders  may  be  united  when  necessary. 


HEAT.  597 

v 

In  order  to  use  the  apparatus,  the  valve  C  is  removed  from 
the  cylinder  J.,  called  the  generator,  and  a  charge  is  introduced, 
consisting  of  one  kilogramme  of  pulverized  bicarbonate  of  soda 
mixed  with  a  litre  of  lukewarm  water.  After  this  has  been 
poured  into  the  cylinder,  a  long  cylindrical  vessel  (J2),  contain- 
ing about  650  grammes  of  common  oil  of  vitriol,  is  carefully  let 
down  by  a  hook  without  spilling.  The  valve-cock,  having  been 
first  carefully  closed,  is  now  screwed  down  tightly  to  the  mouth 
of  the  generator,  which  is  then  turned  upon  its  supporting-pivots 
so  as  completely  to  invert  it,  and  thus  mix  the  acid  with  the  car- 
bonate of  soda.  The  carbonic  acid  of  the  salt,  which  amounts 
to  more  than  half  of  its  weight,  is  now  rapidly  disengaged,  and 
accumulates  in  the  vacant  part  of  the  generator,  exerting  great 
elastic  force.  The  generator  is  next  connected,  as  represented  in 
the  figure,  with  the  second  large  cylinder  (^B),  which  serves  as  a 
receiver,  and  which  is  surrounded  by  a  mixture  of  ice  and  salt. 
On  op9ning  the  two  valves,  the  condensed  gas  rapidly  passes  over 
and  collects  in  the  cold  receiver.  The  cylinders  are  then  dis- 
connected, after  first  closing  the  valves,  and,  the  generator  having 
been  carefully  emptied,  the  same  process  is  repeated.  After  two 
or  three  charges  have  been  in  this  way  conveyed  into  the  receiver, 
the  pressure  becomes  sufficient  to  liquefy  the  gas  ;  and  after  ten 
or  twelve  charges  the  receiver  may  contain  several  litres  of  liquid 
carbonic  acid.  The  receiver  is  then  finally  detached,  and  the 
liquid  which  it  contains  preserved  for  use.  If  this  liquid  is  al- 
lowed to  flow  out  into  the  air,  a  portion  of  it  evaporates,  and,  as 
we  should  expect,  with  great  rapidity  ;  but,  what  is  more  won- 
derful, the  cold  caused  by  the  evaporation  is  so  great,  that  the 
larger  part  of  the  liquid  freezes,  changing  into  a  white  flocculent 
solid  resembling  snow.  This  very  remarkable  phenomenon  will 
be  best  studied,  however,  in  connection  with  the  latent  heat  of 
vapors.  In  order  to  show  the  substance  in  its  liquid  condition, 
a  small  quantity  may  be  drawn  off  from  the  receiver  into  the 
thick  glass  tube  P,  which  is  then  closed  by  a  valve-cock  like  that 
of  the  receiver  itself.  It  is  always  dangerous,  however,  to  con- 
fine liquid  carbonic  acid  in  glass. 

Although  the  apparatus  of  Thilorier  is  exceedingly  conven- 
ient, and  yields,  with  little  labor,  a  large  supply  of  liquid  carbonic 
acid,  yet  its  use  is  not  unattended  with  danger  ;  and  a  fatal  acci- 
dent, caused  by  the  bursting  of  one  of  the  iron  generators,  at  the 


598 


CHEMICAL  PHYSICS. 


School  of  Pharmacy  in  Paris,  has  brought  it  into  general  dis- 
favor. The  danger  arises  from  the  circumstance  that  the  chem- 
ical action  of  the  sulphuric  acid  on  the  carbonate  of  soda  is 


Fig.  427. 


Fig.  426. 

attended  with  the  evolution  of  heat,  which  raises  the  tempera- 
ture of  the  generator,  and  very  greatly  increases  the  maximum 
tension  of  the  gas.  In  the  receiver,  when  surrounded  by  ice 
and  salt,  the  tension  is  comparatively  feeble,  and  all  danger  may 
be  avoided  by  condensing  the  gas  with  a  force-pump  directly  into 
the  cold  receiver.  An  apparatus  for  this  purpose  is  constructed 
both  by  Natterer,  in  Vienna,  and  by  Bianchi,  in  Paris.  It  con- 
sists of  a  con  den  sing-pump  (ITS),  represented  at  /  in  Fig.  426, 
which  draws  the  gas  from  a  gasometer  through  the  flexible  hose 
s,  and  forces  it  into  an  iron  receiver,  which  is  represented  in 
Fig.  427,  of  one  fifth  of  its  usual  size.  This  receiver  screws 


HEAT. 


599 


upon  the  upper  end  of  the  pump-barrel,  and  it  is  closed  below 
by  a  self-acting  valve,  and  above  by  the  valve-cock  g*,  as  shown 
in  Fig.  427.  A  crank  and  fly-wheel  facilitate  the  working 
of  the  pump  ;  but  it  requires  several  hours  of  hard  work  to 
liquefy  only  500  grammes  of  gas.  After  the  receiver  is  about 
two  thirds  filled  with  liquid,  it  is  unscrewed  from  the  pump- 
barrel,  and  the  liquid  can  then  be  drawn  out  by  inverting  it  and 
opening  the  valve  g.  This  apparatus  has  been  especially  used 
for  liquefying  nitrous  oxide  gas. 

Professor  Faraday  succeeded  in  liquefying  several  gases  which 
had  not  been  condensed  before,  by  combining  the  action  of  intense 
cold  and  great  pressure,  the  last  obtained  with  a  very  powerful 
condensing  apparatus.  This  apparatus  consisted  of  two  condens- 
ing syringes.  The  first  had  a  piston  of  an  inch  in  diameter,  the 
second  of  only  half  an  inch  ;  these  syringes  were  connected  by  a 
pipe,  so  that  the  first  syringe  forced  the  gas  through  the  valves 
of  the  second,  and  the  second  syringe  was  then  used  to  compress 
still  more  highly  the  gas  which  had  already  been  condensed  by 
the  action  of  the  first,  with  a  pressure  varying  from  ten  to  twenty 
atmospheres.  The  gases  were  condensed  by  this  apparatus  into 
tubes  of  green  bottle-glass  bent  at  the  middle  into  the  form  of  a  U, 
and  closed  at  the  ends  with  brass  caps  and  stopcocks,  securely 
fastened  by  means  of  a  resinous  cement.  The  curved  portion  of 
the  tube  was  immersed  in  a  bath  of  solid  carbonic  acid  and  ether, 
and  at  times  a  still  greater  degree  of  cold,  estimated  at — 110°, 
was  obtained  by  placing  the  bath  under  the  receiver  of  an  air- 
pump  and  exhausting  the  air.  When  exposed  to  this  very  low 
temperature,  most  of  the  liquefied  gases  froze,  as  is  shown  by 
the  following  table,  which  contains  the  results  of  Faraday :  — 


Gases  not  yet  Liquefied. 

Air. 

Oxygen. 

Nitrogen. 

Hydrogen. 

Oxide  of  Carbon.  " 

Marsh  Gas. 

Deutqxide  of  Nitrogen. 


Gases  Liquefied, 
but  not  Frozen. 


Gases  Liquefied, 
and  also  Frozen. 


Olefiant  Gas. 
Chlorohydric  Acid. 
Fluohydric  Acid. 
Fluosilicic  Acid. 
Phosphide  of  Hydrogen. 
Arsenide  of  Hydrogen. 
Chlorine. 

Protoxide  of  Nitrogen,  — 100 

More  recently,  Natterer  of  Vienna,  has  constructed  a  vastly 
more  powerful  condensing  apparatus  than  that  of  Faraday,  al- 


Bromohydric  Acid, 
Cyanogen, 
lodohydric  Acid, 
Carbonic  Acid, 
Ammonia, 
Sulphurous  Acid, 
Sulphide  of  Hydrogen, 


Melting- 
Point. 

—8° 
25 
51 
58 
75 
76 
86 


600  CHEMICAL  PHYSICS. 

though  on  a  similar  principle,  by  which  he  has  been  able  to  ex- 
exert  a  pressure  of  nearly  three  thousand  atmospheres  ;  but  the 
gases  enumerated  in  the  first  column  of  the  above  table  did  not 
yield  even  to  this  immense  pressure,  and  indeed  were  not  con- 
densed so  much  as  we  should  be  led  to  expect  from  the  law  of 
Mario tte.  For  a  description  of  this  apparatus,  the  student  may 
consult  the  memoir  already  referred  to  (page  299). 

The  facts  of  this  section  all  tend  to  show  how  completely  the 
mechanical  condition  of  matter  depends  on  the  temperature  of 
the  globe.  If  the  mean  temperature  were  100°  below  the  present 
point,  by  far  the  larger  number  of  known  gases  would  be  either 
solids  or  liquids.  To  the  inhabitants  of  such  a  climate  (whom 
we  may  suppose  to  use  a  Centigrade  thermometer  on  which 
— 100°  of  our  scale  would  be  the  zero-point),  protoxide  of  nitro- 
gen would  be  a  very  volatile  liquid,  freezing  at  0°  and  boiling  at 
13°  ;  cyanogen  would  be  a  crystalline  solid,  melting  at  65°  and 
boiling  at  80°  ;  and  sulphurous  acid  would  be  a  solid,  melting  at 
24°  and  boiling  at  90°.  On  the  other  hand,  were  the  mean  tem- 
perature of  the  globe  100°  above  the  present  point,  many  of  our 
most  familiar  liquids  would  be  known  chiefly  as  gases.  Ether, 
alcohol,  and  water  would  stand  very  nearly  in  the  same  relation 
in  such  a  climate  that  sulphide  of  hydrogen,  cyanogen,  and  sul- 
phurous acid  do  in  ours. 

There  is  every  reason  to  believe  that  all  gases  might  be  con- 
densed to  liquids,  if  a  sufficient  degree  of  cold  and  pressure  could 
be  attained  ;  and  we  ought  not  to  be  surprised  at  the  difficulty 
experienced  in  liquefying  the  gases  above  enumerated,  when  we 
remember  how  very  rapidly  the  maximum  tension  of  vapors  in- 
creases with  the  temperature,  and  how  very  limited  our  means  of 
reducing  the  temperature  are,  as  compared  with  our  means  of 
elevating  it.  We  can  easily  attain  a  temperature  of  5,000°  C., 
while  we  can  scarcely  reduce  the  temperature  of  bodies  to  — 150°. 
At  1,000°  the  maximum  tension  of  the  vapor  of  water  would  be, 
unquestionably,  equal  to  many  thousand  atmospheres,  and  it 
would  undoubtedly  be  found  as  difficult  to  condense  to  a  liquid 
the  vapor  of  water  in  the  highly  rarefied  condition  which  it  would 
have  at  that  temperature  under  the  mere  pressure  of  the  air,  as 
it  is  now  found  to  condense  the  so-called  permanent  gases. 

(297.)  Greatest  Density  of  Vapor.— By  referring  to  the  table 
on  page  571,  it  will  be  seen  that  the  weight  of  one  cubic  metre 


HEAT.  601 

of  the  vapor  of  water  —  and  hence,  also,  its  density  (68)  —  in- 
creases very  rapidly  with  the  temperature.  This  is  also  shown 
by  the  curve  a  bfg-  of  Fig.  412.  The  ordinates  of  this  curve 
represent  the  weight  of  one  cubic  metre  of  vapor  at  the  corre- 
sponding temperatures  indicated  by  the  abscissas,  and  the  dis- 
tance between  any  two  horizontal  lines  of  the  figure  corresponds 
to  a  difference  of  weight  equal  to  588.73  grammes.  At  230°. 9 
the  weight  of  one  cubic  metre  of  vapor  is  already  -fa  of  the 
weight  of  a  cubic  metre  of  water  at  4°,  and  at  the  same  rate  of 
increase  the  weight  of  the  vapor  at  no  great  elevation  of  temper- 
ature would  be  equal  to  that  of  its  own  volume  of  water.  At 
such  a  temperature  water  would  change  into  vapor  without  in- 
creasing its  volume,  provided  that  a  vessel  could  be  made  suffi- 
ciently strong  to  bear  the  immense  pressure  which  it  would  then 
exert.  The  same  must  also  be  true  of  the  vapors  of  other  liquids, 
so  that  at  a  temperature  more  or  less  elevated  the  density  of  the 
vapor  will  become  equal  to  the  original  density  of  the  liquid, 
which  will  then  change  into  vapor  without  increasing  its  volume. 
An  approach  to  these  phenomena  has  been  observed  by  M. 
Cagniard  de  la  Tour.*  He  sealed  up  in  a  strong  glass  tube  a 
volume  of  water  equal  to  about  one  fourth  of  the  capacity  of  the 
tube,  and  exposed  it  to  a  gradually  increasing  temperature.  At 
a  fixed  temperature  the  water  entirely  volatilized,  and  the  tube 
appeared  empty.  This  temperature,  at  which  water  thus  evapo- 
rates into  a  space  of  about  four  times  its  own  bulk,  is  near  the 
melting-point  of  zinc  (360°).  So  great  was  the  solvent  power 
of  water  on  glass  at  this  high  temperature,  that  it  soon  destroyed 
the  integrity  of  the  tubes,  and  a  small  amount  of  carbonate  of 
soda  was  added  to  the  water  to  diminish  this  action.  As  the 
vapor  cooled,  a  point  was  observed  at  which  a  sort  of  cloud  filled 
the  tube,  and  in  a  few  moments  after,  the  liquid  reappeared 
almost  instantaneously.  M.  de  la  Tour  made  similar  experi- 
ments with  alcohol,  ether,  and  sulphide  of  carbon,  with  the  fok 
lowing  results :  — 

Temperature      Volume  of  V»por      Tension  of 
of  i  icappear-     as  compared  with        Vapor  in 
ance.  Volume  of  Liquid.    Atmospheres. 


Alcohol  (36°  Baume), 

.     259° 

3 

119 

Ether,    .... 

200 

2 

37 

Sulphide  of  Carbon,  . 

.     275 

2 

78 

*  Annales  de  Chimie  et  de  Physique,  2"  Serie,  Tom.  XXL,  XXII. 

51 


602  CHEMICAL   PHYSICS. 

The  tension  of  the  vapors,  as  given  in  the  above  table,  is  far 
less  than  we  should  have  expected  ;  for,  if  Mariotte's  law  held 
good  in  these  cases,  ether  should  have  exerted  a  pressure  equal 
to  about  209  atmospheres,  and  alcohol  of  at  least  242.  Here, 
then,  we  have  a  very  marked  example  of  the  principle  previously 
enunciated  (166),  that  as  the  point  of  liquefaction  is  approached, 
the  compressibility  of  a  gas  deviates  more  and  more  widely  from 
the  law  of  Mariotte.  The  experiments  of  De  la  Tour  also  show, 
that  under  these  enormous  pressures,  even  before  the  whole  of 
the  liquid  has  evaporated,  the  tension  of  the  vapor  varies  with 
the  proportion  which  the  liquid  bears  to  the  space  in  which  it  is 
confined. 

(298.)  Smallest  Density  of  Vapor.  —  Having  seen  that  the 
highest  limit  of  the  density  of  vapor  is  probably  at  least  as  great 
as  the  density  of  the  liquid  from  which  it  is  formed,  we  naturally 
next  inquire,  Is  there  any  lowest  limit  ?  Do  substances  continue 
to  evaporate  at  all  temperatures,  however  low,  or  is  there  some 
limit  of  temperature  at  which  they  cease  all  at  once  to  emit 
vapors  ?  By  again  referring  to  the  table  of  maximum  tensions 
(page  571),  it  will  be  seen  that  even  at  10°  below  the  freezing- 
point  water  forms  a  vapor  weighing  2.284  grammes  to  the  cubic 
metre,  and  having  a  tension  of  0.2078  c.  m. ;  and  even  at  20° 
below  the  freezing-point  it  forms  a  vapor  with  a  tension  of  0.1383 
c.  m.  It  was  formerly  supposed  that  substances  which  were  de- 
cidedly volatile  at  the  ordinary  temperature  continued  to  emit 
vapor,  however  far  the  temperature  might  be  depressed,  although 
the  quantity  became  less  and  less,  until  it  was  inappreciable  to 
our  senses.  It  was  even  thought  by  some,  that  fixed  solids,  such 
as  the  metals  and  the  rocks,  gave  out  a  sensible  amount  of  vapor, 
so  that  traces  of  these  substances  were  always  to  be  found  float- 
ing in  the  atmosphere.  Some  researches  of  Faraday,  however, 
appear  to  establish  an  opposite  conclusion.  He  found  that  mer- 
cury gave  out  a,  perceptible  vapor  during  the  summer,  but  none 
during  the  winter ;  and  also  that  some  chemical  agents  which 
may  be  volatilized  at  temperatures  above  150°  did  not  undergo 
the  slightest  evaporation  during  four  years  at  the  ordinary  tem- 
perature of  the  air.  The  best  opinion,  therefore,  appears  to  be, 
that  there  is  for  every  body  a  temperature  at  which  it  ceases  all 
at  once  to  give  out  vapor.  With  mercury,  this  temperature  lies 
between  4°  and  15°. 


HEAT.  603 


HEAT  OF  VAPORIZATION. 

(299.)  Latent  Heat  of  Vapor.  —  The  change  of  state  from 
liquid  to  vapor  is  accompanied  with  a  very  great  amount  of  ex- 
pansion ;  thus, 

IcT^3  of  Water     at    100°   forms  about  1700  ^.s  of  steam  at  100? 
1    «     "    Alcohol    "      78.4     "         "         485    «     «  vapor   «     78.4. 
1    "     «   Ether      «      35.6     "         "         357    "    "       "       "     35.6. 

And,  indeed,  the  heaviest  known  vapor,  that  of  iodide  of  ar- 
senic (£;?.  6rr.  =  16.1  as  compared  with  air,  or  0.021  as  com- 
pared with  water),  is  thirty  times  lighter  than  the  lightest  known 
liquid,  eupion  (Sp. Gr.  =  0.633).  We  should  naturally  expect 
that  such  great  expansion  would  be  attended  with  a  large  absorp- 
tion of  heat.  A  single  experiment  will  enable  us  to  illustrate 
this  fact,  and  also  roughly  to  estimate  the  amount  absorbed  in  the 
case  of  water. 

Take  a  glass  flask,  and  having  placed  in  it  one  kilogramme  of 
ice-cold  water,  expose  it  to  such  a  source  of  heat  that  equal  amounts 
of  heat  shall  enter  it  during  equal  times.  Observe  carefully  the 
time  which  elapses  before  the  water  boils.  We  will  assume  that 
it  is  twenty  minutes.  Observe  also  the  temperature  of  the  water 
and  of  the  steam  which  fills  the  upper  part  of  the  flask.  It  will 
be  found  to  be  100°,  and  both  will  remain  at  this  temperature 
until  the  whole  of  the  water  has  boiled  away.  Continue  the 
boiling  for  fifty-four  minutes,  and  at  the  end  of  this  time  weigh 
the  water  remaining  in  the  flask,  when  it  will  be  found  that 
exactly  one  half  has  been  converted  into  steam  and  escaped. 
We  assumed  that  it  required  twenty  minutes  to  boil  the  water, 
that  is,  to  raise  the  temperature  of  one  kilogramme  of  water  from 
0°  to  100°.  During  this  time,  then,  one  hundred  units  of  heat 
must  have  entered  the  liquid.  Hence  it  follows,  that,  during 
the  succeeding  fifty-four  minutes,  two  hundred  and  seventy 
units  of  heat  entered  the  water  ;  but  this  amount  of  heat  has 
not  raised  the  temperature  in  the  slightest  degree,  for  both 
the  water  and  the  steam  have  retained,  during  the  whole  inter- 
val, the  constant  temperature  of  100°.  What,  then,  has  become 
of  the  heat  ?  The  answer  is,  that  it  has  been  absorbed  in  con- 
verting 500  grammes  of  water  at  100°  into  500  grammes  of  steam 
at  the  same  temperature.  It  follows,  then,  that  one  kilogramme 


604 


CHEMICAL  PHYSICS. 


of  water  at  100°  absorbs,  in  changing  into  steam  of  the  same 
temperature,  540  units  of  heat.  The  latent  heat  of  steam,  as 
well  as  that  of  other  vapors,  can  be  ascertained  with  great  accu- 
racy by  means  of  the  apparatus  represented  in  Fig.  428,  contrived 
by  Brix,*  of  Berlin.  It  consists  of  a  small  glass  retort,  Ry  con- 
necting with  a  small  metallic  cylindrical  condenser,  B.  This 
condenser  has  an  opening  into  the  atmosphere  by  the  tube  .L, 
and  is  supported  in  the  centre  of  a  larger  cylindrical  box,  A, 
which  is  filled  with  water.  A  thermometer  passing  through  a 
tubulature  in  the  cover  enables  the  experimenter  to  observe  the 
temperature  of  the  water,  while  by  agitating  the  water  with  the 

metallic  disk  C,  its  tempera- 
ture can  be  rendered  uni- 
form throughout.  In  con- 
ducting the  experiment,  the 
water  around  the  condenser 
is  first  cooled  a  few  degrees 
below  the  temperature  of 
the  atmosphere  ;  then  the 
vapor  is  distilled  over  from 
the  retort  until  the  tem- 
perature of  the  water  has 
risen  an  equal  number  of 
degrees  above  that  of  the 
atmosphere.  In  this  way 
any  loss  of  heat  from  the 
water  is  avoided,  since  the 
apparatus  is  for  an  equal 
length  of  time  warmer  and 
cooler  than  the  air.  The 
weight  of  vapor  condensed 
is  then  ascertained  by  the 
loss  of  weight  of  the  retort, 

and  the  amount  of  heat  evolved  by  its  condensation  is  readily 
calculated  from  the  weight  of  the  water  around  the  condenser, 
and  the  number  of  degrees  through  which  it  has  been  heated. 
This  amount  of  heat  corresponds  to  the  latent  heat  of  the  vapor 
plus  the  amount  of  heat  given  out  by  the  condensed  steam  in 


Fig.  428. 


*  Poggendorff  's  Annalen,  Band  LV. 


HEAT.  005 

cooling  from  the  boiling-point  to  the  temperature  of  the  con- 
denser. To  illustrate  this  by  an  example,  we  will  suppose  that 
we  know 

The  weight  of  water  around  the  condenser,      .         .         .   500  grammes. 

The  temperature  at  the  beginning  of  the  experiment,  .          12°. 

The  temperature  at  the  end  of  the  experiment,         .         .18°. 

The  weight  of  the  water  distilled  over,         .         .  .        4.82  grammes. 

Hence  it  follows  (231),  that 

The  amount  of  heat  which  entered  the  water  equals  .       3         units. 

By  (233)  the  amount  of  heat  required  to  raise  the  temper- 
ature of  4.82  grammes  of  water  from  18°  to  100°  is 
equal  to 0.395  " 

And  hence  the  quantity  of  heat  given  out  by  4.82  grammes 

of  steam  in  liquefying  equals  .....  2.605  u 

One  kilogramme  of  steam  would  then  set  free,  in  liquefying,    540  " 

It  is  evident  that,  in  these  experiments,  as  in  the  determination 
of  the  specific  heat  by  the  method  of  mixtures,  it  is  necessary  to 
take  into  account  the  amount  of  heat  absorbed  by  the  metals  and 
glass  of  which  the  apparatus  is  made.  This  can  easily  be  calcu- 
lated, since  the  specific  heat  of  these  substances  is  known,  and 
their  weight  can  be  easily  determined.  The  formulae  for  similar 
calculations  have  already  been  given  [158]  and  [159],  and  they 
can  readily  be  modified  by  the  student  for  any  special  case. 

By  means  of  the  apparatus  described  above,  Brix  obtained  for 
the  latent  heat  of  the  vapors  of  several  well-known  liquids  the 
following  values.*  These  values  are,  in  each  case,  the  number 
of  units  of  heat  required  to  convert  one  kilogramme  of  the  liquid 
at  its  boiling-point  into  one  kilogramme  of  vapor  at  the  same 
temperature. 


• 

Latent  Heat  of 
equal  Weights. 

Latent  Heat  of 
equal  Volumes. 

Sp.  Or.  of  Vapor 
at  Boiling-point. 
Air  =  1. 

Water,      .     /.        . 

540  units. 

315.05 

0.451 

Alcohol,      '  .   "  "  . 

214     « 

348.26 

1.258 

Ether,     "V  ;    -.      *  .• 

90     « 

265.45 

2.280 

Oil  of  Turpentine, 

74     « 

307.00 

3.207 

Oil  of  Lemons,           . 

80     « 

*  Determinations  of  the  Intent  heat  of  vapors  have  also  been  made  by  Andrews 
(Quarterly  Journal  of  the  Chemical  Society,  Vol.  I.  p  27),  by  Despretz,  and  by  Favre 
and  Silbermann  (Comptcs  Rcndns,  Tom.  XXIII.  p.  524). 

51* 


606 


CHEMICAL  PHYSICS. 


Since  the  number  which  expresses  the  specific  gravity  of  a 
substance  is  the  same  as  the  weight  of  one  litre  in  kilogrammes, 
it  follows,  that,  if  we  multiply  the  specific  gravity  of  a  vapor  at  the 
boiling-point  (referred  to  water)  by  1,000,  we  shall  obtain  the 
weight  in  kilogrammes  of  one  cubic  metre  of  this  vapor  at  this 
temperature  ;  and,  furthermore,  it  follows  from  what  has  been 
said,  that,  if  we  multiply  this  weight  by  the  latent  heat  of  the 
vapor,  we  shall  have  the  number  of  units  of  heat  required  to 
generate  from  these  liquids  at  their  boiling-points  one  cubic  metre 
of  vapor.  Making  these  calculations,  we  should  obtain  the  num- 
bers given  in  the  above  table  as  the  latent  heats  of  equal  volumes; 
and  it  will  be  noticed  that,  with  the  exception  of  that  of  ether, 
these  numbers  are  approximatively  equal.  The  same  is  also 
true  of  other  liquids  not  included  in  the  table  ;  hence  we  may 
say,  roughly,  that  the  same  volume  of  vapor  will  be  produced 
from  all  liquids  by  the  same  expenditure  of  heat.  No  important 
advantage,  therefore,  could  be  gained  by  substituting  any  other 
liquid  for  water  in  the  steam-engine. 

(300.)  Latent  Heat  of  Steam  at  Different  Temperatures.  — 
The  latent  heat  of  steam  has  the  value  given  in  the  above  table 
only  when  its  tension  is  76  c.m.  and  its  temperature  100°,  which 
is  the  case  when  the  steam  is  formed  by  boiling  water  under  the 
normal  pressure  of  the  atmosphere.  If  the  tension  and  temper- 
ature of  the  vapor  have  greater  values  than  the  above,  then  the 
latent  heat  is  less  than  540  units  ;  and,  on  the  other  hand,  if 
these  values  are  less  than  76  c.  m.  and  100°,  then  the  latent  heat 
of  the  vapor  is  more  than  540  units.  Watt  concluded,  from  his 
experiments,  that  the  same  weight  of  vapor  always  contained  the 
same  quantity  of  heat,  or,  in  other  words,  he  supposed  that  the 
same  quantity  of  heat  would  convert  one  kilogramme  of  water  at 
0°  into  one  kilogramme  of  vapor,  whatever  the  tension  or  tem- 
perature of  the  vapor  might  be.  If  this  were  the  case,  the  sum 
of  the  latent  and  sensible  heat  of  steam  would  be  the  same  at  all 
temperatures,  and  we  should  have  for  the  latent  heat  the  follow- 
ing values : — 

Temperature.  Latent  Heat  of  Vapor.  Sum. 

0  640  units  640 

50  590  «  « 

100  540  «  « 

200  440  «  « 


HEAT.  607 

Among  the  other  numerical  data  connected  with  the  steam- 
engine,  Regnault  has  carefully  determined  the  latent  heat  of 
steam  at  different  temperatures  between  5°  and  196°.  These 
experiments  were  made  with  an  apparatus  constructed  with  every 
possible  refinement,  and  were  conducted  with  the  usual  skill  of 
this  eminent  experimentalist  ;  but  for  a  description  both  of  the 
apparatus  and  of  the  methods,  we  must  refer  the  student  to  the 
original  memoir.*  It  was  proved  by  this  investigation,  that  the 
law  of  Watt,  as  the  principle  above  stated  is  frequently  called,  is 
far  from  being  an  exact  expression  of  the  facts,  and,  like  so  many 
other  phenomenal  laws  of  nature,  can  only  be  regarded  as  ap- 
proximatively  true  (compare  page  300).  The  sum  of  the  latent 
and  sensible  heat  of  steam  actually  increases,  although  only  very 
slowly,  with  the  temperature  ;  and  Regnault  found  that  the 
results  of  his  experiments  were  very  nearly  satisfied  by  the  em- 
pirical formula 

A  ==  606.5  +  0.305  t ,  [202.] 

in  which  >t  represents  the  sum  of  the  latent  and  sensible  heat, 
while  606.5  is  the  latent  heat  of  the  vapor  at  0°,  and  t  the  given 
temperature.  By  means  of  this  formula,  we  can  very  easily  cal- 
culate the  latent  heat  of  the  vapor  at  any  temperature.  Thus, 
at  100°  we  have  A  =  637,  and  consequently  the  latent  heat  is  637 
units  less  the  number  of  units  required  to  raise  the  temperature 
of  one  kilogramme  of  water  from  0°  to  100°.  By  the  table  on 
page  472,  we  find  that  this  amount  is  equal  to  1.005  X  100  =» 
100.5,  and,  subtracting  this  quantity  from  637,  we  find  the  latent 
heat  of  steam  at  100°  to  be  536.5  units.  In  like  manner,  the 
other  values  in  the  following  table  have  been  calculated. 

The  second  column  of  the  table  gives  the  tension  of  the 
vapor  of  water  in  centimetres.  The  fourth  column  gives  the 
number  of  units  of  heat  required  to  change  one  kilogramme  of 
water  at  0°  into  one  kilogramme  of  vapor  at  t°.  The  third  col- 
umn gives  the  number  of  units  of  heat  required  to  change  one 
kilogramme  of  water  at  t°  into  one  kilogramme  of  vapor  at  the 
same  temperature. 

*  Memoires  de  1'Acadcmie  des  Sciences,  Tom.  XXI. 


608 


CHEMICAL   PHYSICS. 


Tem- 
pera- 
ture. 

Tension. 

Latent 
Heat. 

Sum  of 

Latent  and 
Sensible 
Heat. 

Tem- 
pera- 
ture. 

Tension. 

Latent 
Heat. 

Sum  of 
Latent  and 
Sensible 
Heat. 

e 

0 

0.460 

606.5 

606.5 

120 

149.128 

522.3 

613.1 

10 

0.916 

599.5 

609.5 

130 

203.028 

515.1 

646.1 

20 

1.739 

592.6 

612.6 

140 

271.763 

508.0 

649.2 

30 

8.155 

585.7 

615.7 

150 

358.123 

500.7 

652.2 

40 

5.491 

578.7 

618.7 

160 

465.162 

493.6 

655.3 

50 

9.198 

571.6 

621.7 

170 

596.166 

486.2 

658.3 

60 

14.879 

564.7 

624.8 

180 

754.639 

479.0 

661.4 

70 

23.309 

557.6 

627.8 

190 

944.270 

471.6 

664.4 

80 

35.464 

550.6 

630.9 

200 

1168.896 

464.3 

667.5 

90 

52.545 

543.5 

633.9 

210 

1432.480 

456.8 

670.5 

100 

76.000 

536.5 

637.0 

220 

1739.036 

449.4 

673.6 

110 

107.537 

529.4 

640.0 

230 

2092.640 

441.9 

676.6 

(301.)  Illustrations.  —  The  fact  that  heat  is  absorbed  during 
evaporation  is  illustrated  by  many  familiar  phenomena.  The 
chill  which  is  felt  on  leaving  a  bath  is  caused  by  the  rapid  evap- 
oration of  water  from  the  surface  of  the  skin,  whereby  heat  is 
withdrawn  from  the  body.  In  a  similar  way,  the  air  of  a  heated 
room  is  cooled  by  sprinkling  water  on  the  floor.  This  principle 
also  explains  how  man  is  enabled  to  bear  the  scorching  heat  of 
the  hottest  climates,  and  even,  if  properly  protected,  to  enter  an 
oven  heated  above  100°,  his  blood  not  exceeding  40° ;  a  copious 
perspiration  is  excited,  which  removes  heat  from  the  body  as 
rapidly  as  it  is  received  from  without.  The  porous  water-jars, 
which  are  used  in  Spain  and  in  Eastern  countries  to  keep  liquids 
cool,  also  owe  their  efficacy  to  the  latent  heat  of  vapors.  They 
are  made  of  biscuit  earthen-ware,  and  the  water  which  slowly 
percolates  through  the  walls  and  evaporates  from  the  surface 
withdraws  so  much  heat  from  the  vessel  as  to  retain  the  tem- 
perature of  the  water  considerably  below  the  temperature  of  the 
surrounding  air.  The  effect  is  enhanced  by  placing  the  jar  in  a 
current  of  air,  which  accelerates  evaporation.  In  like  manner, 
the  evaporation  from  the  surface  of  the  body  is  increased  in  a 
current  of  air,  and  hence  the  sensation  of  coolness  which  a  draught 
produces ;  while,  on  the  other  hand,  the  oppression  which  we  feel 
in  an  atmosphere  saturated  with  moisture  arises  from  the  fact 
that  the  evaporation  is  in  great  measure  arrested. 

The  same  principles  may  also  be  illustrated  by  a  great  variety 


HEAT.  609 

of  experiments.     One  of  the  most  striking  of  these  is  that  of 

Leslie,  in  which  water  is  frozen  by  its 
own  evaporation.  A  small  and  shallow 
pan  of  water  is  supported  over  a  dish 
of  sulphuric  acid,  and  under  a  bell-glass 
standing  on  the  plate  of  an  air-pump 
(Fig.  429).  On  exhausting  the  air 

from  the  bell,  the  heat  absorbed  by  the  very  rapid  evapora- 
tion of  the  water  which  ensues  is  so  great,  that  the  larger  por- 
tion of  the  liquid  is  converted  into  ice.  The  sulphuric  acid 
absorbs  the  vapor  as  fast  as  it  forms,  and  thus  accelerates  the 
evaporation. 

A  similar  experiment  can  be  made  with  the  instrument  rep- 
resented in  Fig.  430,  called  the  cryophorus  (frost-bearer).  It 
consists  of  two  glass  bulbs,  connected  together  by  a  long  tube, 
one  of  which  is  partially  filled  with  water.  In  making  the  in- 
strument, it  is  hermet- 
ically sealed  while  filled 
with  steam,  so  that  on 
cooling  a  vacuum  is  left 
above  the  water,  except 

f  ,,  \  Fig.  430. 

in  so  far  as  the  space  is 

filled  with  vapor.  If  now  the  empty  bulb  is  surrounded  by  a 
freezing-mixture,  this  vapor  is  condensed  as  fast  as  it  is  formed, 
and  a  very  rapid  evaporation  ensues  from  the  surface  of  the  water 
in  the  first  bulb,  which  soon  reduces  the  temperature  of  the  liquid 
to  the  freezing-point.  Even  more  marked  effects  than  these  can 
be  obtained  by  the  evaporation  of  very  volatile  liquids,  like  ether 
or  sulphide  of  carbon.  The  rapid  evaporation  of  ether  poured 
upon  the  hand  occasions  a  very  distinct  sensation  of  cold,  and 
water  can  be  frozen  by  the  evaporation  of  ether  from  the  surface 
of  a  glass  bulb  covered  with  muslin  and  kept  moistened  with  the 
liquid.  If  the  evaporation  is  accelerated  by  placing  the  apparatus 
under  the  receiver  of  an  air-pump,  even  mercury  can  be  frozen  in 
this  way.  Indeed,  an  apparatus  has  been  invented  for  making 
ice  in  warm  countries,  by  the  evaporation  of  ether  in  a  partial 
vacuum. 

The  principles  of  latent  heat  can  in  no  way,  however,  be  more 
strikingly  illustrated  than  with  liquid  carbonic  acid.  When  this 
highly  volatile  liquid  is  allowed  to  escape  into  the  air,  it  erap- 


610 


CHEMICAL   PHYSICS. 


orates  with  such  rapidity,  as  has  been  stated,  that  the  larger  por- 
tion of  it  almost  instantaneously  freezes.  This  frozen  carbonic 
acid  can  easily  be  obtained  in  large  quantities  by  means  of  the 
apparatus  of  Thilorier.  From  the  valve  of  the  receiver  5,  Fig. 
425,  a  tube  descends  to  near  the  bottom  of  the  vessel,  so  that,  on 
opening  the  valve,  the  liquid  is  forced  out  by  the  tension  of  the 
gas  in  the  interior.  A  cylindrical  brass  box,  O,  connected  with 
the  valve  of  the  receiver  by  the  coupler  L  (which  fits  in  the 
socket  Tkf),  and  so  constructed  as  to  break  the  force  of  the  jet, 
receives  the  liquid  as  it  issues  from  the  receiver,  and  soon  be- 
comes filled  with  solid  carbonic  acid,  which  resembles,  in  its 
general  appearance,  freshly  fallen  snow.  This  experiment,  it  will 
be  noticed,  is  analogous  in  principle  to  that  of  Leslie,  in  which 
water  was  frozen  by  its  own  evaporation. 

A  further  illustration  of  the  principles  of  latent  heat  is  afforded 
by  the  fact,  that  the  solid  carbonic  acid  —  if  in  considerable  quan- 
tity and  surrounded  by  poor  conductors  —  may  be  kept  exposed  to 
the  air  for  hours  before  it  entirely  disappears.  Although  exceed- 
ingly volatile,  it  evaporates  only  slowly,  for  the  same  reason  that  a 
bank  of  snow  melts  gradually  during  a  warm  spring  day.  The 
non-conducting  nature  of  the  vessel,  and  of  the  atmosphere  of  gas 
which  surrounds  it,  prevents  the  absorption  of  the  heat  which  is 
necessary  for  the  change  of  state.  If,  however,  it  is  brought  into 
close  contact  with  a  good  conductor,  like  metallic  mercury,  the  ra- 
pidity of  its  evaporation  is  greatly  accelerated,  and  the  temperature 
of  the  substance  reduced  to  that  of  the  solid  gas,  which  has  been 
estimated  as  low  as  — 90°  C.  In  this  way  large  masses  of  mercury 
can  easily  be  frozen.  A  greater  degree  of  cold  can  be  obtained  by 
mixing  the  solid  gas  with  a  little  ether,  which  forms  with  it  a  semi- 
fluid mass  capable  of  being  brought  in  closer  contact  with  sub- 
stances, and  thus  removing  their  heat  more  rapidly.  A  still  greater 
degree  of  cold  was  produced  by  Faraday,  by  placing  this  mixture 
tinder  the  receiver  of  an  air-pump  from  which  the  air  and  gaseous 
carbonic  acid  were  rapidly  removed.  An  alcohol-thermometer 
placed  in  this  mixture  sinks  to  the  temperature  of  — 110° ;  at 
this  low  temperature  the  mixture  of  solid  carbonic  acid  and  ether  ' 
is  not  more  volatile  than  alcohol  at  the  ordinary  temperature. 

Similar  experiments  can  be  made  with  the  liquid  protoxide 
of  nitrogen,  which  is  obtained  in  Bianchi's  apparatus.  As  this 
does  not  freeze  so  readily  as  liquid  carbonic  acid,  it  can  be  drawn 


HEAT.  611 

out  from  the  condenser  in  a  liquid  state,  and  retains  its  condition 
when  exposed  to  the  air  longer  than  solid  carbonic  acid.  It  can 
readily  be  frozen  by  its  own  evaporation,  and  it  furnishes  the 
means  of  producing  the  lowest  temperature  yet  attained.  When 
mixed  with  solid  carbonic  acid  and  ether,  it  produces  a  cold  so  in- 
tense, that  absolute  alcohol  exposed  to  it  assumes  the  consistency 
of  a  thick  oil,  and  a  thermometer  immersed  in  a  bath  formed 
by  mixing  this  liquid  with  sulphide  of  carbon  was  observed  by 
Natterer  to  fall  to  — 140°  when  the  bath  was  placed  in  vacuo. 

(302.)  Applications  of  the  Latent  Heat  of  Steam.  —  The  great 
amount  of  heat  which  steam  contains  renders  it  exceedingly  val- 
uable in  the  arts  as  a  heating  agent.  Water  may  be  heated,  and 
even  boiled,  in  wooden  tanks,  by  blowing  steam  into  it,  or  by 
causing  the  steam  to  circulate  through  a  coil  of  copper  pipe  at 
the  bottom  of  the  tank.  Buildings,  also,  are  very  frequently 
warmed  by  the  heat  of  steam.  The  steam  generated  in  a  boiler 
placed  in  the  basement  is  conveyed  by  iron  pipes  to  the  differ- 
ent apartments.  There  it  is  condensed  to  water  in  a  coil  of 
iron  pipes,  or  in  a  condenser  of  some  other  form,  and  the  heat 
thus  set  free  is  radiated  from  the  iron  surface  of  the  condenser. 
Steam  is  likewise  used  as  a  source  of  heat  in  the  process  of  distil- 
lation, especially  when  the  substance  to  be  heated  is  liable  to  al- 
teration from  too  high  a  temperature.  For  this  purpose,  the  walls 
of  the  still  are  frequently  made  double,  and  the  steam  admitted 
between  the  two.  It  is  sometimes  found  advantageous  to  blow  the 
steam  through  the  mass  of  liquid  in  the  still,  in  which  case  the 
volatile  product  passes  over  in  vapor  mixed  with  the  steam,  and 
the  two  are  condensed  together  in  the  worm  or  receiver.  This 
method  is  constantly  used  in  the  distillation  of  volatile  oils  from 
organic  materials.  Sometimes  the  steam  is  highly  heated  by 
passing  it  through  red-hot  tubes  before,  it  is  introduced  into  the 
still.  In  this  way  the  fat  acids  and  many  other  substances  can 
be  distilled,  which  could  not  be  distilled  in  the  ordinary  way. 
This  method  is  in  fact  the  basis  of  an  important  process  used  in 
the  arts  for  decomposing  tallow  and  other  fats,  and  extracting 
from  them  the  fat  acids  and  glycerine,  substances  which  are  used 
in  the  manufacture  of  candles  and  of  soap. 

(303.)  Spheroidal  Condition  of  Liquids. — It  has  already  been 
stated,  that  when  a  liquid  is  dropped  upon  a  heated  surface,  the 
temperature  being  made  to  vary  with  the  nature  of  the  liquid,  it 


612 


CHEMICAL  PHYSICS. 


Fig.  431. 


assumes  the  spheroidal  condition,  and  rolls  round 
on  the  surface  like  globules  of  mercury  on  a  porce- 
lain plate  (Fig.  431).  It  was 
also  stated,  that  the  temperature 
of  the  liquid  in  this  condition  is 
constant,  and  always  below  its 
boiling-point.  This  fact  can  be 
proved  by  testing  the  tempera- 
ture with  a  thermometer,  as 
shown  in  Fig.  432,  The  following  table  shows  in 
each  case,  first,  the  temperature  at  which  the  liquid 
assumes  the  spheroidal  condition  in  a  heated  silver 
capsule  ;  and,  secondly,  the  temperature  of  the 
liquid  while  in  this  condition :  — 

i.  ii. 

Water,        ',         .         .         .     171° 
Alcohol,    ....         134 


Ether,  . 
Sulphurous  Acid, 


61 


96.5 
75.8 
34.2 
—10.5 


Fig.  432. 

Boiling-Point 
100° 

78 

35 

—10 


When  in  the  spheroidal  condition,  the  globules  of  liquid  have 
a  gyratory  motion  on  the  bottom  of  the  capsule,  and  not  only 
does  the  liquid  not  boil,  but  it  evaporates  vastly  more  slowly 
than  when  it  is  in  actual  ebullition.     If  the  source  of  heat  is 
removed,  the  temperature  of  the  capsule  will  fall  until  a  point  is 
reached   at  which  the  liquid  wets   the  metallic 
surface,  and  then  the  liquid  will  boil  violently, 
and  be  thrown  in  all  directions  with  almost  ex- 
plosive violence  (Fig.  433).     This  singular  phe- 
nomenon can  also  be   shown 
by  pouring  a  small  quantity 
of  water  into  a  thick  copper 
flask    intensely   heated,    and 
corking  the  flask  while   the 
liquid  is  in   the   spheroidal   condition.     For 
a  time,  all  remains  quiet ;  but  when  the  flask 
has  cooled  sufficiently,  the  water  will  be  sud- 
denly  converted   into   steam,   and  the   cork 
thrown  out  with   great  violence  (Fig.  434). 
It  has  also  been  proved  that  a  liquid,  when 


Fig.  433. 


HEAT.  613 

in  a  spheroidal  condition,  is  not  in  contact  with  a  heated  sur- 
face.    Boutigny  was  able  to  see  the  flame  of  a  candle  between 
a  globule  of  water  rendered 
opaque  by  lampblack  and 
the  heated  surface  on  which 
it  rested  (Fig.  435)  ;  and, 
moreover,  Wartmann  and 
PoggendorfF  found  that  a 
current  of  electricity  would 
not  pass  between  the  liquid 

spheroid  and  the  metallic  Fig.  435. 

disk. 

The  explanation  of  these  singular  phenomena  has  already  been 
in  part  given.  We  have  seen  that,  whenever  by  the  action  of 
heat  the  adhesion  of  a  liquid  to  the  surface  on  which  it  rests 
becomes  less  than  twice  as  great  as  the  cohesion  between  the 
liquid  particles  themselves,  the  liquid  will  no  longer  moisten  the 
surface,  and  we  can  readily  conceive  that  it  may  be  even  re- 
pelled by  it,  and  with  a  force  sufficiently  great  to  overcome  the 
weight  of  the  liquid  mass.  That  such  a  repulsion  really  exists 
Boutigny  proved  by  two  curious  experiments.  He  poured  water 
into  a  basket  made  of  platinum  wire-netting  and  heated  to  redness, 
and  found  that  the  liquid  did  not  drop  through  the  interstices. 
He  also  whirled  round,  in  a  sling,  a  heated  capsule  containing  a 
liquid  globule  in  the  spheroidal  state,  and  found  that  the  cen- 
trifugal force  was  not  able  to  compel  contact.  Assuming,  then, 
that  the  liquid  globule  is  sustained  at  a  small  distance  above  the 
heated  surface  by  the  repulsive  force  of  heat,  it  is  easy  to  explain 
the  rest.  The  vapor  forming  on  the  lower  surface  of  the  sphe- 
roid would  raise  it  still  further  from  the  heated  metal,  and,  escap- 
ing unequally  around  the  contour  of  the  spheroid,  would  tend  to 
give  to  it  its  singular  motions.  Then,  again,  since  the  liquid 
is  not  in  contact  with  the  source  of  heat,  it  can  only  be  heated 
by  radiation.  Now  a  part  of  the  rays  of  heat  will  be  reflected 
from  the  surface  of  the  liquid  ;  and,  moreover,  the  greater  part  of 
those  which  penetrate  it  will  pass  through  it  without  being  ab- 
sorbed. It  is  evident,  then,  that  the  spheroid  will  retain  but  a 
small  portion  of  the  heat  radiated  from  the  walls  of  the  metallic 
capsule ;  and  since  it  is  all  the  time  losing  heat  by  evaporation, 
52 


614  CHEMICAL   PHYSICS. 

it  is  not  wonderful  that  its  temperature  should  be  reduced  several 
degrees  below  the  boiling-point. 

By  following  out  the  principles  of  this  section  to  their  extreme 
consequences,  we  are  able  to  produce  some  very  paradoxical 
effects.  It  has  before  been  stated,  that  water  may  be  frozen  by 
pouring  it  into  liquid  sulphurous  acid  while  the  latter  is  in  the 
spheroidal  condition,  although  the  capsule  containing  it  may  be 
red-hot.  So  also,  by  substituting  for  liquid  sulphurous  acid  the 
mixture  of  solid  carbonic  acid  and  ether,  even  mercury,  placed 
within  the  red-hot  capsule  in  a  small  platinum  crucible,  may  be 
frozen  with  equal  certainty.  The  wonder  disappears  from  these 
phenomena  when  we  know  that  these  highly  volatile  liquids  are 
not  in  contact  with  the  heated  surface  of  the  capsule,  for  they 
simply  produce  the  same  effects  in  their  spheroidal  condition  that 
they  would  under  other  circumstances.  A  still  more  paradoxical 
result  can  be  obtained  with  liquid  protoxide  of  nitrogen.  For 
this  experiment,  the  liquid  should  be  drawn  into  a  tube  sus- 
pended in  a  bottle  containing  a  few  lumps  of  chloride  of  cal- 
cium, by  means  of  a  cork  adjusted  to  the  neck.  Without  this 
precaution,  the  moisture  of  the  air  would  condense  as  hoar-frost 
on  the  tube,  and  render  the  wall  opaque.  If  we  pour  some  mer- 
cury into  this  tube,  it  will  sink  to  the  bottom  and  immediately 
freeze.  On  the  other  hand,  if  a  piece  of  burning  charcoal  is 
dropped  in,  it  will  float  on  the  liquefied  gas,  which  will  assume 
the  spheroidal  condition  around  it ;  but,  moreover,  what  is  very 
remarkable,  the  charcoal  will  burn  with  the  usual  intense  bril- 
liancy in  the  protoxide  of  nitrogen  gas  which  surrounds  it,  and 
we  shall  thus  have  in  the  same  test-tube  burning  charcoal  and 
frozen  mercury.  But  perhaps  the  most  marvellous  result  is  the 
impunity  with  which  the  moistened  hand  may  be  dipped  into 
melted  lead,  or  even  into  molten  cast-iron  as  it  flows  from  the 
furnace.  In  these  cases  the  adhering  moisture  is  converted  into 
vapor,  which  forms  an  envelope  to  the  skin  sufficiently  non- 
conducting to  prevent  the  transmission  of  any  injurious  quantity 
of  heat  during  the  short  period  of  the  immersion. 


HEAT.  615 


STEAM-ENGINE. 

(304.)  It  would  lead  us  beyond  the  design  of  the  present 
work  to  enter  upon  any  detailed  description  of  this  wonderful 
application  of  the  laws  of  vapors.  We  shall  only  be  able  to 
point  out  the  general  principles  of  the  machine,  and  to  illus- 
trate by  figures  some  of  its  most  important  forms.  It  has  al- 
ready been  shown,  that  when  water  is  confined  in  a  vacuous 
space,  this  space  becomes  filled  with  vapor,  whose  tension  de- 
pends on  the  temperature,  and  rapidly  increases  as  the  tempera- 
ture rises.  It  is  the  object  of  the  steam-engine  to  convert  this 
tension  into  mechanical  effect.  Every  steam-engine  must,  then, 
consist  of  two  parts  :  first,  the  boiler ,  in  which  the  steam  is  gen- 
erated ;  secondly,  the  machine  proper,  by  which  the  tension  of 
the  steam  is  made  to  do  mechanical  work.  We  shall  do  well  to 
examine  the  various  forms  which  are  given  to  these  parts  sepa- 
rately. 

(305.)  The  Boiler.  —  The  form  of  the  steam-boiler  varies  very 
greatly  with  the  purposes  to  which  it  is  to  be  applied,  and  on  its 
proper  construction  the  safe  and  economical  working  of  the  ma- 
chine in  great  measure  depends.  The  boiler  is  the  origin  of  the 
power  ;  it  is  where  the  heat  evolved  by  the  burning  combustible 
is  combined  with  water,  to  reappear  in  the  expansive  force  of 
steam.  The  machine  proper  merely  transmits  this  force,  and, 
like  any  other  machine,  it  can  neither  increase  nor  diminish  it, 
except  so  far  as  the  force  is  expended  in  overcoming  friction  or 
other  resistances  in  the  machine  itself. 

The  two  chief  requisites  for  a  steam-boiler  are  evidently,  first, 
the  strength  required  to  resist  the  expansive  force  of  the  steam 
without  an  unnecessary  expense  of  materials  ;  and,  secondly,  the 
capability  of  furnishing  the  amount  of  steam  required  by  the  en- 
gine in  any  given  time,  with  the  smallest  possible  expenditure  of 
fuel.  The  boilers  are  usually  made  of  plates,  either  of  wrought- 
iron  or  of  copper,  riveted  together,  and,  wheu  necessary,  are 
strengthened  by  cross  iron  stays  in  the  interior.  Copper  is  the 
best  material,  but  iron  is  almost  invariably  preferred  on  account 
of  its  cheapness.  The  thickness  of  the  plates  is  made  such  that 
the  boiler  will  resist  a  very  much  greater  tension  than  any  to 
which  it  can  ever  be  expected  to  be  exposed. 

It  is  generally  assumed,  that,  in  order  to  supply  a  steam-engine, 


616  CHEMICAL   PHYSICS. 

85  litres  of  water  must  be  evaporated  in  the  boiler  each  hour  for 
every  horse-power.  Now,  we  know  that  at  least  650  X  35  = 
22,750  units  of  heat  are  required  in  order  to  convert  35  kilo- 
grammes of  water  into  steam  ;  and  this  amount  must  therefore 
be  transmitted  during  an  hour  through  the  boiler-plates  for  every 
horse-power  of  the  engine.  But  since,  even  through  the  best 
conductors,  heat  is  transmitted  with  extreme  slowness,  so  large 
a  quantity  can  only  be  made  to  pass  by  exposing  a  large  surface 
to  the  action  of  the  flame.  Hence  the  extent  of  the  heating  sur- 
face^ and  not  the  amount  of  water  contained  in  a  boiler,  is  the 
measure  of  its  capacity  to  generate  steam.  It  is  the  general  rule 
to  allow  about  1.7  square  metres  of  heating  surface,  and  about  70 
square  centimetres  of  grate-bars  to  every  horse-power.  Moreover, 
in  order  to  obtain  the  full  effect  of  the  combustible,  it  is  essential 
that  the  heated  products  of  combustion  should  be  kept  in  con- 
tact with  the  surface  of  the  boiler  until  the  temperature  of  the 
smoke  is  reduced  as  nearly  as  possible  to  that  of  the  water  in 
the  boiler.  This  is  accomplished  by  making  the  smoke  circulate 
through  tortuous  flues  in  contact  with  the  surface  of  the  boiler. 
The  quantity  of  heat  produced  by  the  burning  combustible  is  far, 
however,  from  being  entirely  economized.  It  has  been  found,  by 
experiment,  that  the  whole  amount  of  heat  evolved  by  burning 
one  kilogramme  of  bituminous  coal  is  equal  to  about  7,500  units, 
which  would  change  into  steam  JB\°nQ  =  11.5  kilogrammes  of 
water,  if  it  all  passed  through  the  boiler-plates  into  the  water ; 
but  so  much  heat  is  lost  by  incomplete  combustion,  by  radiation, 
by  conduction  through  the  mass  of  the  furnace,  and,  finally,  by 
the  smoke,  which  must  be  discharged  into  the  chimney,  still 
heated  to  between  200°  and  400°  in  order  to  sustain  the  draught, 
that  practically  one  kilogramme  of  coal  will  not  evaporate  more 
than  from  five  to  seven  kilogrammes  of  water  with  the  best  con- 
structed furnaces. 

The  conditions  of  efficient  ac- 
tion just  considered  are  best  com- 
bined  in  what  is  termed  the  Corn- 
ish boiler,  which  is  represented  in 
Fig.  436.  It  is  cylindrical  in 
form,  frequently  over  forty  feet 
in  length,  and  from  five  to  seven 
Fte- 436.  feet  in  diameter,  with  two  flues, 


HEAT. 


617 


which  extend  the  whole  length  of  the  boiler ;  they  are  perfectly 
cylindrical,  and  of  sufficient  magnitude  to  admit  a  furnace  in 
each.  After  the  heated  gases  have  traversed  these  iron  flues, 
they  are  returned  around  the  surface  of  the  boiler  by  external 
flues  made  in  the  brick-work  which  supports  it.  The  circuit 
which  the  hot  gases  perform  in  contact  with  the  boiler  surface  is, 
not  unfrequently,  150  feet  long,  and  the  heating  surface  exposed 
to  their  action  over  3,000  square  feet.  Another  form  of  boiler 
much  used  for  stationary  engines  in  France  is  represented  in 
Figs.  437  and  438.  This  boiler  is  also  cylindrical,  but  in  the 


Fig.  437. 

place  of  the  internal  flues  used  in  the  Cornish  boiler,  the  heating 
surface  is  increased  by  means  of  two  tubes  bouilleurs,  B,  Fig. 
437,  which  are  connected  with  the  main  cylinder  by  the  vertical 
tubes  P,  P,  P.  The  flame  of  the  furnace  plays  directly  against 
the  tubes  bouilleurs ;  the  heated  gases  are  then  returned  under 
the  main  cylinder  in  the  flue  O,  Fig.  438,  and  are  finally  dis- 
charged into  the  chimney  through  the  side  flues  #,  a;,  while  a 
damper  at  R  serves  to  regulate  the  draught. 

With  a  stationary  boiler,  economy  of  fuel  is,  as  a  general  rule, 
the  great  desideratum  ;  and  in  most  cases  that  form  can  be  given 
to  it  by  which  this  end  is  best  attained.  It  is  different  with  the 
boiler  of  a  steamship  or  of  a  locomotive  engine.  With  the  first, 
economy  of  fuel  is  also  the  primary  consideration,  because,  other- 
wise, long  voyages  would  be  impossible  ;  but  economy  of  space 
must  also  be  considered,  and  it  is  therefore  essential  that  the  size 
of  the  boiler  should  be  restricted  to  quite  narrow  limits.  With 
the  locomotive,  on  the  other  hand,  speed  is,  as  a  general  rule,  the 
great  object,  and  this  must  be  attained  at  any  cost  of  fuel.  But 
52* 


618  CHEMICAL  PHYSICS. 

speed  implies  a  very  rapid  consumption  of  steam,  since  for  every 
revolution  of  the  driving-wheel  of  a  locomotive  its  two  cylinders 
must  be  filled  and  vented  twice  ;  hence  the  chief  requisite  of 
a  locomotive  boiler  is,  that  it  should  generate  the  greatest  pos- 
sible amount  of  steam  in  a  given  time.  In  all  cases,  the  ma- 
chinist endeavors  to  combine  the  requisite  conditions  as  well  as 
the  circumstances  admit,  and  the  efficiency  of  his  engine  depends 
in  great  measure  on  his  success.  Unfortunately,  he  is  guided 
almost  entirely  by  empirical  rules  ;  and  there  are  few  branches 
of  practical  art  in  which  so  much  remains  to  be  determined  and 
improved,  and  scarcely  any  which  theoretical  science  has  done  so 
littb  to  advance. 

The  usual  form  given  to  the  boiler  of  a  locomotive  is  repre- 
sented in  Fig.  4o9.  The  furnace  J.,  called  the  fire-box,  is  within 

the  boiler,  and  surrounded 
by  water  except  at  the  door 
D  and  at  the  ash-pit.  The 
flame  is  conducted  from  this 
fire-box  to  the  smoke-box  B 
through  a  large  number  of 
brass  tubes,  which  are  all 
surrounded  by  the  water  of 
the  boiler.  There  it  meets 
Fig.  439.  with  a  jet  of  steam  coming 

from    the    cylinders,    which 

creates  a  strong  draught  and  drives  the  waste  gases  up  the  chim- 
ney. The  boiler  of  a  locomotive  is  surmounted  by  the  steam- 
dome,  E ;  and  a  tube  with  a  funnel-shaped  orifice,  opening  near 
the  top  of  this  dome,  receives  the  steam  and  conveys  it  to  the 
cylinders  through  F.  This  arrangement  prevents,  to  a  great 
degree,  the  spray,  which  rises  from  the  water  of  the  boiler 
and  is  mixed  with  the  steam  in  the  upper  part  of  it,  from 
reaching  the  cylinders  ;  as  the  steam  ascends  the  steam-dome, 
this  spray  falls  back,  and  nothing  but  pure  steam  enters  the 
tube. 

The  steam-boiler  is  always  provided  with  several  appendages 
for  the  purpose  of  regulating  the  quantity  of  water,  for  meas- 
uring the  tension  of  the  steam,  and  for  preventing  the  accu- 
mulation of  a  pressure  which  would  endanger  the  safety  of  the 
boiler. 


HEAT.  619 

It  is  essential  for  the  good  working  of  the  boiler,  that  the 
water  should  always  cover  the  whole  heating  surface ; '  hence 
it  must  be  maintained  above  the  level  of  the  flues.  The  water 
is  supplied  to  the  boiler  through  the  pipe  a  (Fig.  437),  which 
reaches  nearly  to  the  bottom.  This  pipe  communicates  either  with 
an  elevated  reservoir,  or  with  a  force-pump  moved  by  the  engine, 
the  size  of  the"  pump  being  so  adjusted  that  the  amount  of  water 
forced  into  the  boiler  during  a  given  time  shall  be,  as  nearly  as 
possible,  equal  to  that  which  escapes  in  the  condition  of  steam 
through  the  steam-pipe  v  during  the  same  interval.  This  adjust- 
ment, however,  is  necessarily  imperfect ;  and  hence  a  great  variety 
of  inventions,  by  which  the  supply  of  water  is  regulated  automati- 
cally, and  made  to  depend  on  the  position  of  the  water-level  in 
the  boiler.  Various  contrivances  are  in  use  for  indicating  to  the 
engineer  the  height  of  the  water.  One  of  the  simplest  of  these  is 
the  glass  gauge  represented  at  n  (Fig.  437).  It  consists  of  a  thick 
glass  tube  firmly  cemented  into  iron  caps,  by  means  of  which  it 
communicates  with  the  interior  of  the  boiler.  It  is  so  placed, 
that,  when  the  water  is  at  the  proper  level,  the  lower  end  shall 
open  below  the  surface  of  the  water,  and  the  upper  end  above  it ; 
consequently,  the  water  will  always  stand  at  the  same  level  in  the 
tube  as  in  the  boiler.  Another  kind  of  indicator  is  .represented  at 
/'.  It  consists  of  a  float,  which  is  connected  with  a  counterpoise 
by  a  metallic  wire  passing  over  a  pulley,  and  through  a  packing- 
box  in  the  top  of  the  boiler.  The  position  of  the  level  of  the 
water  is  indicated  either  by  the  position  of  the  counterpoise,  or  by 
a  needle  attached  to  the  axis  of  the  pulley,  and  moving  over  a 
graduated  disk.  Some  boilers  are  also  provided  with  an  alarm- 
whistle,  $,  so  arranged  that  it  is  opened  by  the  float  /  when  the 
level  of  the  water  falls  too  low. 

The  tension  of  the  steam  in  the  interior  of  the  boiler  is  indi- 
cated by  a  manometer,  which  may  be  either  of  those  already 
described  (Figs.  104,  273,  or  279). 

In  order  to  limit  the  tension  of  the  steam,  every  boiler  is  fur- 
nished with  one  or  more  safety-valves,  represented  at  P  (Fig.  437), 
and  also  in  detail  in  Fig.  440.  The  valve  is  kept  closed  by  the 
weight  P,  acting  on  the  lever  O,  and  this  weight  is  so  adjusted 
to  the  area  of  the  valve,  that  the  valve  will  open  as  soon  as 
the  tension  of  the  steam  exceeds  a  limited  amount.  The  area  of 
the  valve  is  adjusted  to  the  extent  of  the  heating  surface  of  the 


620  CHEMICAL   PHYSICS. 

boiler,  and  to  the  maximum  tension  at  which  the  boiler  can  be 
worked  with  safety.  It  is  determined  by  means  of  the  empirical 
formula, 

d  =  23 


//— 0.412 


in  which  d  is  the  diameter  of  the  valve,  S  the  area  of  the  heating 
nirface  of  the  boiler,  and  H  the  maximum  tension  of  the  steam. 
It  has  been  found  that  a  valve  with  the  dimensions  given  by  this 


Fig.  440. 

formula  will  allow  all  the  steam  to  escape  which  can  be  generated 
by  the  most  active  fire  ;  but,  for  greater  security,  a  boiler  is  gen- 
erally provided  with  two  valves  of  these  dimensions. 

We  can  also  limit  the  tension  of  the  steam  by  fixing  a  limit  to 
its  temperature.  This  can  be  done  by  closing  a  tubulature 
adapted  to  the  upper  part  of  the  boiler  with  a  plate  made  of 
fusible  alloy,  whose  proportions  have  been  so  adjusted  (272)  that 
it  shall  melt  when  the  steam  attains  the  temperature  which  cor- 
responds to  the  maximum  tension  which  the  boiler  is  calculated 
to  sustain.  This  plate,  which  is  quite  brittle,  is  held  in  its  place 
by  an  iron  collar,  and  protected  by  an  iron  grating,  which  ena- 
bles it  to  resist  the  pressure  of  the  steam.  The  use  of  these 
plates,  however,  is  liable  to  serious  objections.  They  not  only 
render  the  boiler  unserviceable  for  the  time,  if  they  yield,  but, 
moreover,  the  melting-point  of  the  plate  is  liable  to  a  change 
from  the  eliquation  of  the  more  fusible  metal. 

(303.)  Dimensions  of  Steam-Boilers.  —  As  in  the  last  sec- 
tion the  dimensions  of  the  steam-boiler  were  given  in  French 
measure,  it  may  be  well  to  add  the  following  English  data,  taken 
from  the  Encyclopaedia  Britannica,  Article  Steam-Engine,  pre- 
mising that  by  a  horse-power  is  meant  a  force  of  that  intensity 
which  will  raise  33,000  pounds  one  foot  per  minute,  or  nearly 
2,000,000  pounds  one  foot  per  hour. 


HEAT.  621 

Conditions  for  each  Horse-Power.         Ordinary      Cornish 

Standard.         Boiler. 

Quantity  of  water  to  be  evaporated  per  hour  in  cubic  feet,  1              1 

Volume  of  water  in  boiler  in  cubic  feet,          .         .  10  or  more. 

Volume  of  steam  in  steam-chamber  in  cubic  feet,        .  10  or  more. 

Area  of  fire-grate  in  square  feet,            ....  1              2 

Area  of  heating  surface  in  square  feet,      .         .         .  15  60  to  70 

Circuit  of  flues  in  linear  feet,        .....  60         150 

Results. 

Bituminous  coal  per  hour  for  each  horse-power,     .         .  lOlbs.    5*lbs. 

Water  evaporated  by  each  pound  of  coal,          .         .  6  "    llf  " 
Bituminous  coal  consumed  per  hour  for  each  square  foot 

of  grate, 10  "      2|  " 

(307.)  Watt's  Condensing- Engine.  —  The  steam-engine,  in 
its  present  form,  was  invented,  between  the  years  1763  and  1769, 
by  James  Watt,  originally  a  maker  of  philosophical  instruments 
in  Glasgow.  This  invention  stands  without  a  parallel  in  the 
history  of  the  mechanic  arts.  Perfect  almost  from  its  first  con- 
ception even  in  its  minutest  details,  it  has  since  received  no 
improvement  involving  a  single  principle  unknown  to  Watt.  It 
is  true  that  we  have  machines  at  the  present  day  which,  not 
only  in  magnitude,  but  also  in  the  perfection  of  the  mechanical 
details,  and  in  the  beauty  and  simplicity  of  the  combination  of 
the  several  parts,  far  exceed  any  Watt  ever  saw  ;  but  all  these 
improvements  have  been  only  the  necessary  development  of  his 
first  conception. 

Most  of  the  parts  of  the  condensing-engine  are  shown  in  Fig. 
441,  which,  although  necessarily  imperfect  in  its  details,  will 
serve  to  illustrate  the  relation  of  the  parts.  The  most  essential 
part  of  the  machine  is  the  large  cast-iron  cylinder  (shown  on  the 
left-hand  side  of  the  cut),  within  which  moves  the  piston  P. 
The  interior  of  this  cylinder  is  turned  on  a  lathe,  so  as  to  be 
perfectly  true,  and  the  sides  of  the  piston  are  made  elastic  by 
what  is  termed  the  packing,  which  prevents  any  leakage  of  the 
steam  around  the  edge.  The  surfaces  of  this  piston  receive 
directly  the  pressure  of  the  steam  ;  and  it  is  therefore  to  be  re- 
garded as  the  point  of  application  of  the  expansive  force,  and 
the  origin  of  the  motion  of  the  engine.  The  steam  generated 
in  the  boiler  just  described,  and  conveyed  to  the  machine  through 
the  steam-pipe,  is  first  received  into  the  valve-chest  b  through  the 


622 


CHEMICAL  PHYSICS. 


aperture  o,  and  from  this  it  is  admitted  alternately  into  the  top 
and  bottom  of  the  cylinder  by  a  sliding-valve,  which  is  moved  by 
the  rod  b  m,  passing  through  a  packing-box  on  top  of  the  valve-chest. 


Fig.  441. 

The  same  valve  also  opens  and  closes  the  vent-hole  a,  by  which 
the  steam,  after  having  done  its  work  in  moving  the  piston,  is 
discharged  alternately  from  either  end  of  the  cylinder  through 
the  eduction-pipe  U.  When  the  valve  is  in  the  position  repre- 
sented in  Fig.  441,  the  steam  has  free  access  to  the  upper  part  of 
the  cylinder,  and  presses  on  the  top  of  the  piston,  while  from  the 
space  below  the  piston  a  vent  is  opened  through  the  tube  a  U. 
Consequently  the  piston  falls ;  but  when  it  reaches  the  bottom  of 
the  cylinder,  the  position  of  the  valve  is  suddenly  changed  to  that 
represented  in  Fig.  442,  and  a  connection  is  opened  between  the 
upper  part  of  the  cylinder  and  the  eduction-pipe,  while  at  the 
same  time  the  steam  is  admitted  below  the  piston,  whose  motion 
is  thus  reversed.  When  the  piston  reaches  the  top  of  the  cylin- 


HEAT. 


623 


der,  the  position  of  the  valve  is  again  changed ;  and  thus  continu- 

rvndv    sn  t.hnt.  n.  rpp.inror.atirifr  motion  i<j  t.lip  rtxmlf        TMiic    mrvtinn 


ju&iiiuii  UA  LUC  vtiivc  10  a^ixm  uiictngtju ;  ana  uiuo  coiiiinu- 
ously,  so  that  a  reciprocating  motion  is,  the  result.     This  motion 
communicated  by  the  piston-rod  A,  which  passes  steam-tight 


is 


Fig.  442. 


through  the  packing-box  d,  on  the  head  of  the  cylinder,  to  one 
arm  of  the  large  lever  L,  called  the  beam,  and  by  the  beam  it  is 
further  transmitted  through  the  connecting-rod  I  to  the  crank  K, 
which  turns  the  shaft  of  the  engine,  and  gives  motion  to  the  ma- 
chinery connected  with  it. 

Fly- Wheel. — When  the  piston  is  at  the  top  of  the  cylinder,  the 
crank  is  in  its  lowest  position  ;  and,  on  the  other  hand,  when  the 
piston  is  at  the  bottom  of  the  cylinder,  the  crank  is  in  its  highest 
position.  In  either  of  these  positions,  called  the  dead  points,  it 
is  obvious  that  the  pressure  of  the  steam  can  communicate  no 
motion  to  the  crank,  and  the  machine  would  come  to  rest  were  it 
not  for  the  large  iron  wheel  V,  called  the  fly-wheel,  which  is 
attached  to  the  shaft  and  revolves  with  it.  This  wheel,  which 
has  a  large  mass  of  matter  in  its  rim,  having  once  received  a 
certain  velocity  of  rotation  on  its  axis,  carries  by  its  inertia  the 
crank  and  piston  through  the  dead  points,  and  brings  them  into 
a  position  in  which  the  power  becomes  effective. 


624  CHEMICAL  PHYSICS. 

The  fly-wheel,  moreover,  equalizes  the  motion  of  the  machine, 
and  gives  a  uniformity  to  its  action  it  could  not  otherwise  have, 
owing  to  the  imequal  leverage  at  which  the  connecting-rod  acts 
on  the  crank  in  its  different  positions.  Then,  again,  the  uni- 
form rotation  of  the  wheel  acts  back  upon  the  piston  through 
the  crank  with  the  happiest  effect,  bringing  the  piston  slowly  to 
rest  at  the  end  of  each  stroke,  and  thus  preventing  the  jar  which 
would  result  from  a  sudden  change  in  the  direction  of  the  mo- 
tion. Indeed,  this  whole  combination  is  one  of  the  happiest 
results  of  mechanics,  and  will  repay  the  most  careful  study.  A 
fly-wheel  is  only  essential  in  a  stationary  engine.  In  the  engine 
of  a  steamboat  or  a  locomotive,  the  same  effect  is  produced  by 
the  momentum  of  the  moving  mass. 

Parallel  Motion. — The  system  of  jointed  rods  CDE  (Fig.  441), 
by  which  the  piston-rod  is  connected  with  the  beam,  called  the 
parallel  motion,  is  an  ingenious  invention  of  Watt  to  prevent  any 
lateral  strain  on  the  former.  Since  the  end  of  the  piston-rod  must 
move  in  a  vertical  line,  while  the  end  of  the  beam  describes  the  arc 
of  a  circle  coinciding  with  this  line  only  at  one  point,  it  is  easy 
to  see  that  they  could  not  be  directly  jointed  together ;  and  it 
can  also  be  readily  shown,  by  the  principle  of  the  composition  of 
forces,  that,  if  they  were  connected  by  the  rod  D  alone,  a  lateral 
strain  would  be  exerted  on  the  piston-rod  which  would  soon  de- 
range the  machinery.  By  means  of  the  system  of  rods  repre- 
sented in  the  figure,  the  end  of  the  piston-rod  is  suffered  to 
move  in  a  vertical  direction,  and  the  lateral  force  resulting  from 
the  decomposition  of  the  motion,  in  its  transmission  to  the  beam, 
is  balanced  by  the  resistance  of  the  rods  C  and  E,  called  radius 
bars,  which  are  connected  by  joints  to  the  frame  of  the  engine. 

The  parallel  motion  of  Watt  does  not  completely  answer  its 
object,  that  is,  it  does  not  cause  the  end  of  the  piston-rod  to  move 
in  an  absolutely  straight  line  ;  and  when  the  stroke  of  the  piston 
bears  a  large  proportion  to  the  length  of  the  beam,  the  deviation 
from  a  straight  line  becomes  of  practical  importance.  Hence, 
a  large  number  of  other  parallel  motions  which  have  been  in- 
vented to  remedy  this  defect.  One  of  the  simplest  contrivances 
for  the  purpose,  and  the  one  generally  used  in  this  country, 
consists  in  directing  the  motion  of  the  piston-rod  by  a  cross-piece 
sliding  in  vertical  grooves,  which  are  kept  in  their  place  by  a 
stiff  frame-work. 


HEAT.  625 

The  Eccentric. —  It  has  already  been  shown  that  the  connec- 
tions between  the  ends  of  the  cylinder  and  the  boiler  or  vent- 
tube  may  be  alternately  opened  and  closed  by  a  sliding  motion 
given  to  the  valve  ;  it  now  remains  to  show  how  this  motion 
is  obtained  automatically.  A  wheel  (J£,  Fig.  442),  called  the 
eccentric,  is  so  attached  to  the  main  shaft  of  the  engine  that  its 
centre  does  not  coincide  with  the  axis  of  rotation.  This  eccen- 
tric revolves  within  a  metallic  ring,  (7,  and  imparts  to  it  a  back- 
ward and  forward  motion,  which  is  transmitted  by  the  arm  Z  Z 
to  a  bent  lever,  S  o  y ,  and  by  that  to  the  rods  d  and  6,  which  act 
directly  on  the  valve.  The  extent  of  the  motion  of  the  valve 
is  easily  regulated  by  the  length  of  the  arms  of  the  lever,  and 
the  moment  at  which  it  begins  to  move  in  either  direction  is 
determined  by  the  position  of  the  eccentric  on  the  shaft.  In 
starting  the  engine,  or  in  reversing  its  motion,  the  valves  aro 
moved  by  hand,  and  there  is  always  a  handle  connected  with  the 
lever  S  o  y  for  the  purpose.  It  is  not  until  after  the  fly-wheel 
has  acquired  a  certain  momentum,  that  the  arm  Z  Z  of  the 
eccentric  is  geared  on  to  the  lever  at  S.  In  order  to  stop  the 
engine,  the  arm  is  ungeared  and  the  motion  of  the  valves  regu- 
lated, as  before,  by  hand.  There  is  no  part  of  the  steam-engine 
on  which  more  ingenuity  has  been  shown  than  on  the  valves,  and 
the  automatic  machinery  for  opening  and  closing  them.  The  form 
of  the  valve  represented  in  the  above  figures  is  the  simplest,  and 
is  very  generally  used  in  small  engines ;  but  in  large  engines 
there  are  frequently  four  separate  valves,  which  are  opened  and 
closed  independently. 

The  Condenser.  —  If  the  eduction-pipe  U (Fig.  441)  opened  di- 
rectly into  the  atmosphere,  the  engine  would  work  perfectly  well 
with  only  the  parts  which  have  been  now  described  ;  only  there 
would  be  a  loss  of  power :  for  a  portion  of  the  expansive  force  of 
steam  would  be  expended  in  overcoming  the  pressure  of  the  air. 
Watt  avoided  a  part  of  this  loss  by  an  application  of  the  well- 
known  law  (287),  that  the  tension  of  any  vapor  in  vessels  com- 
municating with  each  other  is  always  that  which  corresponds  to 
the  temperature  of  the  coldest  vessel.  He  connected  the  educ- 
tion-tube of  his  engine  with  a  larged  closed  iron  box  ( O,  Fig, 
441),  called  the  condenser,  so  that  whenever  by  the  motion  of 
the  valve  the  orifice  of  the  eduction-tube  is  opened,  the  waste 
steam  rushes  at  once  into  the  cold  vessel,  leaving  a  partial 
53 


626  CHEMICAL  PHYSICS. 

vacuum  in  the  cylinder,  against  which  the  fresh  steam  acts  with 
nearly  its  full  force. 

The  gain,  however,  thus  obtained  is  not  so  great  as  it  would 
at  first  sight  seem,  since  a  portion  of  the  power  thus  realized  is 
expended  in  working  the  pumps  connected  with  the  condenser. 
In  order  to  produce  a  sudden  condensation  of  the  steam,  it  is 
necessary  to  discharge  into  the  condenser  a  constant  stream  of 
water.  This  water,  forced  in  by  the  atmospheric  pressure  through 
the  pipe  T  (Fig.  441),  which  ends  in  what  is  termed  a  rose,  is 
showered  in  fine  jets  through  the  chamber.  The  amount  of  water 
which  it  is  thus  necessary  to  introduce  is  at  least  twenty  times  as 
great  as  the  weight  of  steam  condensed,  and  would  soon  fill  the 
condenser.  Hence  the  necessity  of  the  pump  M,  worked  from 
the  beam  of  the  engine,  by  which  both  the  hot  water  and  any 
air  that  may  be  mixed  with  it  are  rapidly  removed,  and  the 
water  discharged  into  the  hot  well  N.  The  piston  of  this  pump, 
called  the  air-pump,  has  generally  about  one  half  of  the  area  and 
one  half  of  the  stroke  of  the  large  piston,  and  the  general  ar- 
rangement of  its  valves  may  be  seen  in  Fig.  443.  The  condenser 
is  usually  entirely  immersed  in  a  tank  of  water,  called  the  cold 
well,  which  is  fed,  when  possible,  by  an  aqueduct,  or  otherwise 
by  a  suction-pump,  as  R,  Fig.  441,  worked  by  a  rod  attached 
to  the  beam  of  the  engine,  and  drawing  its  water  from  some 
neighboring  well.  Still  a  third  pump  is  frequently  attached  to 
the  beam,  which  draws  water  from  the  hot  well  and  forces  it  into 
the  boiler.  The  supply  of  water  to  the  condenser  is  regulated 
by  a  valve  so  placed  as  to  be  at  the  command  of  the  engineer, 
and  before  stopping  the  machine  it  is  necessary  to  close  "this 
valve. 

The  machine  which  has  just  been  described  may  be  regarded 
as  a  representative  steam-engine.  The  student  must  not  expect 
to  find  the  parts  of  an  actual  working  engine  as  simple,  or  com- 
bined in  the  same  way,  as  those  represented  in  Fig.  441 ;  but 
having  once  become  familiar  with  the  parts,  as  they  are  shown  in 
this  figure,  he  will  be  able  readily  to  recognize  them  in  a  work- 
ing engine,  and  to  trace  out  the  connection  of  their  motions. 

(308.)  Single-acting'  Steam-Engine. — When  the  steam-engine 
is  used  for  pumping  water,  which  was  at  first  its  only  practical 
application,  its  force  is  required  only  in  raising  the  pump-rods 
with  their  load  of  water,  their  own  weight  being  more  than 


HEAT. 


627 


sufficient  for  their  descent.  If  the  piston  and  pump  rods  are 
attached  to  opposite  ends  of  a  working-beam,  the  force  of  the 
steam  is  only  required  in  pressing  the  piston  down ;  and  there  is, 


Fig.  443. 

therefore,  no  necessity  of  admitting  the  steam  to  the  bottom  of 
the  cylinder.  Engines  constructed  for  this  purpose,  in  which  the 
steam  acts  only  on  one  side  of  the  piston,  are  called  single-acting 
engines,  to  distinguish  them  from  the  double-acting  engines  de- 
scribed in  the  last  section.  They  are  generally  used  for  pumping 
water  from  mines,  and  are  frequently  called  Cornish  engines, 
because  they  were  brought  to  perfection  in  the  mining  district  of 
Cornwall,  in  England.  A  representation  of  one  of  these  engines 
is  given  in  Fig.  443. 

The  steam  from  the  boiler  enters  the  valve-chest  by  the  tube 
T.  A  rod,  d,  passing  through  a  packing-box  in  the  top  of  the 
valve-chest,  moves  three  valves,  w,  w,  o.  The  valves  m  and  o 
open  upward,  while  the  valve  n  opens  downward.  When  the 
valves  are  in  the  position  represented  in  the  figure,  m  and  o  open 
and  n  closed,  the  steam  from  the  boiler  exerts  its  full  effect  on 
the  upper  surface  of  the  piston,  and  presses  it  down ;  but  just 


628  CHEMICAL  PHYSICS. 

before  the  piston  reaches  the  lowest  point  of  its  course,  a  projec- 
tion, 6,  on  the  rod  -F,  moved  by  the  beam,  strikes  the  arm  of  a 
bent  lever,  d  c  k,  which,  acting  on  the  valve  rod  at  d,  causes  it  to 
descend,  thus  closing  the  valves  w,  o,  and  opening  the  valve  w, 
called  the  equilibrium  valve.  All  connection  between  the  cylin- 
der and  either  the  boiler  or  condenser  is  now  closed  ;  but  the  two 
ends  of  the  cylinder  freely  communicating  together,  the  piston  is 
raised  by  the  weight  of  the  pump-rod  Q,  while  the  steam  passes 
from  the  top  to  the  bottom  of  the  cylinder  through  the  tube  C. 
As  the  piston  now  reaches  the  top  of  the  cylinder,  a  second  pro- 
jection, a,  on  the  rod  F,  strikes  the  end  of  the  bent  lever  and 
restores  the  valves  to  their  first  position  ;  then  the  piston  descends 
as  before,  and  so  continuously.  Parallel  motion  is  obtained  in 
these  engines  by  the  very  simple  arrangement  represented  in  the 
figure,  and  the  condenser  is  the  same  as  that  described  in  the  last 
section.  The  efficiency  of  these  engines  is  estimated  by  the 
number  of  pounds  of  water  which  they  are  capable  of  elevating 
one  foot  by  the  combustion  of  one  bushel  of  coal.  This  number 
is  termed  the  duty  of  the  engine.  By  a  careful  construction 
and  management  of  the  engine  and  boiler,  this  duty  has  been 
raised  as  high  as  125,000,000  pounds. 

(309.)  The  Non-condensing  Engine. — This  form  of  the  steam- 
engine  differs  from  those  just  described  only  in  this,  that  it  has 
no  condenser,  and  the  steam  is  vented  from  the  cylinder  directly 
into  the  atmosphere.  Although,  for  the  reasons  already  stated,  it 
cannot  be  worked  so  economically  as  the  condensing  engine,  it 
has  the  advantage  of  greater  simplicity  and  compactness,  and  its 
first  cost  is  much  less  than  that  of  its  more  cumbrous  rival.  It 
is  therefore  frequently  preferred  when  these  considerations  are  of 
more  importance  than  the  saving  of  a  few  tons  of  coal.  There  is 
nothing  peculiar  in  the  construction  of  this  form  of  engine,  and 
.either  of  the  machines  just  described  might  be  converted  into  a 
non-condensing  engine  by  simply  cutting  off  the  eduction-tube 
and  disconnecting  the  pump-rods  from  the  beam.  Of  this  class 
the  most  important  is  the  locomotive  engine  (Fig.  444),  and 
we  have  selected  it  as  an  example.  The  construction  of  the 
boiler  of  a  locomotive  has  already  been  described  ;  and  since 
we  are  now  acquainted  with  the  construction  of  the  single  parts 
of  a  steam-engine,  it  will  only  be  necessary  to  point  them  out 
in  the  figure. 


HEAT. 


629 


X  X  is  the  main  body  of  the  boiler  ;  JD,  the  lower  part  of  the 
fire-box ;  Y,  the  smoke-box ;  o,  the  brass  tubes  connecting  the 
two ;  O,  the  fire-door,  by  which  the  fuel  is  introduced  ;  n,  the 


water-gauge,  indicating  the  level  of  the  water  in  the  boiler ; 
H,  the  vent-cock,  by  which  the  water  can  be  discharged  from  the 
boiler  ;  E,  H,  the  feeders  which  conduct  water  from  the  tender 
to  two  force-pumps  (not  shown  in  the  drawing),  by  which  it  is 


630  CHEMICAL   PHYSICS. 

forced  into  the  boiler ;  Z  Z,  the  dome  of  the  boiler ;  t,  the  safety- 
valves,  which  are  held  in  place  by  spiral  springs  enclosed  in  the 
cases  e;  g,  the  steam-whistle  ;  /,  the  valve  opening  into  the 
steam-pipe  ;  6r,  a  rod  which  controls  the  motion  of  the  valve. 
In  the  drawing,  the  engineer  holds  in  his  hand  the  lever  by  which 
this  rod  is  turned  and  the  valve  opened  more  or  less,  as  cir- 
cumstances may  require  ;  a  graduated  arc,  over  which  the  lever 
moves,  enables  him  to  adjust  the  valve  to  any  position,  and  thus 
to  regulate  the  speed  of  the  engine.  A  is  the  steam-tube,  which 
conducts  the  steam  from  the  top  of  the  dome  to  the  two  cylin- 
ders ;  this  tube  passes  through  the  boiler  into  the  smoke-box, 
where  it  branches,  as  shown  by  dotted  lines  in  the  figure  ;  by 
this  arrangement  any  condensation  of  the  steam,  while  passing 
through  the  pipe,  is  prevented.  F  is  one  of  the  cylinders  ;  there 
is  another  on  the  other  side  of  the  smoke-box  ;  the  steam  is 
admitted  into  the  ends  of  these  cylinders  and  discharged  from 
them,  by  means  of  sliding  valves  worked  by  eccentrics  on  the  axle 
of  the  driving-wheels ;  there  are  generally  two  sets  of  these  ec- 
centrics placed  in  opposite  positions  on  the  axle,  one  set  for  the 
forward  and  the  other  for  the  backward  motion  of  the  locomotive, 
and  so  arranged  that  they  can  be  thrown  out  of  gear  or  brought 
into  action  at  the  pleasure  of  the  engineer.  All  this  part  of  the 
machinery,  however,  being  beneath  the  boiler,  is  not  visible  in 
the  drawing.  E  is  the  eduction-tube,  by  which  the  steam  is 
discharged  from  the  cylinder  into  the  smoke-pipe  Q ;  £,  t  are  stop- 
cocks, by  which  any  water  condensed  in  the  cylinders  may  be 
vented  ;  P  is  the  piston  ;  F,  the  packing-box,  through  which 
passes  the  piston-rod  ;  r  r  are  guides,  corresponding  to  the  par- 
allel motion  of  the  stationary  engine,  by  which  the  piston-rod  is 
forced  to  move  in  a  straight  line,  and  any  lateral  strain  pre- 
vented ;  and,  finally,  K  is  the  connecting-rod,  by  which  the 
motion  of  the  piston  is  communicated  to  the  crank  M  on  the 
axle  of  the  large  driving-wheels.  In  starting  the  locomotive,  as 
in  the  other  forms  of  the  steam-engine,  the  valves  must  be  moved 
by  hand  ;  a  lever,  communicating  with  the  valves  by  means  of 
connecting-rods,  marked  B  and  C  in  the  figure,  is  always  pro- 
vided for  this  purpose  near  the  front  of  the  engine.  It  is  only 
when  the  train  is  in  motion,  and  its  momentum  sufficient  to 
.regulate  the  movements  of  the  machine,  that  the  eccentrics  are 
thrown  into  gear. 


HEAT.  631 

(310.)  Mechanical  Power  of  Steam.  —  We  can  easily  calcu- 
late the  mechanical  power  generated  by  the  conversion  of  water 
into  steain  from  the  known  increase  of  volume  *  which  accompa- 
nies this  change.  For  this  purpose,  let  us  assume  that  we  have 
a  tall  cylindrical  vessel,  open  at  the  top,  the  area  of  whose  base 
is  one  square  decimetre.  Let  us  further  assume  that  the  cylinder 
is  filled  with  water  at  4°  to  the  depth  of  one  decimetre,  and  con- 
tains, therefore,  one  litre  or  one  kilogramme  of  the  liquid  ;  and, 
lastly,  let  us  assume  that  a  piston  without  weight,  and  moving 
steam-tight  without  friction  in  the  cylinder,  rests  on  the  surface 
of  the  water.  If  now  we  raise  the  temperature  of  this  cylinder 
to  100°,  and  furnish  it  with  a  constant  supply  of  heat,  the  water 
will  change  into  steam,  occupying  1,698.5  times  its  former  vol- 
ume, and  having  a  tension  of  76  c.  m.,  or  one  atmosphere  ; 
which  will  therefore  raise  the  piston  1,697.5  decimetres  under  the 
atmospheric  pressure,  that  is,  will  raise  103.33  kilogrammes  to 
the  height  of  169.75  metres.  The  mechanical  power  thus  exerted 
is,  then,  equal  to  17,540  kilogramme-metres  (compare  238).  If 
we  raise  the  temperature  to  120°. 6,  and  furnish  a  constant  supply 
of  heat,  as  before,  the  water  will  change  into  steam  occupying 
896.22  times  its  former  volume,  and  having  a  tension  of  two 
atmospheres.  It  will,  therefore,  raise  the  piston  895.22  decime- 
tres under  the  pressure  of  the  air,  when  loaded  with  an  additional 
weight  of  103.33  kilogrammes,  thus  exerting  a  mechanical  power 
of  206.66  X  89.522  =  18,501  kilogramme-metres.  In  like  man- 
ner, the  other  values  given  in  the  fourth  column  of  the  following 
table  may  be  easily  calculated  :  — 


Tempera- 
ture of 
Steam. 

Tension 
in  Atmos- 
pheres. 

Volume  of 
1  Kilogramme 
in  Litres. 

Power  in 
Kilogramme- 
metres. 

Total  Heat 
absorbed  in 
Evaporation. 

Power  from 
1  Heat  Unit  in 
Kilog.-metres. 

ioo!o 

1 

1.698.5 

17,540 

637.0 

27.53 

120.6 

2 

896.22 

18,501 

643.3 

28.76 

144.0 

4 

474.81 

19,583 

650.4 

30.11 

170.8 

8 

252.67 

20,804 

658.6 

31.59 

By  comparing  the  conditions  assumed  above  with  those  in  an 
actual  steam-engine,  it  will  be  seen  that  the  power  given  in  the 

*  The  volume  of  the  steam,  as  compared  with  that  of  an  equal  weight  of  water  at 
4°,  can  always  he  obtained  by  dividing  the  weight  of  one  cubic  metre  of  water  at  4° 
(one  million  grammes)  by  the  weight  of  one  cubic  metre  of  steam  as  given  in  the  table 
on  page  571. 


632  CHEMICAL   PHYSICS. 

above  table  is  the  greatest  possible  power  which  can  be  obtained 
by  the  conversion  into  steam  of  one  kilogramme  of  water  at  the 
different  temperatures ;  provided,  as  we  assumed  in  the  descrip- 
tion of  the  steam-engine  (307),  that  the  tension  of  the  steam 
does  not  change  from  the  time  it  leaves  the  boiler  until  it  is  dis- 
charged into  the  condenser,  and  provided,  also,  that  the  steam 
acts  against  a  perfect  vacuum.  These  conditions  are  never  fully 
realized  in  practice,  so  that  even  with  the  best  regulated  ma- 
chines we  only  obtain  from  one  half  to  two  thirds  of  the  theo- 
retical effect. 

The  total  number  of  units  of  heat  required  to  change  one 
kilogramme  of  water  into  steam  of  one,  two,  four,  and  eight 
atmospheres'  pressure,  as  calculated  by  [202],  is  given  in  the 
fifth  column  of  the  above  table,  and  the  sixth  column  shows  the 
power  obtained  in  each  case  by  the  expenditure  of  one  unit  of 
heat.  It  will  be  noticed  that  the  power  is  nearly  the  same  in 
all  cases,  and  hence  it  follows,  apparently,  that  no  important  gain 
is  obtained  by  the  use  of  steam  of  high  tension.  There  is,  how- 
ever, a  mode  of  working  the  steam-engine  in  which  the  gain  thus 
effected  is  very  great. 

Let  us  suppose  that  the  boiler  is  supplying  steam  of  four  atmos- 
pheres, which,  as  the  table  shows,  it  can  supply  at  only  a  little 
greater  expenditure  of  heat  (in  other  words,  of  fuel)  than  steam 
of  one  atmosphere  pressure.  If  the  engine  were  worked  with 
steam  of  one  atmosphere  pressure  under  the  conditions  described 
above,  each  volume  of  steam  equivalent  to  the  capacity  of  the 
cylinder,  and  weighing,  as  we  will  suppose,  one  kilogramme,  will 
do  the  work  of  raising  103.33  kilogrammes  through  a  height 
equal  to  the  length  of  the  stroke  of  the  piston.  Speaking  ap- 
proximatively,  the  same  weight  of  steam  of  four  atmospheres' 
tension  will  do  an  equivalent  work  during  the  first  quarter  of  the 
stroke  ;  for  it  will  raise  four  times  103.33  kilogrammes  through 
one  fourth  of  the  previous  height.  Suppose,  now,  that  the  con- 
nection between  the  cylinder  and  the  boiler  is  closed  at  this  point, 
it  is  evident  that  the  steam  will  continue  to  exert  an  expansive 
force,  although  a  force  lessening  gradually  as  the  capacity  of  the 
cylinder  increases.  When  the  piston  has  been  raised  through 
one  half  of  the  stroke,  the  volume  of  the  kilogramme  of  steam 
will  have  doubled,  and  its  tension  have  been  reduced  to  two  at- 
mospheres ;  when  it  has  achieved  three  fourths  of  the  stroke,  the 


HEAT.  633 

volume  will  have  trebled,  and  the  tension  have  been  reduced  to 
1£  atmospheres  ;  and  even  at  the  end  of  the  stroke,  when  the  vol- 
ume has  quadrupled,  the  pressure  will  still  be  one  atmosphere. 
Here,  then,  is  a  very  large  gain  of  power  without  any  additional 
expenditure  of  fuel.  In  practice,  these  conditions  are  realized 
by  closing  the  valve  admitting  steam  into  the  cylinder  after  a 
certain  fraction  of  the  stroke,  by  means  of  various  forms  of  au- 
tomatic machinery,  called  cut-offs.  The  actual  theoretical  advan- 
tage gained  in  any  case  can  readily  be  calculated.  It  is  evidently 
the  greater,  the  higher  the  tension  of  the  steam  in  the  boiler  and 
the  sooner  it  is  cut  off  after  the  beginning  of  the  stroke  In  no 
case,  however,  is  the  total  practical  effect  as  great  as  the  theoret- 
ical power  given  in  the  table  on  page  631.  When  thus  worked, 
the  engine  is  said  to  be  worked  expansively. 

We  are  far  from  obtaining  with  the  steam-engine  the  full  me- 
chanical equivalent  of  heat,  even  when  working  under  the  most 
favorable  circumstances  It  will  be  remembered,  that,  according 
to  Joule's  experiments  (238),  one  unit  of  heat  is  capable  of  gen- 
erating a  power  equal  to  423  kilogramme-metres,  which  is  13.4 
times  greater  than  31.59  kilogramme-metres,  the  greatest  pos- 
sible effect  which  could  be  obtained  with  the  steam-engine  when 
not  worked  expansively,  even  under  a  pressure  of  eight  atmos- 
pheres. Considering,  then,  that  we  do  not  realize,  even  under 
the  best  circumstances,  much  more  than  one  half  of  this  theoreti- 
cal effect,  it  will  be  seen  that  we  actually  obtain  with  the  steam- 
engine  only  about  one  twentieth  of  the  power  which  the  fuel  is 
capable  of  yielding.  To  find  a  more  economical  means  than  this 
of  converting  heat  into  mechanical  effect,  is  one  of  the  great  prob- 
lems of  the  present  age. 

(311.)  Low  and  High  Pressure  Engines.  —  As  the  tension  of 
the  steam  used  in  non-condensing  engines  (309)  is  necessarily 
greater  than  the  pressure  of  the  air,  they  are  frequently  called 
high-pressure  engines,  while  the  condensing  engines  are  known 
as  low-pressure  engines.  These  terms,  however,  do  not  correctly 
express  their  nature,  since,  although  the  non-condensing  engine 
must  necessarily  be  worked  at  a  high  pressure,  yet,  as  we  have 
just  seen,  a  great  advantage  is  gained  by  working  the  condensing 
engine  under  a  similar  pressure  ;  and,  in  fact,  the  so-called  low- 
pressure  engines  are  frequently  worked  under  as  great  a  head  of 
steam  as  the  high-pressure  engines. 


634  CHEMICAL  PHYSICS. 

PKOBLEMS. 
Heat  of  Fusion. 

352.  Three  kilogrammes  of  ice  at  0°  are  mixed  with  10  kilogrammes 
of  water  at  100°.     Required  the  temperature  of  the  mixture  after  the  ice 
is  melted. 

353.  How  much  ice  at  0°  must  be  added  to  200  kilogrammes  of  water 
at  16°  in  order  to  reduce  its  temperature  to  10°  ? 

354.  Solve  the  same  problem,  substituting  letters  for  the  numbers. 

355.  How  much  ice  at  O3  is  required  to  cool  10  kilogrammes  of  mer- 
cury from  100°  to  0°? 

356.  A  mass  of  tin  weighing  55  grammes  and  heated  to  100°  was  en- 
closed in  a  cavity  made  in  a  block  of  ice.     Required  the  amount  of  ice 
melted. 

357.  Eight  kilogrammes  of  ice  at  0°  were  mixed  with  35  kilogrammes 
of  water  at  59°  ;  after  the  ice  had  melted,  the  temperature  of  the  water 
was  33°.3.     Required  the  heat  of  fusion  of  ice. 

358.  In  order  to  determine  the  heat  of  fusion  of  lead,  200  grammes  of 
melted  lead  at  the  melting-point  were  poured  into  1,850  grammes  of  water 
at  10°.     After  the  lead  had  cooled,  the  water  was  found  to  have  acquired 
a  temperature  of  11°.64.     Required  the  heat  of  fusion  of  the  metal. 

Tension  of  Vapors. 

359.  Before  filling  a  barometer  with  mercury,  a  small  quantity  of  water 
was  poured  into  the  tube.     How  high  will  the  mercury  stand  in  the  ba- 
rometer when  the  temperature  is  20°  and  the  pressure  of  the  air  77  c.  m.  ? 
Solve  the  same  problem,  assuming  that  alcohol  was  used  instead  of  water. 

360.  Determine  the  height  of  the  mercury-column  in  a  barometer-tube 
whose  walls  are  moistened  with  water  at  the  temperatures  and  pressures 
indicated  below :  — 


1.  H=  76.22  c.  m.    t  =  20°. 

2.  #=75.11     "       t  =  40°. 

3.  H  =  74.56     "       t  =  10°. 


4.  H  =  77.20  c.  m.     t  =    30°. 

5.  H  =  76.54     "        t  =    60°. 

6.  //=  78.10     "        t  =  100°. 


361.  Solve  the  last  problem,  assuming,  first,  that  chloroform,  and,  sec- 
ondly, that  oil  of  turpentine,  were  used  instead  of  water. 

362.  Calculate  by   [199]   the  tension  of  the  vapor  of  water  at  the 
following   temperatures  :   — 10°.24,  15°.45,  40°.25,  60°.58,  150°.5,   and 
220°.85. 

363.  Determine  the  tension  of  the  vapors  of  alcohol,  of  ether,  and  of 
chloroform  at  the  following  temperatures,  assuming  that  the  principle  of 
page  582  is  correct:  20°.12,  15°.64,  10°.22,  and  5°.12. 

364.  Datermine  the  boiling-point  of  water  under  the  following  pres- 
sures :  74.24  c.  m.,  55.54  c.  m.,  34.20  c.  m.,  10.50  c.  m.,  and  5  c.  m. 


HEAT.  635 

365.  Determine   the    boiling-points   of    alcohol   under   the   following 
pressures  :  4.40  c.  m. ;  163.5  c.  m. ;  725.78  c.  m. 

366.  A  cylindrical  vessel  at  the  temperature   of  120°.  6  is  filled  with 
vapor  of  water  having  a  tension  of  100  c.  m.     What  will  be  the  tension 
of  the  vapor  if  its  volume  is  reduced  to  one  half  by  pushing  down  the 
piston  ?     What  will  be  the  tension  of  the  vapor  if  its  volume  is  doubled  ? 

367.  A  glass  vessel  is  filled  with  dry  steam  which  at  the  temperature 
of  100°  has  a  tension  of  54.22  c.  m.     To  what  temperature  must  the  ves- 
sel be  cooled  before  the  steam  begins  to  condense  ?     What  will  be  the  ten- 
sion of  the  steam,  if  the  vessel  is  heated  to  200°  ? 

368.  In  a  strong  iron  vessel,  whose  capacity  equals  5,000  c^iT.8,  15.24 
grammes  of  water  are  hermetically  sealed.     Required  the  tension  of  the 
vapor  in  the  interior  of  the  vessel  at  the  following  temperatures  :   50°, 
100°,  160°,  180°,  and  250°. 

Latent  Heat  of  Vapors. 

369.  How  much  free  steam  must  be  condensed  in  order  to  raise  the 
temperature  of  20  kilogrammes  of  water  from  0°  to  90°  ?     How  much  to 
raise  the  temperature  of  246  kilogrammes  of  water  from  13°  to  28J? 

370.  How  much  vapor  of  alcohol  must  be  condensed  in  order  to  raise 
the  temperature  of  5  kilogrammes  of  alcohol  from  15°  to  30°  ? 

371.  Twenty-five  kilogrammes  of  free  steam  condensed  in  a  mass  of 
water  raised  its  temperature  from  4°  to  61°.4.     Required  the  volume  of 
the  water  before  and  after  the  condensation. 

372.  How  many  kilogrammes  of  ice  at  0°  would  be  required  to  con- 
dense 25  kilogrammes  of  free  steam,  and  reduce  the  temperature  of  the 
water  formed  to  0°. 

373.  Calculate  the  latent  heat  of  steam  at  the  following  temperatures  : 
25°,  32°,  112°,  175°,  198°,  and   222°. 

374.  Calculate  how  much  heat  is  required  to  convert  one  litre  of  water 
at  15°  into  steam  at  its  maximum  tension  at  130°. 

375.  How  much  heat  would  be  evolved  by  the  condensation  of  one 
cubic  metre  of  steam  of  140°  at  its  maximum  tension  into  water  at  20°  ? 

Steam-Engine. 

376.  How  much  mechanical  force  is  generated  by  the  conversion  of  25 
kilogrammes  of  water  at  0D  into  steam  at  140°,  and  how  much  heat  is 
required  for  the  conversion  ? 

377.  The  piston  of  a  steam-engine  has  a  diameter  of  44  c.  m.,  and  it 
moves  1.15  m.  each  second.     Required  the  weight  which  the  machine  can 
raise  to  the  height  of  8  metres  in  one  second,  assuming  that  there  is  no 
resistance,  and  that  the  tension  of  the  steam  is  2.75  atmospheres.     Deter- 
mine, also,  the  quantity  of  heat  required  to  furnish  the  steam  employed  in 
producing  this  effect. 


636  CHEMICAL  PHYSICS. 


HYGROMETRY. 

(312.)  Formation  of  Vapor  in  an  Atmosphere  of  Gas.  —  If 
we  repeat  the  experiment  with  the  vessel  of  one  cubic  metre  ca- 
pacity described  in  (284),  with  only  this  change,  that  it  is  left 
filled  with  air,  we  shall  find  that  the  same  amount  of  aqueous 
vapor  will  be  formed  as  in  a  perfect  vacuum.  For  each  tem- 
perature there  will  be  found  to  exist  simultaneously  in  the  cubic 
metre,  first,  an  atmosphere  of  air  ;  secondly,  an  atmosphere  of 
aqueous  vapor,  having  the  weight  and  tension  which  are  given 
in  the  table  on  page  571.  The  only  difference  between  the  cir- 
cumstances attending  the  formation  of  vapor  in  air  or  any  other 
gas,  and  in  a  vacuum,  is  in  the  time  required.  The  cubic  vessel, 
when  freed  from  air,  would  be  almost  instantaneously  filled  with 
vapor  of  the  given  tension  and  weight ;  but  in  the  same  vessel 
filled  with  air,  the  vapor  would  attain  its  maximum  tension  and 
density  only  after  several  minutes. 

The  tension  of  the  mixture  of  aqueous  vapor  and  air  is  always 
equal  to  the  sum  of  the  tensions  which  each  would  have  if  it 
filled  the  vessel  separately.  This  tension  can  then  be  found  for 
any  temperature  by  adding  to  the  tension  of  the  air,  as  indicated 
by  a  barometer,  the  tension  of  aqueous  vapor  taken  from  the 
table  of  maximum  tensions  opposite  to  the  given  temperature. 
Thus,  if  the  temperature  were  20°,  and  the  barometer  indicated 
a  tension  of  76  c.  m.,  the  tension  of  the  mixture  of  air  and 
vapor  would  be  equal  to  76  +  1.739  =  77.739,  and  a  barometer 
immersed  in  the  vessel  would  stand  at  that  height. 

If  now  we  suppose  the  vessel  to  be  extensible,  and  exposed  on 
the  outside  to  an  invariable  pressure  of  76  c.  m.,  it  is  evident 
that  it  will  be  expanded  until  the  tension  of  the  confined  mixture 
is  reduced  to  the  same  value  ;  and  it  is  frequently  a  problem 
of  great  practical  importance  to  determine  what  the  increased 
volume  will  be.  In  the  first  place,  it  is  evident  that,  as  the  vol- 
ume of  the  vessel  increases,  more  water  will  evaporate,  so  as 
to  keep  the  vapor  at  the  maximum  tension  for  the  temperature. 
Hence,  in  the  expanded  state,  the  tension  of  the  vapor  will  still 
be  1.739  c.  m.  It  is,  therefore,  only  the  air  which  expands,  and 
as  the  tension  of  the  mixture  in  its  expanded  state  is  equal  by 
assumption  to  76  c.  m.,  it  is  evident  that  the  tension  of  the  air 
will  be  equal  to  76  —  1.739  =  74.261  c.  m.  Moreover,  since  the 


HEAT.  637 

volume  of  the  air  (which  is,  of  course,  also  the  volume  of  the 
mixture)  must  be  inversely  as  its  tension  in  the  two  conditions, 
we  have,  by  [200], 

1  :  V  =  74.261  :  76,        whence        V  =  1.023  m.3 

This  solution  may  easily  be  made  general.  Let  HQ  represent 
the  invariable  pressure  to  which  the  gas  is  exposed,  and  $0  the 
tension  of  water  vapor  at  the  given  temperature.  Then,  in  the 
expanded  state,  the  tension  of  the  air  is  HO  —  §0.  We  have, 
by  substituting  these  values  in  [200],  F:  V  =  H0  —  §0  :  H; 
whence 

(1.)  V  =  F  TT^V,     and  (2.)  F=  V  ^~^.     [203.] 

— 


-"o 

By  means  of  (1)  we  can  always  calculate  the  increased  volume, 
F',  of  a  gas  when  saturated  with  moisture,  if  the  volume  of  the 
dry  gas  is  known  ;  and  by  means  of  (2)  we  can  calculate  from  the 
measured  volume  of  the  moist  gas  the  volume,  F,  which  it  would 
have  measured  had  the  gas  been  perfectly  dry.  The  last  problem 
is  one  of  great  importance,  and  generally  presents  itself  in  a  form 
like  that  of  the  following  example. 

A  volume  of  gas  confined  in  a  bell-glass  over  water  measures 
250  c^m.3  when  the  temperature  is  20°  and  the  barometer  76  c.  m. 
What  would  be  the  volume  if  the  gas  were  perfectly  dry  ?  By 
substituting  the  data  given  in  (203.  2)  we  obtain, 


F=  250  —  =  244.25  ens.'.  [204.] 

The  formula  just  employed  gives  in  any  case  the  volume  of  dry 
gas  for  the  temperature  and  pressure  at  which  the  volume  of  the 
moist  gas  was  observed  ;  only  it  is  necessary  to  remember,  in 
using  the  formula,  that  H0  represents  the  pressure  to  which  the 
mixture  of  gas  and  vapor  was  exposed  at  the  time  the  volume 
was  measured.  This  can  always  be  ascertained  by  the  method 
described  in  (169).  When  the  volume  of  dry  gas  has  been  in 
this  way  determined  for  any  given  temperature  and  pressure, 
dt  can  easily  be  reduced  to  0°  and  76  c.  m.  by  means  of  [98] 
and  [184]. 

What  has  been  illustrated  above  in  the  case  of  the  vapor  of 
54 


688  CHEMICAL  PHYSICS. 

water,  is  also  true  of  the  vapors  of  other  liquids.  The  same  quan- 
tity of  liquid  will  evaporate  into  a  cubic  metre,  and  a  vapor  will 
be  formed  of  the  same  tension  and  density,  whether  the  space  be 
empty  or  filled  with  gas  ;  the  only  difference  being  that  the  liquid 
will  evaporate  very  much  more  slowly  in  the  last  case  than  in  the 
first.  What  is  true  of  one  liquid  must  also  be  true  of  any  num- 
ber of  liquids  ;  provided  only  that  these  do  not  act  chemically  on 
each  other,  each  of  them  will  evaporate  and  form  a  vapor  of  the 
same  tension  and  density  as  if  the  space  were  a  perfect  vacuum. 
At  least  this  is  true  theoretically,  and  it  would  probably  be  true 
practically  could  we  enclose  the  vapor  within  walls  formed  by  the 
volatile  liquids  themselves.  But  in  the  glass  vessels  with  which 
we  are  obliged  to  experiment,  the  result,  as  above  stated,  is  not 
perfectly  realized.  This  is  apparently  owing  to  an  adhesive  action 
of  the  glass,  by  which  the  tension  of  the  vapor  is  reduced  below 
the  maximum  tension  for  the  temperature.  This  subject  has 
been  carefully  examined  by  Regnault,  and  we  would  refer  to 
his  memoir*  for  further  details. 

The  principles  of  this  section  may  be  summed  up  in  the  two 
following  propositions,  first  enunciated  by  Dalton,  and  therefore 
known  as  the  Law  of  Dalton.  The  last  proposition,  however,  is 
only  a  necessary  consequence  of  the  first. 

1.  The  tension  and  the  amount  of  the  vapor  which  will  satu- 
rate a  given  space  at  a  given  temperature  are  the  same,  whether 
the  space  be  completely  empty  or  filled  with  gas. 

2.  The  elastic  force  of  a  mixture  of  gas  and  vapor  is  equal  to 
the  sum  of  the  tensions  which  each  would  have  separately. 

This  law  may  be  illustrated  by  means  of  the  apparatus  repre- 
sented in  Fig.  445.  It  consists  of  a  glass  tube,  A,  closed  at  both 
ends  by  the  iron  stopcocks  b  and  d.  The  lower  stopcock  is  pro- 
vided with  a  side  tubulature,  into  which  the  tube  B  is  cemented, 
and  a  graduated  scale  placed  between  the  tubes  serves  to  meas- 
ure the  relative  heights  of  the  columns  of  mercury  they  con- 
tain. In  using  this  apparatus,  the  tube  A  is,  in  the  first  place, 
about  half  filled  with  dry  air,  or  any  other  gas  from  the  globe  M, 
which  can  be  screwed  on  to  the  stopcock  b  in  place  of  the  tunnel 
C.  The  tunnel  C  is  provided  with  a  stopcock  of  a  peculiar 
construction.  The  plug  of  the  cock,  represented  at  n,  is  not 

*  Comptes  Bendus,  Tom.  XXXIX.  p.  345. 


HEAT. 


639 


pierced,  as  usual,  completely  through,  but  has  simply  a  small 
cavity  on  one  side.  Having  now  adjusted  the  quantity  of  mer- 
cury in  the  apparatus  so  that  it  shall 
stand  at  the  same  height  in  both  tubes, 
and  having  poured  a  quantity  of  liquid 
into  the  tunnel,  we  open  the  cock  b 
and  turn  the  plug  of  the  cock  a  so 
that  the  liquid  may  be  introduced 
drop  by  drop  into  the  tube  A.  The 
confined  gas  becomes  thus  saturated 
with  vapor,  and,  expanding,  depress- 
es the  mercury-column.  "We  then 
restore  the  original  volume  by  pour- 
ing mercury  into  the  tube  B.  The 
tension  of  the  mixture  of  gas  and 
vapor  is  now  evidently  equal  to  the 
pressure  of  the  air  plus  the  pressure 
of  the  mercury-column  B  o,  thus  prov- 
ing that  the  tension  of  the  confined 
gas  has  been  increased  by  the  tension 
of  the  vapor.  By  referring  to  the 
tables,  it  will  be  found  that  the  in- 
crease of  tension  is  exactly  equal  to 
the  maximum  tension  of  the  same 
vapor  in  a  vacuum,  when  exposed  to 
the  same  temperature. 

(313.)  Hygrometers.  —  Every  cubic  metre  of  the  atmosphere 
in  immediate  contact  with  the  earth  is,  in  all  respects,  similarly 
situated  towards  the  ponds  and  rivers  of  the  globe  as  is  the  air 
of  the  cubic  vessel  towards  the  water  it  contains.  Every  cubic 
metre  of  the  atmosphere  is  capable  of  holding,  for  any  tempera- 
ture, the  same  amount  of  aqueous  vapor,  and  vapor  of  the  same 
tension,  as  the  vessel ;  moreover,  water  will  continue  to  evaporate 
into  the  atmosphere  until  the  vapor  has  acquired  the  tension 
and  specific  gravity  which  correspond  to  the  temperature.  There 
are,  therefore,  around  the  globe,  as  in  the  cubic  vessel,  two  at- 
mospheres, one  of  air  and  the  other  of  vapor.  When  the  air 
has  taken  up  all  the  vapor  which  it  is  capable  of  holding  at 
the  temperature,  it  is  said  to  be  saturated  or  moist ;  when  less, 
it  is  said  to  be  dry.  In  the  last  case,  it  is  capable  of  absorbing 


Fig.  445. 


640  CHEMICAL  PHYSICS. 

more  water,  and  of  course  dries  up  the  moisture  from  sub- 
stances with  which  it  may  be  in  contact.  Thus,  if  the  temper- 
ature is  20°,  the  air  is  saturated  with  vapor  when  it  con- 
tains in  every  cubic  metre  17.157  grammes  (see  table  on  page 
571)  ;  if  it  contained  only  12.746  grammes  it  would  be  dry, 
since  then  every  cubic  metre  of  air  could  absorb  4.411  grammes 
more.  But  if  the  temperature  falls  to  15°.  then  by  the  table 
12.746  grammes  will  completely  saturate  each  cubic  metre  ;  so 
that  a  cubic  metre  of  air  containing  12.746  grammes  of  vapor 
is  saturated  when  the  temperature  is  15°,  although  dry  when 
it  is  20°. 

The  moisture  of  the  atmosphere  at  any  temperature  depends, 
then,  not  simply  on  the  amount  of  vapor  which  it  contains,  but 
on  the  proportion  which  this  amount  bears  to  the  whole  quantity 
which  it  could  possibly  contain  at  the  given  temperature.  The 
fraction  which  is  obtained  by  dividing  the  actual  weight  of  vapor 
in  a  cubic  metre  of  the  atmosphere  by  the  weight  which  it  would 
contain  were  it  completely  saturated  with  aqueous  vapor,  is  called 
the  relative  humidity.  It  follows  from  Mariotte's  law,  that  the 
weights  of  two  masses  of  vapor  occupying  equal  volumes  are  to 
each  other  as  their  tensions,  W:  W'=  $„  :  §'„;  hence  the  rela- 
tive humidity  may  also  be  obtained  by  dividing  the  tension  of  the 
vapor  actually  contained  in  the  air  by  the  tension  the  vapor  would 
have  if  the  atmosphere  were  saturated,  that  is,  by  the  maximum 
tension  for  the  temperature,  as  given  in  Table  X.  In  order  to 
find,  then,  the  relative  humidity  of  the  atmosphere  at  any  given 
time,  we  in  the  first  place  observe  its  temperature ;  and  in  the 
second  place,  we  ascertain  by  experiment  the  tension  of  the  vapor 
which  it  actually  contains.  The  tension  is  found  in  the  following 
manner. 

If  we  cool  down  a  cubic  metre  of  the  atmosphere,  we  shall 
come,  sooner  or  later,  to  a  temperature  at  which  the  tension  of 
the  vapor  is  at  its  maximum.  Thus,  for  example,  if  the  temper- 
ature of  the  atmosphere  is  20°,  and  the  tension  of  the  vapor  it 
contains,  and  which  we  wish  to  find,  is  1.2699  c.  m.,  we  shall,  by 
cooling  one  cubic  metre  to  15°,  reach  a  temperature  at  which 
1.2699  c,m.  is  the  maximum  tension,  and  consequently  a  tem- 
perature at  which  the  air  will  be  saturated  by  the  vapor  contained 
in  it.  If  now  we  cool  it  below  this  point,  a  portion  of  the  vapor 
will  be  deposited  in  the  form  of  mist  or  dew.  The  temperature, 


HEAT.  641 

then,  at  which  dew  would  be  deposited,  were  the  atmosphere 
cooled  down,  is  the  temperature  at  which  the  tension  of  the  vapor 
contained  in  it  would  be  at  its  maximum.  This  temperature 
is  technically  termed  the  dew-point.  It  can  easily  be  observed  in 
the  following  way.  Take  a  brightly  polished  silver  cup  and  fill 
it  with  water.  Place  in  it  a  sensitive  thermometer,  which  will 
indicate  promptly  any  changes  of  temperature,  and  then  add 
ice  in  small  pieces,  waiting  until  one  piece  is  melted  before  add- 
ing another,  and  constantly  stirring  the  water  with  the  thermom- 
eter in  order  to  render  the  temperature  uniform  throughout 
the  mass.  The  silver  cup,  as  it  is  thus  slowly  cooled,  will  cool 
in  its  turn  the  thin  layer  of  air  which  immediately  surrounds  it, 
and  sooner  or  later  this  air  will  be  reduced  to  the  temperature  at 
which  the  vapor  it  contains  completely  saturates  it.  At  that  mo- 
ment the  polished  surface  of  the  cup  will  be  dimmed  by  a  depo- 
sition of  dew.  Note  carefully  the  temperature  at  which  this  first 
takes  place  ;  and  then  allow  the  cup  to  warm,  and  note  carefully 
the  temperature  at  which  the  dimness  disappears.  The  two  tem- 
peratures should  very  nearly  correspond,  and  the  mean  may  be 
taken  as  the  dew-point.  Having  found  the  dew-point,  we  can  easily 
ascertain  the  relative  humidity  of  the  air  by  means  of  the  table 
of  tensions.  Opposite  to  the  dew-point  we  find  the  actual  tension 
of  the  vapor  in  the  atmosphere.  Opposite  to  the  temperature  of 
the  air  at  the  time  of  the  experiment,  we  find  the  maximum 
tension  which  the  vapor  could  attain  ;  and  since,  as  we  have 
seen,  the  weight  of  vapor  is  proportional  to  the  tension,  we  can 
obtain  at  once  the  relative  humidity  by  dividing  the  first  by  the 
last.  To  illustrate  this  by  an  example :  — 

The  temperature  of  the  air  is  20°.  The  dew-point,  found  as 
just  described,  is  15°.  What  is  the  relative  humidity?  The 
maximum  tension  of  vapor  at  the  dew-point  is  12.699  m.  m.,  and 
this  is  the  actual  tension  of  the  vapor  in  the  atmosphere.  The 
maximum  tension  of  vapor  at  20°  is  17.391  m.  m.,  and  this  is  the 
tension  which  the  vapor  would  have  were  the  atmosphere  satu- 
rated. g|g  =  .73  is,  then,  the  relative  humidity.  The  at- 
mosphere, therefore,  contains  73  per  cent  of  the  whole  amount 
it  could  possibly  contain  at  20°.  From  the  relative  humidity,  it 
is  easy  to  calculate  the  amount  of  vapor  contained  in  a  cubic 
metre.  By  referring  to  the  table,  we  ascertain  the  total  amount 
which  the  cubic  metre  could  contain  at  the  given  temperature  ; 
54* 


642 


CHEMICAL  PHYSICS. 


and  by  multiplying  this  by  the  fraction  expressing  the  relative 
humidity,  we  ascertain  the  amount  which  it  actually  contains. 
Thus,  in  the  example  just  given,  the  total  amount  of  vapor  which 
one  cubic  metre  of  air  at  20°  can  contain  is  17.157  grammes. 
It  actually  contains  only  73  per  cent  of  this  amount,  that  is, 
17.157  X  .73  =  12.525  grammes. 

It  appears,  then,  that  the  determination  of  the  amount  of  vapor 
in  the  atmosphere  resolves  itself  practically  into  the  observation 


Fig.  446. 

of  tne  dew-point.  This  can  be  observed  with  sufficient  accuracy, 
for  most  purposes,  with  a  thin  silver  cup  and  thermometer,  as 
described  above  ;  but  where  greater  accuracy  is  required,  the  ob- 
servations can  be  made  more  rapidly,  as  well  as  with  greater  cer- 
tainty, with  the  hygrometer  of  Regnault,  which  is  represented  in 
Fig.  446.  It  consists  of  two  silver  thimbles  4.5  c.  m.  high  and 
20  m.  m.  in  diameter,  made  very  thin,  and  brightly  polished  on 
the  outside.  These  thimbles  are  cemented  to  the  bottom  of  two 
glass  tubes  Z>,  E.  Each  of  these  contain  thermometers  gradu- 
ated to  tenths  of  a  degree,  kept  in  place  by  corks.  Through  the 
cork  of  the  tube  D  passes  a  small  tube,  A,  open  at  both  ends 
and  extending  to  the  bottom  of  the  silver  thimble.  The  upper 


HEAT. 


643 


part  of  the  tube  D  communicates,  through  the  lateral  tubulature 
and  through  the  stem  of  the  support,  with  an  aspirator,  G,  by 
means  of  which  air  can  be  drawn  through  the  apparatus.  The 
tube  E,  which  does  not  communicate  with  the  aspirator,  contains 
a  thermometer  for  observing  the  temperature  of  the  air. 

In  order  to  use  the  apparatus,  the  tube  D  is  half  filled  with 
ether ;  then,  on  opening  the  stopcock  of  the  aspirator,  the  water 
which  it  contains  flows  out,  and  the  air  required  to  supply  its 
place  flows  in  at  the  tube  A,  bubbling  up  through  the  ether. 
The  rapid  evaporation  caused  by  this  current  of  air  soon  cools 
the  temperature  of  the  silver  thimble  to  the  dew-point.  At  the 
moment  a  film  of  moisture  appears  on  the  polished  surface,  the 
temperature  indicated  by  the  thermometer  T  is  carefully  noted, 
as  well  also  as  the  temperature  of  the  air  given  by  the  thermom- 
eter £,  and  we  have  then  the  elements  for  calculating  the  rela- 
tive humidity  of  the  atmosphere.  By  careful  manipulation,  the 
dew-point  can  be  observed  with  this  instrument  to  one  tenth  of 
a  Centigrade  degree.  The  second  silver  thimble,  on  the  tube 
E,  serves  not  only  to  protect  the  bulb  of  the  thermometer,  but 
also,  by  comparison,  enables  the  observer  to  detect  a  slight  trace 
of  moisture  011  the  surface  of  the  first,  which  might  otherwise  be 
overlooked. 

The  hygrometer  of  Daniells,  repre- 
sented in  Fig.  447,  is  based  on  the 
same  principle  as  that  of  Regnault, 
but  is  much  less  delicate  in  its  indica- 
tion. It  consists  of  two  bulbs  con- 
nected by  a  siphon-tube,  from  which 
the  air  has  been  expelled  by  hermeti- 
cally sealing  the  instrument  when 
filled  with  ether  vapor.  The  bulb 
A  is  about  half  filled  with  ether, 
and  contains  the  bulb  of  a  small 
thermometer.  Moreover,  a  zone  of 
the  bulb  is  gilt,  and  burnished  so  that 
the  deposition  of  the  dew  upon  it  may 
be  easily  perceived.  The  other  bulb  Fig.  447. 

is  covered  with  muslin.     When  an  ob- 
servation is  to  be  made,  the  muslin  is  moistened  with  ether,  which 
is  dropped  very  slowly  from  a  bottle.     The  evaporation  of  the 


644  CHEMICAL   PHYSICS. 

ether  from  the  muslin,  by  cooling  the  bulb  B  and  condensing  the 
vapor  of  ether  which  it  contains,  causes  a  very  rapid  evaporation 
from  the  surface  of  the  liquid  in  the  bulb  A.  By  this  means  the 
gilt  zone  is  soon  cooled  to  the  dew-point,  a  deposition  of  dew  indi- 
cating when  the  point  is  reached.  The  temperature  at  which  the 
dew  is  first  deposited  is  carefully  observed  by  means  of  the  en- 
closed thermometer,  and  also  the  temperature  at  which  it  disap- 
pears when  the  temperature  of  the  bulb  A  is  afterwards  allowed 
to  rise.  The  two  observations  should  not  differ  much  from  each 
other,  and  their  mean  is  the  dew-point. 

The  relative  humidity  of  the  air  may  also  be  estimated,  though 
with  less  accuracy,  from  the  rapidity  with  which  water  evaporates 
when  exposed  to  it ;  since,  as  is  evident,  the  drier  the  air,  the 
more  rapid  will  be  the  evaporation.  The  instrument  used  for 
this  purpose  is  called  a  psychrometer,  or  a  wet-bulb  hygrometer. 
It  consists  of  two  thermometers,  the  bulb  of  one  of  which  is  cov- 
ered with  muslin  and  kept  constantly  moist,  while  the  bulb  of  the 
other  is  dry.  The  last  indicates  the  temperature  of  the  air ;  but 
the  first  always  indicates  a  lower  temperature,  owing  to  the  latent 
heat  absorbed  by  the  evaporation  of  the  water  from  the  surface  of 
the  bulb,  except  when  the  air  is  fully  saturated  with  moisture. 
The  difference  between  the  two  thermometers  will  be  the  greater 
the  more  rapid  the  evaporation,  that  is,  the  greater  the  dryness 
of  the  air.  From  the  temperatures  of  the  two  thermometers  we 
can  calculate  the  tension  of  the  vapor  in  the  atmosphere  by  means 
of  the  empirical  formula, 

More  than  ^,  Less  than  j^, 

-          0.429  (T —  r')    rr  ™          0.480  (T  —  T')  TT  , 

610  —  T1  620  —  T' 

§   =  maximum  tension  of  vapor  at  lowest  temperature. 
i    =i  temperature  of  dry-bulb  thermometer. 
T'  =  temperature  of  wet-bulb  thermometer. 
HO  =  height  of  barometer. 

610  —  T'  =  latent  heat  of  the  vapor  of  water  (compare  300). 
x    =  tension  of  aqueous  vapor  at  the  time  of  observation. 

From  the  value  of  x  the  relative  humidity  can  be  easily^calculated 
by  dividing  by  the  maximum  tension,  as  before  described. 

The  above  are  the  formulae  of  Regnault  as  modified  from  the 
original  formula  of  August.  They  are  in  a  measure  empirical, 


HEAT. 


645 


and  founded  on  theoretical  considerations,  for  which  we  must 
refer  to  the  original  memoir.  The  last  formula,  as  Regnault 
found,  gives  accurate  results  when  the  air  is  not  more  than  four 
tenths  saturated.  Otherwise,  the  first  should  be  used.  For  tem- 
peratures below  freezing,  which  suppose  the  wet  bulb  to  be  cov- 
ered with  a  film  of  ice,  the  value  610  —  *'  must  be  changed  to 
610  +  79  —  T  =  G89  —  T',  since  the  amount  of  heat  required  to 
change  ice  into  vapor  is  greater  by  79  units  (the  heat  of  fusion) 
than  that  which  would  be  required  to  change  water  into  vapor 
of  the  same  temperature  and  tension.  For  the  value  of  H^  it  is 
generally  sufficient  to  take  the  mean  barometric  pressure  of  the 
place  of  observation.  In  the  Meteorological  Tables  prepared  by 
Professor  Arnold  Guyot,  and  published  by  the  Smithsonian  Insti- 
tution, will  be  found  tables  by  which,  from  the  indications  of  the 
psychrometer,  the  tension  of  vapor  and  relative  humidity  may  be 
ascertained  by  inspection.  As  the  indications  of  the  psychrometer 
are  discovered  by  simple  inspection,  it  would  entirely  supersede 
all  other  hygrometers  were  the  formula  by  which  the  tension  of 
vapor  is  deduced  from  the  observed  data  perfectly  trustworthy. 
They  are  sufficiently  so  for  the  purposes  of  meteorology,  but 
results  obtained  with  Regnault's  hygrometer  are  in  all  cases  to 
be  preferred. 

Still  a  third  class  of  hygrometers  is  based 
upon  the  fact  that  many  solids  swell  on  imbibing 
moisture,  and  contract  again  on  drying.  This  is 
the  case  with  most  dry  organic  substances,  such 
as  whalebone,  wood,  parchment,  and  hair.  The 
hygrometer  of  Deluc  consists  of  a  very  thin  piece 
of  whalebone,  which,  in  expanding  and  contract- 
ing, moves  an  index ;  and  a  variety  of  toys,  in 
which  a  change  in  the  degree  of  humidity  of  the 
air  is  shown  by  the  motion  of  a  pasteboard  figure, 
are  made  on  the  same  principle.  But  the  only 
trustworthy  or  even  approximative^  accurate 
hygrometer  of  this  class  is  the  hair  hygrometer  of 
Saussure,  as  modified  by  Regnault.  It  is  rep- 
resented in  Fig.  448,  and  consists  essentially  of  a 
human  hair,  c,  previously  freed  from  fat  by  being 
soaked  in  ether,  and  so  fixed  in  a  copper  frame  that  its  expansion 
and  contraction  will  move  a  needle  over  a  graduated  arc.  Each 


Fig.  448. 


646  CHEMICAL  PHYSICS. 

instrument  is  graduated  experimentally  by  placing  it  in  a  con- 
fined space  kept  in  a  known  state  of  humidity  by  the  presence 
of  sulphuric  acid  of  different  degrees  of  strength.  Unlike  the 
other  hygrometers,  this  instrument  gives  at  once  the  relative 
humidity  of  the  air,  and  its  indications  are  independent  of  the 
temperature.  Unfortunately,  however,  it  is  liable  to  variations, 
and  must  be  adjusted  from  time  to  time  by  means  of  the  solu- 
tions employed  in  graduating  it. 

The  last,  but  the  most  accurate,  method  of  determining  the 
amount  of  vapor  in  the  air,  consists  in  drawing  through  a  tube 
containing  chloride  of  calcium,  or  some  other  powerful  absorb- 
ent, a  measured  volume  of  air,  by  means  of  an  aspirator.  The 
increased  weight  of  the  tube  will  give  at  once  the  weight  of  vapor 
contained  in  the  known  volume  of  air.  This  process  is  much 
too  complicated,  however,  to  admit  of  general  application  ;  but 
it  may  be  used  to  advantage  where  great  accuracy  is  required,  or 
in  verifying  the  results  of  the  other  more  expeditious  methods.* 
(314.)  Drying  Apparatus.  —  It  is  frequently  necessary  in  the 
practice  of  chemistry  to  remove  from  a  solid  body  the  moisture 
adhering  to  its  surface,  or  otherwise  mechanically  united  with  it. 
This  is,  generally,  readily  accomplished  by  exposing  the  solid  to 
dry  air,  into  which  the  moisture  evaporates.  If  the  solid  will 
bear  the  temperature  of  100°  without  undergoing  change,  we  can 
use  the  drying  oven  already  described  (294)  ; 
but  if  not,  we  effect  the  same  object  at  the 
ordinary  temperature  by  placing  the  solid  un- 
der a  bell-glass,  over  a  dish  containing  concen- 
trated sulphuric  acid.  In  this  case  the  rapid- 
ity of  the  evaporation  is  greatly  accelerated 
by  exhausting  the  air.  The  arrangement  rep- 
resented in  Fig.  449  may  be  used  for  this 
purpose,  and  also  for  concentrating  solutions 
of  chemical  compounds  which  would  be  altered 
Rg.  449.  by  a  high  temperature.  In  drying  goods  on 

a  large  scale  in  the  arts,  it  is  important 
to  keep  in  mind  two  facts  :  first,  that  the  capacity  of  air  for 
holding  moisture  increases  very  rapidly  with  the  temperature; 
and,  secondly,  that  a  very  considerable  time  must  elapse  before 

*  For  a  full  account  of  the  methods  of  hygrometry  as  revised  by  Regnault,  see  his 
"  Etudes  sur  rHygrometrie,"  Annales  de  Chimie  et  de  Physique,  3e  Serie,  Tom.  XV. 


HEAT.  647 

the  air  is  saturated,  —  the  longer,  the  lower  the  temperature. 
An  advantage  is  therefore  gained  by  keeping  the  air  in  the  drying 
chamber  at  as  high  a  temperature  as  is  compatible  with  the  cir- 
cumstances, and  preventing  it  from  escaping  until  it  is  absolutely 
saturated  with  humidity.  In  no  case,  however,  can  water  be 
evaporated  by  heated  air  in  a  drying  stove  as  economically  as 
in  a  close  boiler. 


ORIGIN    OF   HEAT. 

(315.)  Sources  of  Heat.  — The  sun's  rays  are  the  great  source 
of  heat  on  the  surface  of  the  globe.  The  amount  of  heat  which 
thus  enters  the  earth's  atmosphere  from  the  sun  during  a  year 
has  been  estimated  by  Pouillet  to  be  equal  on  an  average  to 
231,675  units  for  every  square  centimetre  of  the  earth's  surface. 
In  order  to  give  an  idea  of  this  quantity,  Pouillet  states  that  it 
would  be  sufficient  to  melt  a  layer  of  ice  enveloping  the  earth 
30.89  metres  thick.  Of  this  amount,  however,  the  surface  of  the 
earth  only  receives  about  two  thirds,  the  rest  being  absorbed  by 
the  atmosphere.  Besides  the  heat  which  it  is  constantly  receiv- 
ing from  the  sun,  the  earth  has  also  a  great  store  of  heat  within 
its  own  mass,  called  the  central  heat.  It  has  already  been  stated, 
that  the  spheroidal  figure  of  the  earth  is  probably  owing  to  the 
fact,  that  the  globe  was  once  a  fluid  mass  ;  and  we  have  reason 
to  believe  that  it  is  so  now,  with  the  exception  of  a  comparatively 
thin  crust  on  the  surface.  From  observations  made  in  mines 
and  Artesian  wells,  we  find  that  the  temperature  of  the  crust 
rapidly  increases  as  we  descend  from  the  surface  of  the  earth. 
The  rate  of  increase  varies  in  different  places,  but  may  be  stated, 
on  an  average,  to  be  about  one  degree  for  every  30  or  40  metres. 
At  this  rate  of  increase,  assumed  to  be  the  same  at  all  depths, 
the  temperature  of  the  crust  at  the  depth  of  about  2,700  metres 
must  be  that  of  boiling  water,  and  at  a  depth  of  35  kilometres 
that  of  melting  iron,  while  at  70  kilometres  all  known  mineral 
substances  would  be  in  complete  fusion.  It  is  probable,  there- 
fore, that  the  thickness  of  the  crust  of  the  earth  is  not  greater 
than .  Titf  of  its  radius,  and  might  be  represented  by  a  sheet  of 
pasteboard  on  a  large  artificial  globe.  Nevertheless,  the  conduct- 
ing power  of  the  crust  is  so  slight,  that  the  effect  of  the  central 
heat  is  hardly  felt  on  the  surface  ;  and  Fourier  has  calculated 


648  CHEMICAL   PHYSICS. 

that  it  does  not  elevate  the  mean  temperature  of  the  surface 
more  than  -^  of  a  degree. 

Besides  these  constant  sources  of  heat,  there  are  many  others 
which  are  more  or  less  accidental  and  intermittent.  In  general, 
any  motion  of  the  molecules  of  a  hody,  whether  it  accompanies 
a  chemical  or  a  physical  change,  is  attended  either  by  an  evolu- 
tion or  by  an  absorption  of  heat ;  but  in  almost  every  case  the 
heat  thus  evolved  may  be  traced  back,  either  directly  or  indi- 
rectly, to  the  sun.  The  accidental  sources  of  heat  may  be  di- 
vided into  two  classes,  the  physical  and  the  chemical. 

(316.)  Physical  Sources.  —  Of  the  physical  sources  of  heat, 
the  most  important  is  friction.  Count  Rumford  succeeded  in 
boiling  water  by  the  friction  from  boring  a  cannon,  and  an  appa- 
ratus has  been  invented  in  France  for  generating  steam  by  means 
of  heat  produced  in  a  similar  way.  It  has  already  been  shown 
(238)  that  there  is  an  exact  equivalence  between  the  heat  gener- 
ated by  friction  and  the  mechanical  power  used  in  producing 
it ;  and  it  is  possible  that,  where  motive  power  is  abundant  and 
fuel  expensive,  such  a  machine  might  be  used  to  advantage. 

Another  physical  source  of  heat  is  percussion,  as  is  illustrated 
by  the  common  flint-lock,  and  by  a  number  of  familiar  facts. 
For  example,  a  small  bar  of  iron  may  be  heated  to  redness  on  an 
anvil  by  blows  of  the  hammer  actively  applied,  and  a  bar  of  lead 
may  even  be  melted  in  this  way.  In  like  manner  all  metals, 
when  rolled  out  into  plates,  drawn  into  wire,  or  submitted  to  any 
other  mechanical  process  by  which  the  relative  position  of  their 
molecules  is  changed,  become  more  or  less  heated.  The  heat 
evolved  in  all  these  cases  appears  to  be  due  to  an  internal  friction 
between  the  particles  of  the  solid,  so  that  this  source  of  heat  does 
not  differ  essentially  from  the  last. 

A  third  source  of  heat  is  mechanical  condensation.  If  we 
diminish  the  volume  of  a  body  by  mechanical  means,  its  tempera- 
ture is  at  once  raised,  and  an  amount  of  heat  is  evolved  which  is 
probably  in  all  cases  equal  to  that  which  would  be  required  to  ex- 
pand the  body  by  an  equivalent  amount  (compare  237).  Since 
both  solids  and  liquids  are  but  slightly  compressible,  we  cannot 
produce  with  them  any  very  marked  calorific  effects  by  condensa- 
tion. It  is  different  with  gases.  They  are  very  compressible,  and 
their  temperature  can  be  greatly  raised  by  sudden  condensation. 
This  is  illustrated  by  the  fire-syringe  (Fig.  450).  It  consists  of  a 


HEAT. 


649 


cylinder  of  glass,  and  of  a  piston,  which  closes  it  hermetically 
and  by  which  the  air  it  contains  may  be  condensed.  On  pushing 
in  the  piston  with  a  quick  and  forcible 
motion,  the  heat  evolved  by  the  condensa- 
tion of  the  air  raises  the  temperature  suffi- 
ciently to  inflame  a  piece  of  tinder,  which 
is  placed  in  a  cavity  provided  for  the  pur- 
pose on  the  under  side  of  the  piston.  This 
requires  a  temperature  of  at  least  800°. 
A  bright  light  is  noticed  in  the  cylinder 
at  the  moment  of  the  maximum  condensa- 
tion, caused  by  the  burning  of  a  portion 
of  the  oil  with  which  the  piston  is  lubri- 
cated. 

The  only  other  mechanical  sources  of 
heat  usually  enumerated  in  this  connec- 
tion are  the  absorption  of  gases  or  liquids 
by  porous  solids,  the  change  of  the  state 
of  aggregation  of  a  substance,  and  elec- 
tricity. The  first  of  these  is  probably 
identical  with  the  one  last  considered, 
the  heat  in  every  case  originating  from 
condensation  caused  by  the  adhesion  of 
the  liquid  or  gas  to  the  surface  of  the  solid ;  the  second  has 
already  (277  and  299)  been  studied  at  length,  and  the  last  will 
be  considered  in  another  portion  of  the  work. 

(317.)  Chemical  Sources.  —  All  chemical  combination  is  at- 
tended with  the  evolution  of  heat ;  indeed,  this  is  the  chief  source 
of  artificial  heat  on  the  surface  of  the  globe.  When  the  combina- 
tion takes  place  slowly,  as  when  iron  rusts  in  the  air,  the  heat  is 
dissipated  as  fast  as  it  is  evolved,  and  does  not  elevate  sensibly 
the  temperature  of  the  combining  substances  ;  but  when  the 
combination  is  rapid,  the  heat  accumulates  in  the  bodies  and  pro- 
duces the  phenomena  of  combustion.  Combustion  is,  therefore, 
simply  a  process  of  chemical  combination,  in  which  heat  is  evolved 
so  much  more  rapidly  than  it  is  conveyed  away  through  the  usual 
channels,  that  the  temperature  of  the  substances  is  retained  above 
the  point  of  ignition.  All  combustion  with  which  we  are  generally 
familiar  consists  in  the  chemical  combination  of  the  burning  sub- 
stance with  the  oxygen  of  the  air ;  but  we  may  have  phenomena 
55 


Fig.  450. 


650  CHEMICAL  PHYSICS. 

of  intense  ignition  without  oxygen,  as  when  antimony  is  dropped 
in  powder  into  a  jar  of  chlorine,  or  when  phosphorus  is  mixed 
with  iodine.  The  quantity  of  heat  evolved  during  chemical  com- 
bination varies  very  greatly  with  the  nature  of  the  substances 
employed  ;  but  it  is  always  constant  for  the  same  substances,  and 
is  exactly  proportional  to  the  weight  of  each  which  is  used  in 
forming  the  compound.  Thus,  for  example,  from  one  kilogramme 
of  the  following  substances  there  is  always  evolved  the  amount  of 
heat  indicated  in  the  following  table  when  they  combine  with 
oxygen,  or,  in  other  words,  when  they  burn. 


Units  of  Heat. 

Hydrogen,       f,'  <$         .     34,462 

Marsh  Gas,          .  .         13,063 
Olefiant  Gas,  .         .         .     11,858 

Beeswax,     .         .  .         10,496 
Spermaceti,     .         .         .     10,342 

StearicAcid,    .  .  9,716 


Units  of  Heat. 

Oil  of  Turpentine,  .  10,662 

Ether,          .         .  .         9,027 

Alcohol,           .         .  .     7,184 

Wood  Charcoal,  .  .         8,080 

Gas  Coke,   ,  ,         .  .     8,047 

Native  Sulphur,  .  .         2,261 


It  has,  moreover,  been  proved  that  the  amount  of  heat  evolved 
during  chemical  combination  is  precisely  the  same  whether  the 
union  be  rapid  or  slow,  and  also  whether  the  compound  be  formed 
at  once  by  direct  combination  or  by  several  successive  processes. 
But  all  these  subjects  can  be  discussed  to  much  greater  advan- 
tage after  the  student  is  familiar  with  the  laws  of  chemical  com- 
bination ;  we  shall,  therefore,  defer  the  further  consideration  of 
them  until  then.  The  same  is  true,  also,  of  the  heat  evolved 
by  the  processes  of  animal  life  ;  for  this  is  probably  due  to  a  slow 
combustion  which  takes  place  in  the  animal  body  under  the  influ- 
ence of  vitality. 

PROPAGATION   OF   HEAT. 

(318.)  Heat  may  be  transmitted  from  one  body  to  another 
through  space,  as  it  is  transmitted  from  the  sun  to  the  earth,  or 
it  may  be  communicated  from  particle  to  particle  by  direct  con- 
tact, as  when  a  bar  of  iron  is  heated  by  placing  one  end  in  contact 
with  ignited  coals.  The  first  of  these  methods  is  called  radiation, 
the  second  conduction.  It  is  probable,  however,  that  conduction 
is  only  a  form  of  radiation,  the  heat  being,  in  all  cases,  radiated 
from  particle  to  particle  through  the  intervening  spaces,  which 
may  be  exceedingly  large  as  compared  with  the  size  of  the  par- 
ticles themselves  (75). 


HEAT.  651 

(319.)  Radiation.  —  "When  we  stand  in  the  bright  sunshine 
or  before  a  blazing  fire,  and  feel  the  effect  of  the  rays  of  heat 
impinging  on  our  bodies,  we  are  led  to  perceive  that  heat  is  emit- 
ted from  the  surfaces  of  hot  bodies,  and  that  it  has  the  power  of 
traversing  space  and  transparent  media  like  the  atmosphere. 
But  it  is  also  probable  that  rays  of  heat  are  emitted  from  the 
surfaces  of  all  bodies  and  at  all  temperatures,  however  low, 
the  only  difference  between  hot  and  cold  bodies  being  that  the 
first  radiate  more  heat  than  the  last.  In  a  room  where  there  is  a 
condition  of  thermal  equilibrium,  each  object  receives  as  much 
heat  as  it  radiates,  and  therefore  retains  its  own  temperature.  If 
one  object,  however,  becomes  warmer  than  the  rest,  —  the  stove, 
for  example, — then  it  radiates  more  heat  than  it  receives,  until  the 
equilibrium  is  again  established.  This  theory  explains  the  appar- 
ent radiation  of  cold,  which  we  feel  when  standing  before  a  large 
mass  of  ice.  It  is  not  that  the  ice  radiates  cold,  since  it  actually 
radiates  heat ;  but  as  the  body  receives  from  the  ice  less  heat 
than  it  radiates  towards  it,  we  feel  a  sensation  of  cold. 

The  phenomena  of  radiailt  heat  are  in  all  respects  similar  to 
those  of  light,  and,  as  is  well  known,  the  rays  of  both  agents  are 
found  mixed  together  in  the  sunbeam  and  in  the  emanations  from 
most  luminous  objects.  Like  light,  radiant  heat  is  transmitted 
with  an  incredible  velocity  in  straight  lines,  and  its  intensity 
diminishes  as  the  square  of  the  distance  from  the  source.  If  the 
rays  of  heat  fall  on  a  polished  surface  they  are  reflected,  and  the 
angle  of  reflection  is  always  equal  to  the  angle  of  incidence.  If 
they  enter  a  transparent  medium  they  are  refracted,  and  for  the 
same  substance  the  sine  of  the  angle  of  refraction  always  bears  a 
constant  ratio  to  the  sine  of  the  angle  of  incidence.  If  they  are 
passed  through  a  prism  of  rock  salt,  they  are  divided  into  rays  of 
different  refrangibility,  which  stand  to  each  other  in  the  same  rela- 
tion as  the  different  colors  of  the  solar  spectrum ;  and,  lastly,  when 
reflected  or  refracted  at  a  certain  angle  by  different  substances, 
the  heat  rays  become  polarized  and  present  properties  similar  to 
those  of  polarized  light.  But  yet,  although  the  thermal  rays  thus 
closely  resemble  the  rays  of  light,  there  are  essential  differences 
between  the  two.  It  does  not  follow,  because  a  medium  transmits 
light  unchanged,  that  it  will  transmit  heat  with  equal  readiness  ; 
thus,  for  example,  a  crystal  of  alum,  even  if  perfectly  transpar- 
ent to  light,  is  almost  opaque  to  heat ;  and,  on  the  other  hand, 


652  CHEMICAL  PHYSICS. 

a  crystal  of  smoky  quartz,  which  will  hardly  transmit  a  ray  of 
light,  is  quite  transparent  to  heat.  Most  solid  ahd  liquid  media 
which  are  transparent  and  colorless  as  regards  light,  act  on  the 
rays  of  heat  in  the  same  way  that  colored  glasses  act  on  light ; 
transmitting  rays  of  certain  degrees  of  refrangibility,  but  not 
others.  Thus,  for  example,  a  pane  of  colorless  glass  will  trans- 
mit nearly  all  the  rays  of  heat  from  the  sun,  while  it  will  inter- 
cept the  greater  part  of  those  from  a  coal  fire,  and  absolutely  all 
the  rays  which  radiate  from  a  steam-pipe  heated  to  100° ;  and  the 
same  is  true  to  a  still  greater  degree  of  water.  The  only  sub- 
stance which  is  perfectly  transparent  to  rays  of  heat  from  every 
source  is  rock-salt,  and  this  can  be  used  in  experiments  on  heat 
in  the  same  way  that  glass  is  used  in  optical  experiments.  The 
phenomena  of  radiant  heat  are  best  explained  by  the  undulatory 
theory,  which  assumes  that  they  are  caused  by  undulations  in  an 
imponderable  medium  filling  all  space  ;  and  they  cannot  be  prof- 
itably studied  until  the  student  is  acquainted  with  the  mechanical 
theory  of  light.  We  shall,  therefore,  notice  in  this  connection 
only  a  few  familiar  facts  connected  with  the  subject. 

The  unequal  power  which  different  bodies  possess  of  radiating 
heat  appears  to  depend  on  the  condition  of  the  surface,  and  not 
on  the  nature  of  the  substance  of  which  the  body  consists.  As  a 
general  rule,  the  greater  the  density  of  the  substance  at  the  sur- 
face, the  less  is  the  radiating  power  of  the  body.  Thus,  the  bur- 
nished surfaces  of  the  metals  are  the  poorest  radiators,  while  the 
surfaces  of  paper  and  similar  loose  materials  are  the  best.  The 
very  best  radiator  of  all  is  a  surface  covered  with  lampblack.  If 
we  represent  the  radiating  power  of  such  a  surface  by  100,  that 
of  a  silver  surface,  hammered  and  well  burnished,  will  be  only  3. 
Those  surfaces  which  radiate  heat  the  best  also  absorb  it  the  most 
readily,  and  it  has  been  proved  that  the  absorbing  power  of  a  sur- 
face is  equal  to  the  radiating  power,  if  the  difference  betiveen  the 
temperature  of  the  radiating'  and  absorbing  surfaces  is  not  great. 
On  the  other  hand,  the  power  which  a  surface  possesses  of  reflect- 
ing heat  is  always  in  the  inverse  ratio  of  its  power  of  absorption ; 
that  is,  the  best  absorbents  are  the  poorest  reflectors,  and  the 
reverse.  Hence  heat  is  best  reflected  by  surfaces  of  metals  which 
have  been  hammered  and  polished  ;  but  so  entirely  does  the 
power  of  reflecting  or  absorbing  heat  reside  in  the  surface,  that 
a  sheet  of  gilt  paper  answers  the  purpose  of  a  reflector  nearly  as 


HEAT.  653 

well  as  a  mass  of  solid  gold.  The  power  which  a  surface  has  of 
absorbing  heat  varies  with  the  nature  of  the  source  from  which  it 
emanates,  while  its  radiating  power  remains  constant ;  the  two  are 
equal  only  under  the  condition  above  stated.  Hence  it  is  not  sin- 
gular that,  while  the  radiating  power  of  any  surface  is  unaffected 
by  its  color,  the  readiness  with  which  bodies  absorb  the  heat  of 
the  sun  depends,  in  great  measure  at  least,  if  not  entirely,  upon  it. 
This  last  fact  was  noticed  by  Dr.  Franklin.  He  placed  pieces  of 
the  same  kind  of  cloth,  but  of  different  colors,  on  the  snow,  where 
they  were  equally  exposed  to  the  direct  rays  of  the  sun.  The 
black  cloth  absorbed  the  most  heat  and  sunk  deepest  into  the 
snow,  while  the  white  cloth  produced  but  little  effect.  The  other 
colored  cloths  produced  intermediate  effects ;  and  they  may  be 
arranged  according  to  their  absorbing  powers  as  follows  :  black, 
violet,  indigo,  blue,  green,  red,  yellow,  white. 

Numerous  illustrations  of  the  above  principles  may  be  found  in 
the  familiar  facts  of  every-day  life.  Water  can  be  heated  most 
rapidly  in  a  dull  iron  kettle,  whose  bottom  is  covered  with  soot, 
while  it  can  be  kept  hot  longest  in  a  bright  silver  teapot.  The 
hot  air  from  a  furnace  is  best  conveyed  to  the  different  apartments 
of  a  building  in  tinned  iron  pipes,  which  are  poor  radiators, 
while  the  smoke-pipe  of  a  stove  is  best  made  of  rough  sheet-iron, 
for  the  opposite  reason.  The  melting  of  a  bank  of  snow  is  accel- 
erated by  sprinkling  over  its  surface  coal-dust,  because  its  very 
feeble  power  of  absorption  is  in  that  way  greatly  increased. 
Light-colored  garments  are  preferable  in  summer,  because  they 
do  not  readily  absorb  the  solar  rays  ;  in  winter,  when  the  object 
is  to  retain  the  heat  in  the  body  and  prevent  radiation,  the  color 
is  unimportant. 

The  phenomenon  of  dew,  first  correctly  explained  by  Dr.  Wells, 
is  another  beautiful  illustration  of  the  principles  of  radiation. 
The  earth  is  constantly  radiating  heat  into  space.  During  the 
daytime  this  loss  is  compensated  by  the  constant  supply  of  heat 
from  the  sun ;  but  as  soon  as  the  sun  sets,  the  supply  ceases, 
while  the  radiation  still  continues.  Consequently,  the  tempera- 
ture of  all  objects  on  the  surface  exposed  to  the  clear  sky  is  rap- 
idly reduced ;  if  their  temperature  falls  below  the  dew-point  (313) 
of  the  atmosphere,  dew  is  deposited  upon  them  as  on  a  glass  of 
iced  water,  or,  if  the  temperature  falls  below  the  freezing-point,  the 
dew  takes  the  form  of  hoar-frost.  On  cloudy  nights,  little  or  no 
55* 


654  CHEMICAL  PHYSICS. 

dew  is  deposited,  because  the  clouds  reflect  back  the  rays  of  heat 
to  the  earth.  The  same  effect  is  produced  by  the  glass  sashes  or 
straw  mattings  which  are  used  by  gardeners  to  protect  young 
plants  from  the  late  frosts  of  spring.  The  direct  rays  of  the  sun 
readily  pass  through  the  glass  during  the  daytime,  but  the  glass 
reflects  back  the  heat  of  less  intensity  which  is  radiated  from  the 
earth  during  the  night.  On  windy  nights,  also,  little  or  no  dew 
is  deposited,  because  the  layer  of  air  in  contact  with  the  radiating 
crust  of  the  earth  is  so  frequently  renewed  that  its  temperature 
does  not  fall  to  the  dew-point ;  and  for  the  same  reason  dew  is 
more  copiously  deposited  in  a  valley  or  a  sequestered  dell  than  on 
the  top  of  a  hill ;  and  it  is  in  such  places,  also,  that  the  early 
frosts  of  autumn  are  first  felt.  As  we  should  naturally  expect, 
we  find  that  in  any  given  place  the  dew  is  deposited  most 
copiously  on  the  best  radiators,  which  are,  at  the  same  time, 
the  poorest  conductors  ;  thus,  while  dew  is  deposited  in  abun- 
dance on  the  shrubs  and  the  grass,  which  derive  most  benefit 
from  the  moisture,  it  is  not  wasted  on  the  dry  path  and  road, 
whose  hard,  beaten  surfaces  render  them  poorer  radiators,  while 
at  the  same  time  their  higher  conducting  power  enables  them  to 
withdraw  heat  from  the  strata  below,  and  thus  in  part  make  good 
the  loss  which  the  radiation  may  have  caused. 

"  In  India,  near  the  town  of  Hooghly,  about  forty  miles  from 
Calcutta,  the  principle  of  radiation  is  applied  to  the  artificial 
production  of  ice.  Flat,  shallow  excavations,  from  one  to  two 
feet  deep,  are  loosely  lined  with  rice  straw  or  some  similar  bad 
conductor  of  heat,  and  upon  the  surface  of  this  layer  are  placed 
shallow  pans  of  porous  earthen-ware,  filled  with  water  to  the 
depth  of  one  or  two  inches.  Radiation  rapidly  reduces  the  tem- 
perature below  the  freezing-point,  and  thin  crusts  of  ice  form, 
which  are  removed  as  they  are  produced,  and  stowed  away  in. 
suitable  ice-houses  until  night,  when  the  ice  is  conveyed  in  boats 
to  Calcutta.  Winter  is  the  ice-making  season,  viz.  from  the  end 
of  November  to  the  middle  of  February."  * 

(320.)  Conduction.  —  That  dense  and  compact  solids  like  the 
metals  are  good  conductors  of  heat,  while  light  and  porous  solids 
like  wood  and  the  various  textile  fabrics  are  poor  conductors, 
is  a  matter  of  common  experience.  The  general  fact  may  be 

*  Miller's  Elements  of  Chemistry,  Part  I.  p.  201. 


HEAT. 


655 


illustrated  by  means  of  the  apparatus 
of  Ingenhousz,  represented  in  Fig.  451. 
The  different  rods  attached  to  the  front 
of  the  brass  box,  made  of  various  ma- 
terials, are  covered  with  a  thin  layer  of 
wax  ;  and  on  turning  boiling  water  into 
the  box,  the  wax  melts  on  the  rods,  after 
a  certain  time,  to  unequal  distances, 
depending  on  their  relative  conducting  power. 

If  we  heat  one  end  of  a  metallic  rod  with  a  lamp,  as  repre- 
sented in  Fig.  452,  the  temperature  of  the  different  parts  of  the 
rod  will  gradually  increase,  until  a  point  is  reached  at  which  the 
heat  lost  by  radiation  is  equal  to  the  heat  received  from  the  flame 
by  conduction  through  the  bar.  If  now  we  test  the  temperature 


Fig.  451. 


Fig.  452. 

of  the  different  parts  of  the  bar  by  means  of  thermometers  placed 
at  equal  intervals,  say  of  one  decimetre  each,  it  will  be  found  that 
it  very  rapidly  decreases  as  we  go  from  the  source  of  heat ;  and 
if  the  distances  from  the  source  of  heat  increase  in  an  arith- 
metical progression,  the  excess  of  the  temperatures  of  the  suc- 
cessive sections  of  the  bar  above  the  temperature  of  the  air  will 
be  found  to  diminish  in  a  geometrical  progression.  Moreover,  it 
is  evident  that  the  rate  of  decrease  will  be  more  rapid  in  propor- 
tion as  the  conducting  power  of  the  bar  is  more  feeble ;  and  we 
can  Determine  the  relative  conducting  powers  of  two  bars  by 
measuring  the  distances  from  the  source  of  heat  of  the  sections 
which  have  the  same  temperature,  for  it  can  easily  be  proved 


656 


CHEMICAL   PHYSICS. 


100 

Steel,        .... 

11.6 

73.6 

Lead,    .... 

8.5 

53.2 

Platinum, 

8.4 

14.5 

Rose's  Metal, 

2.8 

11.9 

Bismuth,  .         ,         . 

1.8 

that  the  conducting  powers  are  to  each  other  as  the  squares  of 
these  distances.  Experimenting  in  this  way,  and  using  a  delicate 
thermo-electric  pile  for  measuring  the  temperatures  of  the  dif- 
ferent sections  of  the  bars,  Messrs.  Wiedmann  and  Franz  de- 
termined the  relative  conducting  powers  of  various  metals,  as 
follows  :  — 


Silver, 
Copper, 
Gold, 
Tin,    . 
Iron, 


The  conducting  power  of  stones,  brick,  and  other  earthy 
materials,  is  very  much  less  than  that  of  the  metals,  and  the 
conducting  power  of  wood  and  other  organic  tissues  is  so  very 
feeble  that  they  are  usually  regarded  as  non-conductors.  It  may 
be  assumed  as  a  rule,  although  it  has  many  exceptions,  that  the 
denser  a  body  the  better  it  conducts  heat. 

Homogeneous  solids  and  crystals  belonging  to  the  regular  sys- 
tem conduct  heat  equally  in  all  directions  ;  but  in  crystals  not 
belonging  to  the  regular  system,  the  conduct- 
ing power  varies  in  the  direction  of  unequal 
axes.  This  fact  is  easily  shown  by  a  simple 
experiment  devised  by  Senarmont.  He  took 
two  slices  of  a  quartz  crystal  (Fig.  453),  one 
cut  perpendicular  to  the  vertical  axis,  and  the 
other  parallel  to  it  ;  through  the  centre  of  each 
plate  he  drilled  a  small  conical  aperture  for 
the  reception  of  a  silver  wire,  one  end  of  which, 
heated  in  the  flame  of  a  lamp,  served  as  a 
central  source  of  heat.  Previously  to  the 
application  of  the  heat,  he  had  covered  the 
slices  of  the  crystal  with  beeswax.  He  found 
that  on  the  first  the  wax  melted  in  the  form 
of  a  circle  round  the  wire,  showing  that 
quartz  conducts  heat  equally  in  the  direction 
of  its  equal  and  lateral  axes  ;  but  on  the 
second  the  wax  melted  in  the  form  of  an  el- 
lipse, whose  longer  diameter  coincided  with  the  vertical  axis  of 
the  crystal,  which  proved  that  the  conducting  power  is  greater 


Fig.  453. 


HEAT.  657 

in  this  direction  than  in  the  one  at  right  angles  to  it.  Similar 
facts  are  also  true  of  organized  structures  ;  thus,  wood  conducts 
heat  much  better  in  the  direction  of  its  fibres  than  across  them. 

Count  Rumford  concluded,  from  his  experiments,  that  liquids 
were  absolutely  non-conductors  ;  but  later  experiments  have 
shown  that  they  do  conduct  heat,  but  only  very  imperfectly.  De- 
spretz  *  experimented  on  a  vertical  column  of  water  contained  in 
a  wooden  cylinder  one  metre  high  and  21.8  c.  m.  in  diameter, 
whose  upper  surface  he  exposed  to  a  constant  source  of  heat. 
By  means  of  thermometers  passing  through  tubulatures  on  the 
sides  of  the  cylinder,  he  observed  the  temperatures  of  horizontal 
sections  of  the  liquid  at  equal  distances  from  each  other.  At  the 
end  of  32  hours  the  thermometers  were  stationary,  and  the  dif- 
ferences between  the  temperatures  indicated  by  the  successive 
thermometers  and  the  temperature  of  the  air  were  found  to  form 
a  decreasing  geometrical  series,  as  in  a  solid  bar.  This  experi- 
ment proves  conclusively  that  water  conducts  heat ;  but,  never- 
theless, the  conducting  power  is  so  feeble,  that  water  may  be 
boiled  for  many  minutes  at  the  top  of  a  test-tube  without  oc- 
casioning the  slightest  inconvenience  to  the  person  who  holds 
the  lower  end.  Gases  are  still  poorer  conductors  of  heat  than 
liquids  ;  but  yet  they  are  not  absolutely  non-conductors,  and  they 
differ  very  greatly  from  each  other  in  this  respect.  This  is 
proved  by*  the  fact  that  a  hot  body  cools  more  rapidly  in  an  at- 
mosphere of  hydrogen  than  in  air,  and  also  by  a  similar  fact, 
first  noticed  by  Grove,  that  a  platinum  wire  can  be  made  to  glow 
in  air  with  a  feebler  galvanic  current  than  it  can  in  hydrogen. 
In  order  to  heat  a  mass  of  liquid  or  gas,  we  always  apply  the 
heat  to  the  lowest  portion  of  the  containing  vessel ;  then,  as 
already  explained  (268),  currents  are  established  by  which  the 
particles  are  brought  into  actual  contact  with  the  source  of  heat. 
This  process  is  sometimes  distinguished  as  a  third  method  of 
communicating  heat,  and  called  convection. 

(321.)  Illustrations.  —  The  laws  of  conduction  furnish  the  ex- 
planation of  many  familiar  facts,  and  receive  many  important 
applications  both  in  the  arts  and  in  every-day  life.  Our  sensa- 
tions of  heat  and  cold  are  very  much  influenced  by  the  conduct- 
ing power  of  the  substances  with  which  the  body  comes  in  contact. 

*  Annales  de  Chimie  et  de  Physique,  3e  S&ie,  Tom.  LXXI. 


658  CHEMICAL  PHYSICS. 

A  hearth,  for  example,  feels  colder  to  the  bare  feet  than  a  wooden 
floor,  and  this,  again,  colder  than  a  woollen  carpet,  even  when  all 
are  at  the  same  temperature.  The  obvious  explanation  is,  that 
stone  is  a  better  conductor  than  either  wood  or  wool,  and  there- 
fore removes  the  heat  from  the  body  more  rapidly.  The  body,  if 
properly  protected  by  poor  conductors,  may  be  exposed  with  im- 
punity to  air  heated  to  150°,  while  it  would  be  burnt  by  contact 
with  a  rod  of  metal  heated  to  only  50°.  The 'oven-girls  of  Ger- 
many, protected  by  thick  woollen  garments,  enter  without  incon- 
venience ovens  where  all  kinds  of  culinary  operations  are  going 
on,  although  the  touch  of  any  metallic  articles  while  there  would 
surely  burn  them. 

Water  in  pipes  laid  at  a  slight  depth  under  ground  is  not 
frozen  during  the  severest  winter,  because  the  soil  is  a  poor  con- 
ductor ;  and  iron  safes  are  rendered  fire-proof  by  making  them 
with  double  walls,  and  filling  the  intervening  space  with  non- 
conducting materials.  Doors  of  furnaces,  ladles,  and  teapots 
are  provided  with  wooden  handles,  to  protect  the  hand  from  the 
heated  metal ;  and  hot  dishes  are  placed  on  woollen  or  straw 
mats,  which  prevent  the  polished  surface  of  the  table  from  being 
scorched.  So  also  vessels  of  glass  'or  porcelain  are  heated  on 
a  sand-bath,  and  when  removed  from  the  fire  are  always  rested 
on  some  non-conductor,  as  they  are  liable  to  crack  when  suddenly 
heated  or  cooled. 

The  efficacy  of  clothing  in  preventing  the  escape  of  the  heat 
of  the  body  depends,  not  only  on  the  non-conducting  power  of 
the  material  itself,  but  also  on  that  of  the  air  which  is  imprisoned 
by  it.  Hence  it  is  that  wool,  fur,  and  eider-down,  which  retain 
large  bodies  of  air  within  their  texture,  are  so  well  adapted  to 
protect  the  body  against  the  extreme  cold  of  winter.  The  order 
of  the  conductibility  of  the  different  materials  used  for  clothing 
is  as  follows  :  linen,  silk,  cotton,  wool,  furs.  Accordingly,  cotton 
sheets  feel  warmer  than  linen  ones,  and  blankets  warmer  than 
either.  In  summer,  coarse  linen  goods  are  used,  "because  they 
allow  the  heat  to  escape  from  the  body  more  readily  than  other 
materials,  while  a  dress  of  fine  and  close  woollen  is  the  best  pro- 
tection from  the  cold  of  winter  except  furs. 

It  is  in  consequence  of  the  non-conducting  property  of  gases, 
that  double  doors  and  windows,  which  include  a  layer  of  air  be- 
tween them,  are  so  useful  in  preventing  the  heat  of  our  houses 


HEAT. 


659 


from  escaping  outwards  ;  and  the  double  walls  of  ice-houses, 
refrigerators,  or  water-coolers,  for  preventing  the  heat  from  en- 
tering. For  the  same  reason,  snow,  which  encloses  large  quanti- 
ties of  air,  prevents  the  escape  of  the  heat  from  the  earth,  and 
limits  the  penetration  of  frost.  It  is  a  well-known  fact,  that 
the  ground  always  freezes  deeper  in  winters  without  snow  than 
when  it  abounds.  But  it  is  unnecessary  to  multiply  these  illus- 
trations further. 

(322.)  Coefficient  of  Conduction.  —  The  number  of  units  of 
heat  which  pass  in  one  second  through  a  solid  wall  1  m.  m.  thick 
and  having  an  area  of  1  5T2,  when  the  difference  between  the 
temperatures  of  the  two  faces  of  the  wall  is  equal  to  1°,  is  called 
the  coefficient  of  conduction  of  the  substance  of  which  the  wall 
consists.  The  coefficient  of  conduction  of  lead  was  determined 
by  Peclet  by  means  of  a  very  ingenious  apparatus,*  and  found 
to  be  3.82.  From  this,  the  coefficients  of  conduction  of  other 
solids  can  be  calculated  when  their  conductibility  as  compared 
with  lead  is  known.  We  give,  in  the  first  column  of  the  follow- 
ing table,  the  relative  conductibility  of  several  solids,  as  deter- 
mined by  Despretz  ;  and  in  the  second  column,  the  coefficients  of 
conduction,  which  have  been  calculated  as  just  described.  The 
results  of  Despretz,  however,  are  not  probably  as  accurate  as  those 
of  Wiedmann  and  Franz,  given  above. 


Gold,    . 
Platinum, . 
Silver,  . 
Copper,      . 
Iron,     . 
Zinc,       .    . 


I. 

100.0 

n. 
21.28 

Tin, 

98.1 

20.95 

Lead,  . 

97.3 

20.71 

Marble,  . 

89.8 

19.11 

Porcelain,    . 

37.4 

7.95 

Baked  Clay, 

36.3 

7.74 

I. 

30.39 

17.95 

2.36 

1.22 

1.14 


n. 

6.46 
3.82 
0.48 
0.24 
0.23 


When  the  coefficient  of  conduction  is  known,  we  can  easily 
calculate  the  amount  of  heat  in  units  which  will  pass  through  a 
given  metallic  plate  in  a  given  time,  by  means  of  the  following 
formula,  which  for  want  of  space  we  must  assume  without  proof. 


C=K  .  S--. 


[205.] 


In  this  formula,  K  represents  the  coefficient  of  conduction,  S  the 


Annales  de  Chimie  et  de  Physique,  3e  S6ie,  Tom.  II. 


660  CHEMICAL  PHYSICS. 

area  of  the  plate,  E  its  thickness,  and  t,  t'  the  temperatures  of 
its  two  faces.  It  is  evident  that  the  quantity  of  heat  passing 
through  such  a  metallic  plate  in  a  second  of  time  increases  in 
direct  proportion  with  the  conductibility  of  the  metal,  with  the 
area  of  the  plate,  and  with  the  difference  of  temperature  between 
its  faces  ;  and  it  is  also  evident  that  the  amount  of  heat  dimin- 
ishes in  direct  proportion  to  the  thickness. 

It  has  already  been  stated  (305),  that,  in  making  boilers  for 
evaporating  water  or  other  liquids,  it  is  necessary  to  pay  regard 
to  the  laws  of  conduction  ;  and  it  is  evident  from  the  above  for- 
mula that  the  greater  the  conducting  power  of  the  metals,  the 
larger  the  area  of  the  heating  surface,  and  the  thinner  the  boiler- 
plates, the  more  rapid  will  be  the  evaporation.  Hence  the  advan- 
tage of  copper  over  iron  boilers,  and  also  the  reason  that  water 
will  evaporate  so  much  more  rapidly  in  a  silver  dish  than  in 
one  either  of  glass  or  porcelain. 


CHAPTER    V. 

WEIGHING  AND  MEASURING. 

• 

(323.)  Recapitulation.  —  Most  methods  of  chemical  investiga- 
tion and  all  processes  of  quantitative  chemical  analysis  involve  the 
accurate  determination  of  the  amounts  of  small  masses  of  mat- 
ter, either  by  measure  or  by  weight.  The  mass  of  a  body,  that 
is,  the  quantity  of  matter  which  it  contains,  is  necessarily  inva- 
riable ;  but  its  weight  and  its  volume  are  liable  to  constant  va- 
riations, arising  from  changes  either  of  temperature  or  of  the 
pressure  of  the  atmosphere,  and  from  other  causes.  It  has  been 
one  great  object  of  the  present  volume  to  develop  the  principles  on 
which  these  variations  depend,  and  to  study  the  laws  which  they 
obey.  We  have  thus  been  led  to  different  methods  by  which  the 
observed  volumes  and  weights  of  bodies  may  be  reduced  to  cer- 
tain assumed  standards,  such  as  a  temperature  of  0°  C.  and  a 
pressure  of  76  c.  m.  ;  and  it  will  be  the  object  of  the  remaining 
chapter  of  this  volume  to  illustrate  these  methods  by  a  few 
examples. 

SOLIDS. 

£324.)  Weight.  —  The  weight  of  a  solid  is  easily  determined 
by  means  of  the  balance.  The  theory  of  this  instrument  has 
been  already  given  at  length  (73),  and  the  methods  of  using  it 
are  so  simple  and  obvious  that  they  need  not  be  described  in 
detail.*  Were  it  not  for  the  presence  of  the  atmosphere,  the 
balance  would  give  at  once  the  exact  relative  weight  (71)  of  a 
body ;  but  weighing  the  body,  as  we  must,  immersed  in  the  air, 
the  difference  of  the  buoyancy  which  the  air  exerts  on  the 
weights  and  on  the  body  may  make  the  apparent  weight  slightly 
different  from  the  actual  weight.  We  can  always,  however,  re 
duce  the  observed  weight  to  the  weight  in  vacua  by  means  of 

*  For  the  best  methods  of  manipulating  a  delicate  balance,  and  for  the  precautions 
required  in  accurate  weighing,  the  student  may  consult  the  standard  work  of  Fresenius 
on  Quantitative  Analysis. 

56 


662  CHEMICAL   PHYSICS. 

[91],  when  either  the  volumes  or  the  specific  gravities  of  both 
the  weights  and  the  body  are  known.  For  this  purpose,  the 
heights  of  the  barometer  and  thermometer  are  observed  at  the 
time  of  weighing,  and  from  these  observed  data  the  weight  of  one 
cubic  centimetre  of  air  (10),  required  in  making  the  reduction,  is 
easily  calculated  by  [215],  or  obtained  by  inspection  from  Table 
XIV.  In  weighing  either  solids  or  liquids,  however,  the  correc- 
tion for  the  buoyancy  of  the  atmosphere  is  at  best  very  small, 
and  may  be  entirely  neglected  except  in  the  very  few  cases  where 
the  greatest  refinement  is  required  ;  as,  for  example,  in  adjusting 
standard  weights.  For  the  method  to  be  followed  in  such  cases, 
the  student  will  do  well  to  consult  the  admirable  memoir  of 
Professor  Miller*  on  the  restoration  of  the  English  standards. 

(325.)  Specific  Gravity.  —  The  specific  gravity  of  a  substance 
has  been  defined  as  the  ratio  of  its  weight  to  that  of  an  equal 
volume  of  pure  water  at  4°,  the  temperature  at  which  the  volume 
of  the  solid  is  measured  being  0°.  The  general  methods  by 
which  the  specific  gravity  of  solids  is  determined  have  been 
already  described  (144-146),  and  we  have  only  to  consider 
the  methods  by  which  results  obtained  at  other  temperatures 
may  be  reduced  to  the  standard  temperatures. 

In  order  to  obtain  the  specific  gravity  of  a  solid,,  we  determine, 
in  the  first  place,  the  relative  weight  ( W)  of  the  body  ;  and 
when  very  great  accuracy  is  required,  the  weight  observed  in  the 
air  may  be  reduced  as  just  described.  We  next  seek,  by  one  of 
the  methods  of  (145)  and  (146),  the  weight  of  pure  water  (  W) 
displaced  by  the  body  when  the  temperature  of  the  water  is  4°, 
and  that  of  the  solid  0° ;  and,  lastly,  we  calculate  the  specific 
gravity  by  dividing  the  first  weight  by  the  last.  Practically, 
the  value  of  W  is  always  determined  at  some  temperature,  2°, 
higher  than  the  standard  temperatures,  and  the  same  for  both 
solid  and  water  ;  and,  before  using  it  in  calculating  the  specific 
gravity,  it  is  necessary  to  determine  what  would  be  its  value 
assuming  that  the  water  was  at  4°  and  the  solid  at  0°.  In  Table 
XVI.  we  have  given  the  specific  gravity  of  water  at  different 
temperatures  referred  to  water  at  4°  as  unity.  Representing, 
then,  the  specific  gravity  at  t°  by  8>  and  also  the  weight  of  water 
displaced  respectively  at  t°  and  4°  by  W?  and  W^,  we  shall 

*  Philosophical  Transactions,  Part  III.     London,  1856. 


I 

WEIGHING  AND   MEASURING.  663 

have,  evidently,  (assuming  that  the  volume  of  the  solid  is  in- 
variable,) 

JT4o  :  W?  =  1  :  a,     or     W^  =  Wf  ^  .          [206.] 

But  the  volume  of  the  solid  is  not  invariable,  and  it  displaces  at 
0°  (the  standard  temperature  for  the  solid)  less  water  than  at  t°. 
Representing  the  volumes  of  the  solid  at  0°  and  t°  by  VQ>  and 

Fto  respectively,  we  have,  by  [166],   FQO  =  T>  — — --.      Since 

the  two  weights  of  water  displaced  by  the  solid  when  at  0°  and  t° 
must  be  proportional  to  the  volumes  of  the  solid  at  these  tempera- 
tures, (assuming  now  that  the  temperature  of  the  water  is  invaria- 
bly at  4°,)  we  shall  also  have  TF4o :  W*  =  V?  :  -^xt '  Hence> 
and  by  [206], 

[207.] 

Having  thus  obtained  the  weight  of  water  at  4°  displaced  by  the 
solid  at  0°,  this  value,  W'^  is  to  be  used  in  place  of  W1  in  [87]. 
The  last  factor  of  [207]  is  always  very  nearly  unity,  and  can  in 
most  cases  be  neglected  without  appreciable  error.  When  the 
coefficient  of  expansion  is  not  accurately  known,  and  great  accu- 
racy is  required,  the  value  of  K  may  be  eliminated  from  [207] 
by  making  two  determinations  of  the  weight  of  water  displaced 
at  temperatures  differing  as  widely  from  each  other  as  the  cir- 
cumstances will  permit.  In  very  accurate  determinations  the 
temperature  of  the  water  should  be  observed  to  the  tenth  of  a 
Centigrade  degree  ;  and  if  the  value  of  8  is  not  given  in  the 
table  for  the  observed  temperature,  it  can  easily  be  determined  by 
interpolation.  Compare  (289).* 

*  The  most  accurate  method  of  determining  the  specific  gravity  of  a  solid  is  the 
one  with  the  hydrostatic  balance  (146),  which  should  always  be  used  when  the  nature 
of  the  substance  will  admit  of  it.  The  body  is  best  suspended  from  the  pan  of  the 
balance  by  a  single  fibre  of  silk,  or  by  a  very  fine  human  hair,  and  the  temperature  of 
the  water  observed  by  means  of  a  very  delicate  thermometer,  adjusted  so  that  the 
bulb  may  be  nearly  in  contact  with  the  body,  and  so  that  the  division  may  be  read  by 
a  telesrope  placed  outside  of  the  balance-case.  When  the  solid  is  in  powder,  it  can  be 
supported  under  water  in  a  small  glass  cup  suspended  to  the  pan  of  the  balance  by  a 
platinum  wire.  In  this  case,  it  is  necessary  to  weigh,  first,  the  cup  under  water,  im- 
mersed to  a  point  marked  on  the  platinum  wire.  We  then  weigh  the  cup  containing 


664  CHEMICAL  PHYSICS. 

(326.)  Volume.  —  The  volume  of  a  solid  can  rarely  be  deter- 
mined with  accuracy  by  direct  measurement.  It  is  therefore 
generally  calculated  from  the  weight  and  the  specific  gravity  by 
means  of  the  formula  [56].  Several  examples  of  such  calcula- 
tions have  already  been  given  among  the  problems. 

the  powder  immersed  to  the  same  point,  taking  care  that  the  temperature  is  the  same 
as  before.  The  difference  between  these  weights  is,  evidently,  the  weight  of  water  dis- 
placed by  the  solid  at  the  observed  temperature,  which  must  be  reduced  to  the  standard 
temperatures  by  [207].  Lastly,  we  wash  the  powder  into  a  tared  beaker-glass,  evapo- 
rate the  water,  and  determine  the  weight  of  the  solid.  The  only  objection  to  this 
method  of  experimenting  arises  from  the  fact  that  the  resistance  of  the  water  to  the 
motion  of  the  cup  renders  the  balance  less  sensitive  and  prompt  in  its  indications. 

When  the  solid  is  in  powder,  very  accurate  results  can  be  obtained  with  a  specific- 
gravity  bottle  (145).  The  neck  of  the  bottle  should  be  made  with  a  thick  rim,  ground 
square  at  the  top,  and  the  glass  stopper  should  be  so  fitted  as  not  to  have  a  channel 
between  the  two  in  which  water  can  collect.  In  order  to  determine  its  specific  gravity, 
a  known  weight,  W,  of  the  powder  is  introduced  into  the  bottle  with  water,  and  after 
the  entangled  air  has  been  removed  by  an  air-pump,  the  bottle  is  suspended  in  a  large 
beaker  of  water  whose  temperature  is  very  slightly  higher  than  that  of  the  room.  This 
temperature,  t,  is  carefully  observed  by  means  of  a  delicate  thermometer,  whose  bulb  is 
placed  near  the  bottle.  After  an  equilibrium  is  established,  the  stopper  is  inserted  into 
the  neck  of  the  bottle  while  it  is  still  under  water.  The  bottle  can  then  be  removed, 
and,  after  having  been  wiped  dry,  weighed  at  leisure.  This  is  the  weight  W>  of  [86]. 
For  every  specific-gravity  bottle,  we  determine  once  for  all  the  weight,  Wo,  of  water 
which  it  contains  at  0°.  This  is  a  constant  for  that  bottle,  and  from  it  we  can  easily 
calculate  the  weight  of  the  bottle  filled  with  water  at  <°,  or  JFi,  by  the  formula, 

Wi  =  W  +  Wo  (1  +  Kt)  3,  [208.] 

in  which  W'  is  the  weight  of  the  glass,  K  the  coefficient  of  expansion  of  glass,  and  8 
the  specific  gravity  of  water  at  f°,  referred  to  water  at  0°  as  unity,  as  given  by  Table 
XVI.  The  weight  of  the  water  displaced  at  t°  is  now  determined  by  the  formula 

We  =  JFi  +  W-  TF2, 

which  is  then  reduced  to  the  standard  temperature  by  [207]. 

The  chemist  frequently  has  occasion  to  determine  the  specific  gravities  of  solids 
which  are  soluble  in  water.  For  this  purpose  he  selects  some  inactive  liquid,  such  as 
alcohol,  glycerine,  or  oil  of  turpentine,  and  first  finds,  by  one  of  the  methods  just  de- 
scribed, the  weight  of  this  liquid  displaced  by  the  body,  exactly  as  when  using  water, 
the  temperature  being  carefully  observed.  He  then  determines  the  specific  gravity  of 
the  liquid  used  at  the  same  temperature  as  before,  and  from  these  data  easily  calculates 
the  specific  gravity  of  the  solid.  The  student  will  be  able  to  devise  a  formula  for  the 
purpose. 

In  all  delicate  determinations  of  specific  gravity  it  is  essential  to  use  several  grammes 
of  the  substance,  since  otherwise  a  very  small  error  in  the  weighing  will  cause  an  im- 
portant error  in  the  result.  It  is  also  essential  to  remove  any  air  which  may  be 
entangled  in  the  interstices  or  cavities  of  the  solid.  This  can  be  done  either  by  boiling 
the  liquid  in  which  the  solid  is  immersed,  or  by  placing  the  vessel  containing  the 
liquid  and  solid  under  the  receiver  of  an  air-pump  and  exhausting  the  air. 


WEIGHING   AND   MEASURING.  665 


LIQUIDS. 

(327.)  Weight  and  Specific  Gravity  .  —  The  weight  of  a  liquid 
can  be  most  accurately  determined  by  direct  weighing,  and  the 
weight  of  the  liquid  in  the  atmosphere  may  be  reduced  to  the 
weight  in  vacuo  exactly  as  in  the  case  of  solids  ;  only  the  tare  of 
the  flask  in  which  the  liquid  is  enclosed  must  be  taken  under  the 
same  circumstances  of  temperature  and  pressure  as  those  under 
which  the  liquid  is  weighed.  Such  niceties,  however,  are  very 
rarely  necessary. 

The  specific  gravity  of  a  liquid  determined  at  an  observed 
temperature,  t*  by  either  of  the  methods  described  in  (145) 
and  (146),  can  easily  be  reduced  to  the  standard  temperature 
when  the  law  of  expansion  of  the  liquid  is  known.  For  this  pur- 
pose, we  first  calculate  the  volume  of  the  liquid  at  t°  (F*°)>  the 
volume  at  0°  being  unity,  by  means  of  the  empirical  formula 
expressing  the  law  of  expansion  (255)  ;  and  since  the  specific 
gravity  at  different  temperatures  must  be  inversely  as  the  volume, 
we  have 


and  [209.] 

- 


In  most  cases  with  which  the  chemist  meets  in  practice,  however, 
the  law  of  expansion  is  not  known.  It  is  then  best  to  determine 
by  direct  experiment  the  specific  gravity  of  the  liquid  at  the  stand- 
ard temperature.  An  apparatus  invented  by  Regnault  (Fig.  454) 
may  be  used  with  advantage  for  this  purpose.  It  is  merely  a 
specific-gravity  bottle,  so  shaped  that  it  can  readily  be  surrounded 
by  melting  ice  and  the  volume  of  the  liquid  measured  with 
great  accuracy.  It  is,  in  the  first  place,  filled,  like  a  thermometer- 
tube,  witli  the  liquid  to  be  examined,  which  is  then  cooled  to  0° 
by  surrounding  the  apparatus  supported  on  its  stand  with  pulver- 

*  By  "  specific  gravity  of  a  liquid  at  the  temperature  t  "  is  meant  the  weight  of  the 
liquid  divided  by  the  weight  of  an  equal  volume  of  water,  the  liquid  being  measured  at  *° 
and  the  water  at  4°.  In  using  a  specific-gravity  bottle  (  145  ),  we  have  only  to  determine 
for  each  substance  the  weight,  VF,  of  liquid  which  exactly  fills  the  bottle  at  «°.  Having 
previously  determined,  once  for  all,  the  weight  of  water  at  4°  which  the  bottle  will  con- 
tain at  the  same  temperature,  we  can  easily  calculate  by  [166]  the  weight  of  water  at 
4°  which  the  bottle  would  hold  at  t°.  In  using  the  hydrostatic  balance,  the  results  may 
be  reduced  in  a  similar  way. 

56* 


666 


CHEMICAL   PHYSICS. 


ized  ice.     After  an  equilibrium  of  temperature  is  established,  the 

excess  of  the  liquid  is  removed  with 
bibulous  paper,  until  the  liquid 
stands  at  a  point  marked  on  the 
fine  tube  which  forms  the  neck  of 
the  bottle.  The  apparatus  is  now 
closed  with  its  glass  stopper,  and  it 
may  then  be  removed  from  the  ice, 
wiped  dry,  and  weighed  at  leisure. 
By  subtracting  from  this  weight  the 
tare  of  the  glass  and  the  brass  stand, 
we  obtain  the  weight  of  liquid  which 
the  apparatus  holds  at  0°,  which,  di- 
vided by  the  weight  of  water  it  con- 
tains at  4°  (previously  determined) , 
gives  the  exact  specific  gravity. 

(328.)  Volume.  —  The  volumes 
of  liquids  are  generally  determined 
by  direct  measurement.  For  this 
purpose  a  great  variety  of  grad- 
uated glasses  are  used,  which  are  described  in  detail  in  most 
works  on  Chemical  Manipulation  or  Chemical  Analysis.* 
These  instruments  for  chemical  purposes  are  usually  gradu- 
ated in  cubic  centimetres,  and  are  only  standard  at  0°.  The 
process  of  measurement  is,  however,  seldom  so  accurate  as  to 
make  it  important  to  regard  the  change  of  volume  which  the 
glass  undergoes  from  changes  of  temperature.  The  same,  how- 
ever, is  not  true  in  regard  to  the  liquid  itself;  where  great 
accuracy  is  required,  it  is  important  to  observe  the  temperature 
at  which  the  measurement  is  made,  and  to  reduce  the  observed 
volume  to  the  standard  temperature  by  means  of  the  empirical 
formula  (255),  which  expresses  the  law  of  expansion  of  the  given 
liquid. 

The  volume  of  a  liquid  can  be  determined  with  greater  accu- 
racy by  [56]  ;  that  is,  by  dividing  the  weight  of  the  liquid  by  its 
specific  gravity  for  the  temperature  at  which  the  volume  is  re- 
quired. This  method  is  frequently  used,  in  chemical  investiga- 
tions, for  measiiring  the  volume  of  a  glass  vessel.  For  this  pur- 


Fig.  454. ' 


*  A  very  complete  description  of  this  class  of  instruments  will  be  found  in  Dr. 
Mohr's  Titrirmethode. 


WEIGHING   AND   MEASURING. 


66T 


pose,  we  determine  with  a  delicate  balance  the  weight  of  mercury 
or  distilled  water  which  the  vessel  contains  at  an  observed  tem- 
perature. This  weight,  divided  by  the  specific  gravity  of  mercury 
or  water  for  the  given  temperature,  gives  the  volume  of  the 
vessel  at  that  temperature.  If  the  weight  is  accurate  to  one 
centigramme,  the  volume  may  thus  be  measured  within  the  thou- 
sandth or  the  hundredth  of  a  cubic  centimetre,  according  as 
mercury  or  water  was  used  in  the  determination.  Knowing  now 
the  volume  of  the  vessel  at  a  given  temperature,  /,  and  also  the 
coefficient  of  expansion  of  glass  (245),  we  can  easily  calculate 
by  [167]  the  volume  at  any  other  temperature  (241). 


GASES   AND    VAPORS. 

(329.)  Weight.  —  The  weights  of  equal  volumes  of  the  best 
known  gases  and  vapors  have  been  determined  with  great  care  by 
several  experimenters,  and  it  is  now  seldom  necessary  to  repeat 
the  determination.  Those  of  air,  oxygen,  nitrogen,  hydrogen,  and 
carbonic  acid  were  determined  by  Regnault,  and  are  among  the 
most  accurate  constants  of  science.  The  method  which  he  used 
will  serve  to  illustrate  the  general  method  followed  in  such  cases. 

Regnault  weighed  the  gases  in  a  large  glass  globe,  whose  volume,  V, 
had  been  measured  in  the  way  just  de- 
scribed. In  order  to  avoid  the  always 
uncertain  correction  made  necessary  by 
changes  in  the  buoyancy  of  the  atmosphere 
during  the  course  of  the  experiments,  he 
equipoised  this  globe  by  another  globe  of 
the  same  size  and  made  of  the  same  kind 
of  glass  (see  Fig.  258)  ;  so  completely 
did  this  simple  provision  effect  its  object, 
that  in  one  experiment  he  saw  the  equi- 
librium maintained  during  fourteen  days,  in 
spite  of  great  change  in  the  temperature, 
pressure,  and  moisture  of  the  air.  The  ex- 
periments were  conducted  in  the  following 
way.  The  globe,  having  been  surrounded 
with  melting  ice  (Fig.  455),  and  connected 
by  a  lead  tube  with  the  manometer  t  t'  and 
also  with  an  air-pump  through  the  branch 
tube  a  m,  was  first  filled  with  perfectly  pure  and  dry  gas.  This  was 


668  CHEMICAL   PHYSICS. 

effected  by  exhausting  it  several  times,  and,  after  each  exhaustion,  con- 
necting it  with  the  vessel  in  which  the  gas  was  generating  through  a  series 
of  U  tubes,  by  which  the  crude  gas  was  dried  and  purified.  The  globe 
was  then  exhausted  again  as  perfectly  as  possible,  and  the  tension  of  the 
small  amount  of  gas  remaining  in  it  ascertained  by  measuring  the  height 
«  /5  with  a  cathetometer.  Represent  this  by  hQ.  This  measurement  hav- 
ing been  made  and  the  stopcock  closed,  the  globe  was  disconnected  from 
the  manometer,  removed  from  the  ice,  and,  having  been  carefully  cleaned, 
suspended  to  one  pan  of  a  very  strong  and  delicate  balance,  and  coun- 
terpoised by  a  second  globe  as  above  described.  The  globe  was  then 
returned  to  its  first  position,  and  the  connection  having  been  made  as 
before,  it  was  again  filled  with  the  same  gas  under  the  pressure  of  the  air. 
Represent  the  pressure,  as  given  by  the  barometer,  by  H0.  Lastly,  the 
globe  was  a  second  time  suspended  from  the  balance,  and  the  increase  of 
weight  determined,  which  we  will  call  W.  This  evidently  was  the  weight 
of  a  volume  of  gas  equal  to  the  volume  of  the  globe  measured  at  0°, 
and  under  a  pressure  of  HQ  —  k0.  The  weight  of  one  cubic  centimetre 
of  the  gas  at  0°,  and  under  a  pressure  of  76  c.m.,  was  then  calculated  by 
the  formula, 

'' 


The  results  obtained  by  Regnault  were  as  follows  :  — 

«5n»Pifi«  Weight  of  1  Litre 

Name  of  Gas.  <g*  measured  at 

Gravity.  0°  and  76  c.m. 

Air,      .         .  .         »'     ...  1.00000  1.293187 

Nitrogen,.         .         .         .  0.97137  1.256167 

Oxygen,    |J  ,4  .      _.£,    ;.  1.10563  1.429802 

Hydrogen,         .         .  ^     .  ^  0.06926  0.089578 

Carbonic  Acid,  .       .'.     "...  1.52901  1.977414 

It  was  discovered  by  Gay-Lussac,  that  all  gases  combine  with 
each  other  in  very  simple  proportions  by  volume.  This  remark- 
able law  will  be  considered  at  length  in  another  portion  of  this 
work.  It  is  sufficient  for  the  present  to  say,  that  it  gives  us  the 
means  of  calculating  from  the  weight  of  one  litre  of  oxygen  the 
weight  of  one  litre  of  any  other  gas  when  the  chemical:  equiva- 
lent and  the  combining  volume  are  known.  In  this  way  the 
values  given  in  the  fifth  column  of  Table  II.  have  been  calcu- 
lated. They  are  not  exactly  equal  to  those  obtained  by  direct 
experiment,  probably  because  the  different  gases  are  unequally 
compressed  by  the  weight  of  the  atmosphere.  The  actual  weights 
as  observed  can  always  be  obtained  by  multiplying  the  "  specific 


WEIGHING   AND   MEASURING.  669 

gravity  by  observation,"  given  in  Tables  III.  and  IV.,  by  1.29206. 
the  weight  of  one  litre  of  air. 

The  weight  of  one  litre  of  a  vapor  at  0°  and  76  c.  m.  is  of 
course  a  fiction,  since  all  those  gases  generally  known  as  vapors 
(292)  would  be  condensed  to  liquids  under  these  conditions  of 
temperature  and  pressure.  It  is  convenient,  however,  in  many 
calculations,  to  know  the  weight  which  one  litre  of  a  vapor  would 
have  at  the  standard  temperature  and  pressure,  assuming  that  it 
could  retain  its  aeriform  condition  under  these  circumstances ; 
the  weights  of  the  vapors  are  therefore  given  in  Table  II.  in 
connection  with  those  of  the  gases. 

Knowing,  then,  the  weight  of  one  litre,  and  hence  also  of  one 
cubic  centimetre,  of  all  the  more  important  gases  and  vapors  at 
0°  and  at  76  c.  m.,  when  perfectly  dry,  we  can  easily  calculate 
from  these  constants  the  weight  of  one  cubic  centimetre  of  any 
of  these  gases  when  saturated  with  aqueous  vapor,  and  at  any 
given  temperature  and  pressure.  The  following  formula  for  the 
purpose  is  easily  deduced  from  [100],  [184],  and  [203],  re- 
membering that  the  weight  of  one  cubic  centimetre  of  any  given 
mass  of  gas  must  be  inversely  as  its  volume. 

"'^  •   1  +  0.00366,    -^-  t211'] 

This  formula  gives  the  weight  of  the  gas  only,  not  including 
the  weight  of  aqueous  vapor  mixed  with  it ;  if  the  gas  is  dry,  § 
becomes  0,  and  of  course  disappears.  Using  the  weight  of  one 
litre  of  aqueous  vapor  at  0°  and  76  c.  m.  given  in  Table  II., 
we  can  easily  calculate  by  [211]  the  weight  of  one  cubic  metre  of 
aqueous  vapor  at  different  pressures  and  temperatures.  It  was  in 
this  way  that  the  values  given  on  page  571  were  obtained.  They 
are  not  absolutely  accurate,  because,  as  we  have  before  seen,  the 
vapor  deviates  from  the  law  of  Mariotte  before  reaching  its  maxi- 
mum tension,  while  the  formula  assumes  that  it  strictly  obeys 
the  law. 

The  weight  of  one  cubic  centimetre  of  a  gas  depends,  to  a  slight 
extent,  on  still  another  cause  not  yet  considered,  namely,  the  va- 
riations in  the  intensity  of  the  force  of  gravity  over  the  surface 
of  the  earth.  What  the  effect  of  such  variation  must  be  can 
easily-  be  seen  by  taking  an  assumed  case.  Suppose,  then,  that 
the  intensity  of  the  earth's  attraction  were  exactly  doubled,  it 
is  evident  that  the  total  weight  of  the  atmosphere,  and  hence 


670  CHEMICAL  PHYSICS. 

its  pressure,  would  be  doubled.  Moreover,  the  density  of  all 
gases  exposed  to  this  pressure  would  be  doubled  also  ;  and  all 
this  change  would  take  place  without  any  variation  in  the  height 
of  the  barometer  ;  for  although  the  pressure  of  the  air  would  be 
thus  increased,  the  weight  of  the  mercury-column  which  meas- 
ures this  pressure  would  be  increased  in  the  same  proportion. 
A  similar  effect  to  this,  although  only  to  a  very  slight  extent,  is 
produced  by  the  small  variations  in  the  force  of  gravity  on  the 
earth's  surface.  Other  things  being  equal,  the  relative  weight  of 
one  cubic  centimetre  of  a  gas  at  different  places  is  proportional 
to  the  force  of  gravity  at  these  places. 

w  :  w1  •=  g  :  g'         and        w1  =  w  ^-  •  [212.] 

The  weights  determined  by  Regnault,  and  given  on  page  668, 
are  only  exact  for  Paris,*  where  g  =  9.8096  ;  but  from  these  the 
weight  for  any  other  latitude  or  elevation  can  easily  be  calcu- 
lated by  [40]  and  [47].  The  weights  given  in  the  fifth  column 
of  Table  II.  were  calculated  for  the  latitude  of  the  Capitol  at 
Washington  (38°  53'  34")  and  the  sea  level.  They  can  be  re- 
duced for  any  other  place  by  the  following  formula,  easily  derived 
from  [212],  [40],  and  [47]  :  — 

1  —  0.00259  cos  2  A  rrH  0  -. 

w1  =  w  —  9h  .  ;  [213.] 

0-99945 


but  such  reduction  is  seldom  necessary. 

(330.)  Specific  Gravity  of  Gases.  —  It  is  usual  to  refer  the 
specific  gravity  of  gases  to  air,  as  a  standard  of  comparison,  in- 
stead of  water,  and  the  specific  gravity  of  a  gas  may  be  defined 
as  the  ratio  of  its  weight  to  that  of  an  equal  volume  of  dry  air, 
both  being  measured  at  0°  and  under  a  pressure  of  76  c.  m. 

RegnaulCs  Method.  —  The  most  accurate  method  of  determining  the 
specific  gravity  of  a  gas  is  due  to  Regnault.  It  consists  in  determining 
with  the  apparatus  described  above  (329)  the  weight  of  the  given  gas 
which  a  large  glass  globe  will  contain  at  0°  and  76  c.  m.,  and  then  divid- 
ing this  weight  by  that  of  an  equal  volume  of  air  previously  determined 
in  the  same  way.  This  method  requires  no  further  description,  as  the 
process  of  determining  the  weight  of  the  gas  has  already  been  given  in 
detail.  It  admits  of  great  accuracy,  and  should  always  be  used  in  normal 
determinations. 

*  The  latitude  of  Regnault's  laboratory,  at  Paris,  is  48°  50'  14",  and  the  elevation 
above  the  sea  level  about  60  metres. 


f 

WEIGHING   AND    MEASURING.  671 

Bunserfs  Method.  —  When,  however,  the  very  greatest  accuracy  is  not 
required,  as  in  the  investigations  usually  made  in  the  laboratory  on  gas- 
eous bodies,  their  specific  gravity  can  be  obtained  by  dividing  the  weight 
of  the  gas  by  the  weight  of  the  same  volume  of  dry  air  taken  at  the 
same  temperature  and  under  the  same  pressure.  This  ratio  is,  strictly 
speaking,  the  specific  gravity  only  when  the  gas  obeys  exactly  the  law  of 
Mariotte,  and  has  the  same  coefficient  of  expansion  as  air ;  but  it  is,  nev- 
ertheless, in  most  cases  near  enough  for  all  practical  purposes.  Bunsen's 
method*  is  an  application  of  this  principle.  He  employs,  for  determining 
the  specific  gravity  of  a  gas,  a  common  light  flask,  g,  Fig.  456.  The  vol- 


Fig.  456. 

ume  of  this  flask  should  be  about  200  or  300  cubic  centimetres,  and  the 
neck,  a,  thickened  before  the  blowpipe,  should  be  drawn  out  so  as  to  have 
an  aperture  of  the  thickness  of  a  straw,  into  which  a  glass  stopper  is 
ground  air-tight  by  means  of  emery  and  turpentine.  Through  this  neck, 
which  is  furnished  with  an  etched  scale  in  millimetres,  mercury  is  poured 
by  means  of  a  funnel  reaching  to  the  bottom  of  the  flask,  until  the  whole 
is  filled.  As  soon  as  this  is  accomplished,  the  flask  is  transferred,  with  its 
mouth  downwards,  into  the  mercury-trough  A  A,  and  gas  is  allowed  to 
enter,  until  the  level  of  mercury  in  the  neck  of  the  flask  stands  a  few 
millimetres  higher  than  in  the  trough.  In  order  to  prevent  the  gas  from 
becoming  mixed  with  air,  it  is  evolved  from  as  small  a  vessel  as  possible, 
and  allowed  to  enter  the  flask  through  a  narrow  delivery  tube,  and  in  the 
moist  state.f  The  gas  is  dried  in  the  flask  itself  by  a  small  piece  of  fused 

*  This  description  is  taken  from  Bunsen's  Gasometry  (Roscoe's  translation),  varying 
only  the  method  of  computing  the  results, 
t  If  the  gas  under  examination  corrodes  mercury,  the  flask  cannot  be  filled  in  this 


672 


CHEMICAL  PHYSICS. 


chloride  of  calcium,  b,  which  has  previously  been  made  to  crystallize  on 
the  side  of  the  flask  by  bringing  it  into  contact  with  a  single  drop  of  water 
and  alternately  heating  and  cooling  the  glass.  This  small  piece  of  chlo- 
ride of  calcium  serves  also  to  free  the  mercury  and  the  sides  of  the  flask 
from  all  adhering  moisture.  In  order  to  be  able  to  close  the  flask  at  any 
time  without  warming  it  with  the  hand,  the  little  lever  cf  is  employed. 
On  the  end  of  this  lever  the  stopper  is  so  fastened  in  a  cork,  that  it  passes 
into  the  neck  of  the  flask  without  closing  it ;  and  the  lever  is  held  in  its 
right  place  by  a  wedge,  d,  pushed  under  the  finger-plate  c.  As  soon  as 
the  flask  has  attained  the  constant  temperature,  £,  of  the  laboratory,*  the 
volume!  of  the  gas,  F,  the  height  of  the  barometer,  H^  and  the  height,  h01 
of  the  column  of  mercury  in  the  neck  above  the  level  of  the  metal  in  the 
trough,  are  carefully  observed.  It  is  now  necessary  to  determine  the 
weight  of  this  volume  V.  For  this  purpose,  the  wedge  d  is  taken  away  ; 
the  flask  g  is  thereby  closed,  and  by  withdrawing  the  pin  e,  it  can  then  be 
removed,  together  with  the  lever  cf,  from  the  trough.  Having  discon- 
nected the  lever  from  the  stopper,  and  carefully  cleaned  the  exterior  surface 

of  the  flask,  it  is  then  weighed. 
Let  W  represent  this  weight,  Jf'Q 
the  height  of  the  barometer,  and 
t1  the  temperature  of  the  balance 
at  the  time.  The  glass  stopper 
is  now  removed,  and  replaced  by 
an  india-rubber  tube,  a,  Fig.  457, 
connected  with  a  drying  tube,  b. 
The  apparatus  thus  arranged  is 
placed  under  the  receiver  of  an 
air-pump,  and,  by  alternately  ex- 
hausting and  admitting  the  air, 
the  gas  in  the  flask  is  replaced 
by  dry  air.  The  drying  appa- 
ratus is  then  disconnected,  and 
the  flask  weighed  again.  Call 
this  weight  W.  Since  the  air 
Fis  457.  has  free  access  both  to  the  inte- 

way ;  but  since  such  gases  are  almost  invariably  heavier  than  air,  it  can  be  filled  by 
displacement.  The  flask  being  placed  in  an  upright  position,  and  the  delivery  tube 
extending  quite  to  the  bottom,  the  gas  is  allowed  to  flow  in  and  overflow  the  mouth 
until  all  the  air  has  been  expelled.  The  tube  is  then  slowly  withdrawn,  the  flow  of  gas 
still  continuing,  and  the  mouth  of  the  flask  closed  by  its  stopper. 

*  These  experiments  should  be  conducted  in  a  cellar-room,  in  which  a  constant 
temperature  can  be  maintained  for  several  hours. 

t  Before  using  the  flask,  it  is  once  for  all  carefully  calibrated,  and  the  volume  corre- 
sponding to  each  division  on  the  neck  inscribed  in  a  table,  which  is  kept  with  the  in- 
strument. 


WEIGHING   AND  MEASURING.  673 

rior  and  the  exterior  surface  of  the  flask,  it  is  evident  that  W  is  sim- 
ply the  weight  of  the  glass  of  the  vessel  and  of  the  small  amount  of 
mercury  and  chloride  of  calcium  which  it  contains,  less  the  weight  of 
air  which  these  materials  displace.  It  is  also  evident  that  W  must  be 
equal  to  W  increased  by  the  weight  of  the  volume  of  gas,  FJ  contained 
in  the  flask,  and  diminished  by  the  weight  of  air  displaced  by  this  volume 
of  gas  when  the  flask  was  weighed.  The  weight  of  the  gas  is,  then,  equal 
to  W  —  W  +  W"  ;  in  which  W"  is  the  weight  of  V  cubic  centimetres 
of  dry  air  at  t'°  and  ff'Q  c.  m.,  calculated  by  [211].  To  obtain  the  specific 
gravity,  we  have  now  only  to  divide  the  weight  of  the  gas  by  the  weight 
of  an  equal  volume  of  air  measured  under  the  same  conditions  of  temper- 
ature and  pressure  at  which  the  gas  was  measured,  that  is,  at  t°  and 
(flu — hu)  c.  m.  This  can  also  be  calculated  by  [211].  Representing 
then  this  last  weight  by  W"1,  we  have  for  calculating  the  specific  gravity 
the  three  following  equations  :  — 

[214.] 

W  =  0.0012921  V  np.1,,3^    •  t ;  [215.] 

W»  =  0-0012921  V  1  +  ^Mt   •  ~°---°  •         [216.] 

As  an  example  of  the  method  of  calculation,  we  cite  the  following  from 
Bunsen's  work.  A  determination  of  the  specific  gravity  of  bromide  of 
methyl,  with  a  small  flask  of  about  44  cTm.8  capacity,  furnished  the  fol- 
lowing data :  — 

TF  =7.9465  gram.  #',  =  74.21  c.m.    F=42.19c7m.*     #0=74.64c,m. 

JF'  =  7.8397     "       1    r=6°.2  t  =16°.8  h,  =  2.43    « 

Calculation  of  W"*  Calculation  of  W'"* 

(1  +  6°.2*)            ar.  co.  9.99025  (1  + 16°.8£)       ar.  co.  9.97409 

ff'0=  74.21               log.  1.87046  ff0—h0=  72.21       log.  1.85860 

76.               ar.  co.  8.11919  8.11919 

V  —  42.19               log.  1.62521  1.62521 

0.0012932     log.  7.11166  _Z:nl6_? 

JF"  =  0.052092       log.  8.71677  W"  =  0.048837     log.  8.68875 

W—  W  +  W"  =         0.158892  log.  9.20110 

Specific  gravity  of  Bromide  of  Methyl,  3.253  log  0.51235 

*  The  values  of  Wn  and  W"  can  be  calculated  much  more  rapidly,  although  with 
less  accuracy,  by  means  of  Table  XIV. 

57 


674  CHEMICAL  PHYSICS. 

(331.)  Specific  Gravity  of  Vapors*  —  As  will  appear  in  an- 
other portion  of  this  work,  the  determination  of  the  specific 
gravity  of  vapors  is  one  of  the  most  important  processes  of  prac- 
tical chemistry.  We  always  make  the  determinations  at  a  tem- 
perature considerably  above  the  boiling-point  of  the  substance  ;  f 
and  since  under  these  circumstances  a  vapor  has  all  the  prop- 
erties of  a  gas  (292),  it  follows  that  its  specific  gravity  may  be 
found  by  dividing  its  weight  by  the  weight  of  an  equal  volume 
of  air  measured  under  the  same  conditions  of  temperature  and 
pressure.  The  method  of  determining  these  two  weights  usually 
followed  in  the  case  of  vapors  is  precisely  similar  to  that  used 
in  the  case  of  gases  and  described  in  the  last  section,  and  the 
same  formulae  may  be  used  in  calculating  the  results.  It  dif- 
fers from  it  only  in  the  details  of  the  manipulation,  and  in  the 
fact  that,  on  account  of  the  high  temperature  to  which  the  vapor 
is  heated,  it  is  necessary  to  take  into  account  the  change  in  the 

*  We  use  the  term  vapor  here  in  its  ordinary  sense. 

t  The  number  of  degrees  above  the  boiling-point  at  which  a  vapor  first  acquires 
fully  the  properties  of  a  permanent  gas  varies  very  greatly  with  different  substances. 
Thus,  under  the  normal  pressure  of  the  air,  the  vapors  of  water  and  alcohol  obey  the 
law  of  Mariotte  at  a  temperature  only  a  few  degrees  above  their  boiling-points,  while 
the  vapor  of  sulphur  does  not  obey  the  law  until  heated  to  at  least  500°  above  its  boil- 
ing-point. Unless  the  experimenter  is  confident  in  regard  to  the  properties  of  the  sub- 
stance under  examination  in  this  respect,  it  is  best  to  make  two  determinations  of  the 
specific  gravity  at  temperatures  differing  by  twenty  or  thirty  degrees.  If  the  two  do 
not  agree  within  the  limit  of  error  of  the  method  employed,  it  is  an  indication  that  the 
temperature  is  not  sufficiently  high.  This  is  illustrated  by  the  experiments  of  Cahours 
on  the  specific  gravity  of  the  vapor  of  monohydrated  acetic  acid.  He  found  that  the 
specific  gravity  did  not  become  constant  until  the  temperature  rose  above  240°  C.,  that 
is  120°  above  its  boiling-point.  The  following  table  contains  his  results  :  — 

Temp.  gp.  Gr.  Temp.  Sp.  Gr. 

125°  3.180  200°  2248 

130  3.105  220  2.132 

140  2.907  240  2.090 

150  2.727  270  2.088 

160  2.604  310  2.085 

170  2.480  320  2.083 

180  2.438  336  2.083 

190  2.378 

It  is  evident  that  a  determination  of  the  specific  gravity  of  the  vapor  of  acetic  acid 
made  at  a  temperature  below  240°  would  have  given  too  large  a  result,  and  one  which 
would  have  been  the  more  erroneous  as  the  temperature  was  lower.  An  error  of  the 
same  kind,  made  in  the  determination  of  the  specific  gravity  of  the  vapor  of  sulphur, 
introduced  an  anomaly  into  the  simple  law  of  equivalent  volumes  which  has  only 
recently  been  explained. 


WEIGHING   AND    MEASURING. 


675 


Fig.  458. 


capacity  of  the  vessel  used.  The  method  may  be  best  explained 
by  an  example.  Suppose,  then,  that  we  wish  to  ascertain  the 
specific  gravity  of  alcohol  vapor. 

We  take  a  light  glass  globe  having  a  capacity  of  from  300  to  500  cTrrT8, 
and  draw  the  neck  out  in  the  flame  of  a  blast  lamp,  so  as  to  leave  only  a 
fine  opening,  as  shown  in  Fig.  458  at  a.  We  then  weigh  the  globe,  which 

gives  us  the  weight  W  of  [214].  The 
second  step  is  to  ascertain  the  weight  of 
the  globe  filled  with  alcohol  vapor  at  a 
known  temperature  and  under  a  known 
pressure.  For  this  purpose,  we  introduce 
into  the  globe  a  few  grammes  of  pure 
alcohol,  and  mount  it  on  the  support  rep- 
resented in  the  figure.  By  loosening  the 
screw,  r,  we  next  sink  the  balloon  beneath 
the  oil  contained  in  the  iron  vessel,  V, 
and  secure  it  in  this  position.  We  now 
slowly  raise  the  temperature  of  the  oil  to 
between  300°  and  400°,  which  we  observe 
by  means  of  the  thermometer,  T.  The  alcohol  changes  to  vapor  and  drives 
out  the  air,  which,  with  the  excess  of  vapor,  escapes  at  a.  When  the  bath 
has  attained  the  requisite  temperature,  we  close  the  opening  a  by  sud- 
denly melting  the  end  of  the  tube  at  a  by  means  of  a  mouth  blowpipe,  and 
as  nearly  as  possible  at  the  same  moment  observe  the  temperature  of  the 
bath  and  the  height  of  the  barometer.  We  have  now  the  globe  filled  with  al- 
cohol vapor  at  a  known  temperature  and  under  a  known  pressure.  Since 
it  is  hermetically  sealed,  its  weight  cannot  change,  and  we  can  therefore 
allow  it  to  cool,  clean  it,  and  weigh  it  at  our  leisure.  This  will  give  us  the 
weight  of  the  globe  filled  with  alcohol  vapor  at  a  temperature  t  and  under 
a  pressure  H.  This  is  the  weight  W  of  [214].  We  also  notice  the  height 
of  the  barometer  H'  and  the  temperature  of  the  balance-case  t'  during  this 
second  weighing,  and  when  we  have  measured  the  capacity  of  the  globe 
Vj  we  can  easily  calculate  by  [215]  the  value  of  W".  Knowing  now 
W—  W  -\-  W",  the  weight  of  alcohol  vapor  which  filled  the  globe  at  t° 
and  under  a  pressure  He,,  m.,  the  next  step  is  to  find  W",  the  weight  of  an 
equal  volume  of  air  under  the  same  conditions  of  temperature  and  pressure. 
By  (241)  the  volume  of  th^e  globe  at  the  temperature  t  was  V(l  -{-  Ki), 
and  by  substituting  this  in  [216],  we  get  at  once,  since  h0  =  0, 


«  =  0.0012932 


[217.] 


by  which  we  can  easily  determine  the  weight  required.     The  last  step  is 


676  CHEMICAL   PHYSICS. 

to  find  the  capacity  of  the  globe,  which,  although  we  have  supposed  it 
known,  is  not  actually  ascertained  experimentally  until  the  end  of  the 
process.  For  this  purpose  we  break  off  the  tip  of  the  tube  a  under  mer- 
cury, which,  if  the  experiment  has  been  carefully  conducted,  rushes  in 
and  fills  the  globe  completely.  We  then  empty  this  mercury  into  a  care- 
fully graduated  glass  cylinder,  and  read  off  the  volume.  We  have  now 
all  the  data  for  calculating  the  specific  gravity,  and  the  calculation  may  be 
conducted  precisely  as  on  page  673,  only  substituting  [217]  for  [216]. 

We  have  assumed  that  the  vapor  expelled  all  the  air  from  the  globe, 
and  hence  that  the  globe  filled  completely  with  mercury  on  breaking  the 
tip  end  of  the  neck.  This,  however,  is  rarely  the  case  ;  there  is  almost 
always  left  in  the  globe  a  bubble  of  air,  and  sometimes  the  volume 
of  air  remaining  is  quite  considerable.  In  such  cases,  however,  we  may 
still  obtain  approximative^  accurate  results  ;  it  is  only  necessary  to  decant 
the  air  into  a  graduated  bell  over  a  pneumatic  trough,  and  measure  ex- 
actly its  volume,  v,  at  an  observed  temperature,  t",  and  under  a  pressure 
of  H".  Its  weight,  Wt,  can  now  be  calculated  by  [215],  and  from  this 
weight  we  readily  deduce  the  weight  of  vapor  which  the  globe  contained 
at  the  moment  of  closing  its  orifice  ;  this  weight  of  vapor  was  evidently 
W—  W  +  W"  —  JF,.  The  volume  which  the  small  amount  of  air  left  in 
the  globe  occupied  at  the  moment  of  closing  the  orifice  (that  is,  at  t° 
and  H  c.  m.)  can  also  be  calculated  from  the  formula, 

1  +  0.00366*         H\ 

'  '   ~ 


which  can  readily  be  deduced  from  [98]  and  [184].  The  volume  of  the 
balloon  at  this  time  was,  as  we  have  seen,  V  (I  -\-Kt).  Hence  the  vol- 
ume of  the  vapor  must  have  been  V(l-\-Kt)  —  v1.  Substituting  this 
value  for  V(l-\-Kt)  in  [217],  we  get  for  the  weight  of  the  vapor  in  the 
globe  at  the  time  of  closing, 


;      [219.] 
and  for  the  specific  gravity, 

sP.Gr.  r  J' 


W, 

The  results  which  are  thus  obtained  are  not,  however,  perfectly  trustwor- 
thy, and  it  is  always  best  to  avoid  these  corrections  by  so  conducting  the 
experiments  that  only  a  very  small  amount  of  air  at  most  shall  be  left  in 
the  globe.  This  end  is  secured  by  adapting  the  size  of  the  globe  to  the 
quantity  of  liquid  which  is  available  for  the  determination. 

In  calculating  the  specific  gravity  of  a  vapor  from  the  observed  data,  we 


WEIGHING   AND   MEASURING.  677 

must  be  careful,  in  the  first  place,  to  reduce  all  the  barometric  heights  to 
0°  by  Table  XVIII.  In  the  second  place,  the  temperature  of  the  bath,  as 
indicated  by  the  mercury-thermometer,  must  be  corrected  for  the  part  not 
immersed  [156],  and  the  corrected  temperature  reduced  by  the  table  on 
page  439  to  the  true  temperature.  When  great  accuracy  is  required,  it  is 
best  to  measure  the  temperature  of  the  bath  directly  with  an  air-thermome- 
ter. This  is  immersed  in  the  oil  at  the  side  of  the  globe,  and  the  orifices  of 
both  thermometer  and  globe  are  closed  at  the  same  time  (264).  In  com- 
puting the  results,  we  use  the  formula  [189],  and  without  actually  calcu- 

1     I      K~  f 

lating  the  temperature,  substitute  the  value  of  rXo5o36^i  *n  E21^' 

We  have  assumed  that  the  bath  in  whirth  the  globe  is  heated  is  filled 
with  a  fixed  oil,  which  is  the  most  convenient  liquid  if  the  temperature 
required  does  not  exceed  250°.  When  heated  above  this  temperature, 
the  fat  oils  emit  very  disagreeable  vapors  ;  and  for  temperatures  between 
250°  and  500°  it  is  necessary  to  fill  the  bath  with  some  easily  fusible 
alloy,  such  as  Rose's  metal  or  soft  solder.  The  pressure  exerted  by  the 
melted  metal  is  necessarily  very  great,  and  tends  to  deform  the  globe, 
so  that  we  are  obliged  to  abandon  this  method  of  experimenting  as 
soon  as  the  glass  begins  to  soften,  which  takes  place  a  little  above  500°. 
By  slightly  modifying  the  apparatus,  however,  Regnault  has  been  able  to 
obtain  accurate  results  at  temperatures  as  high  as  600°  or  650°.  His 
method,  which  is  only  used  for  substances  which  boil  at  a  very  high  tem- 
perature, is  as  follows. 

The  volatile  substance  is  introduced  into  the  cylindrical  reservoir  a'  & 
(Fig.  459)  of  the  tube  a'  d,  which  is  made  of  the  most  infusible  glass,  and 
supported  in  an  iron  frame,  m  m'  m",  at  the  side  of  a  similar  tube,  a  b. 
This  last  tube,  which  may  be  closed  by  the  stopcock  r,  serves  as  an  air- 


i 


Fig.  469. 

thermometer.  The  two  tubes  are  heated  together  in  an  air-bath,  made,  as 
represented  in  Fig.  460,  of  two  or  three  concentric  cylinders  of  sheet-iron 
enclosed  in  an  outer  cylindrical  case  of  cast-iron.  The  frame  m  m"  fits 
the  inner  cylinder/^  h  i,  and  when  in  place  the  metallic  disk  m"  n"  just 
closes  its  mouth,  / 1,  leaving  the  ends  of  the  two  tubes  projecting  in  front 
of  the  bath.  This  apparatus  is  heated  in  a  horizontal  position  on  a  semi- 
cylindrical  grate,  and  so  arranged  that  it  can  be  surrounded  with  burning 
coals.  The  temperature  is  first  rapidly  raised  ;  but  after  the  volatile  sub- 
stance has  distilled  over  and  the  excess  has  been  collected  in  the  cold  por- 
tion of  the  tube  c1  d,  the  temperature  is  increased  very  slowly,  and  before 
57* 


678  CHEMICAL  PHYSICS. 

the  glass  softens,  the  process  is  arrested  by  closing  the  stopcock  of  the  air- 
thermometer  and  withdrawing  the  frame  with  its  two  tubes  from  the  bath. 
"We  now  determine  the  temperature  to  which  the  tubes  were  heated,  by 

K 


Fig  460. 

the  method  already  described  in  detail  (2 Go).  We  next  ascertain  the 
weight  of  vapor  which  was  contained  in  the  reservoir  a'  b'  at  the  moment 
of  withdrawing  the  tube  from  the  air-bath.  For  this  purpose  we  remove 
the  excess  of  the  substance  which  condensed  in  the  part  of  the  tube  c'd, 
and  then  weigh  the  whole  tube,  first  with  the  substance  it  contains,  and 
secondly  after  the  substance  has  been  removed.  The  difference  of  these 
weights  is  the  weight  of  the  vapor  which  filled  the  reservoir  a1  b1  c'  at  a 
known  temperature  and  pressure.  Lastly,  to  find  the  volume  of  the  res- 
ervoir, we  determine  the  weight  of  water  which  fills  it  at  a  known  temper- 
ature ;  and  we  then  have  all  the  data  for  calculating  the  specific  gravity 
of  the  vapor.  The  formulae  already  given  may  be  easily  modified  for 
the  purpose.  If  the  substance  under  examination  absorbs  oxygen  at  a 
high  temperature,  it  is  best  to  fill  the  whole  tube  a'  d  with  nitrogen,  and 
to  adapt  with  a  cork  to  the  open  end  a  small  tube  drawn  to  a  point. 

The  use  of  the  air-thermometer  (which  involves  a  great  expenditure  of 
time)  in  the  determination  of  the  specific  gravity  of  vapors  of  substances 
which  boil  at  a  high  temperature,  is  avoided  in  another  modification  of  the 
general  method  proposed  by  Deville  and  Troost.  They  use  a  glass  bal- 
loon, and  heat  it  in  an  atmosphere  of  vapor  rising  from  boiling  mercury  or 
sulphur.  The  temperature  of  these  vapors  is  so  constant,  that  it  is  not 
necessary  to  use  a  thermometer, — that  of  the  first  at  350°,  and  that  of  the 
second  at  440°.  For  still  higher  temperatures  they  use  a  balloon  of  porce- 
lain, which  is  heated  in  the  vapor  of  boiling  cadmium  (860°)  or  boiling 
zinc  (1040°) ;  but  for  the  details  of  the  apparatus  and  of  the  method,  we 
must  refer  to  the  original  papers.* 

Method  of  Gay-Lussac.  —  The  method  of  determining  the  specific 
gravity  of  vapors  just  described  is  liable  to  one  very  serious  source 
of  error.  In  order  to  insure  that  all  the  air  will  be  expelled  from 
the  globe,  it  is  necessary  to  use  a  considerable  amount  of  liquid ;  and 
it  is  evident  that  any  impurity  which  this  liquid  may  contain  will  be 
left  behind  in  the  globe,  and  tend  to  falsify  the  weight.  This  source  of 

*  Coraptes  Rendus,  Tom.  XLV.  p.  821  ;  also  Tom.  XLIX.  p.  239. 


WEIGHING   AND   MEASURING. 


679 


error  is  entirely  avoided  by  a  method  invented  by  Gay-Lussac ;  but 
unfortunately  the  method  is  applicable  only  to  liquids  which  boil  at  a 
comparatively  low  temperature.  It  consists  in  measuring  with  accu- 
racy the  volume  of  vapor  formed  by  a  known 
weight  of  liquid.  The  liquid  is  first  enclosed  in 
a  very  thin  glass  bulb,  A,  Fig.  461,  which  is  her- 
metically sealed,  and  the  weight  of  the  liquid  is 
determined  by  weighing  the  bulb  both  before  and 
after  it  has  been  filled.  This  bulb  is  then  passed 
up  into  a  graduated  bell-glass,  (7,  filled  with  mer- 
cury, and  standing  in  an  iron  basin  also  partly 
filled  with  the  same  liquid.  Around  the  bell  is 
placed  a  glass  cylinder,  whose  lower  end,  resting 
in  the  mercury  contained  in  the  basin,  is  com- 
pletely closed.  This  cylinder  is  filled  with  water, 
and  the  apparatus  thus  arranged  is  mounted  on 
a  charcoal  furnace.  The  glass  bulb  is  soon 
broken  by  the  expansion  of  the  liquid,  and 
when  the  temperature  is  sufficiently  elevated  the 
liquid  changes  into  vapor,  which  depresses  the 
mercury-column.  The  heat  is  still  increased 
until  the  water  in  the  cylinder  boils,  when  the 
bubbles  of  vapor  rising  through  the  liquid  estab- 
lish a  uniform  temperature  of  100°  throughout 
the  whole  mass.  We  then  observe  accurately  the 
volume  of  the  vapor  and  the  pressure  to  which  it  is 
exposed.  To  obtain  the  last,  we  subtract  from  the  height  of  the  barometer, 
HZ,  the  difference  of  level  between  the  surface  of  the  mercury  in  the  basin 
and  that  in  the  bell.  This  difference  of  level  is  measured  by  a  cathetom- 
eter  with  the  aid  of  the  levelling-screw  r.  Compare  (159).  With  these 
data  we  can  easily  calculate  the  specific  gravity.  We  reduce,  first,  the 
volume  of  the  vapor  to  0°  and  76  c.  m.  by  [166]  and  [107],  and  we  then 
calculate  the  specific  gravity  by  [55]  and  [58].  For  the  different  pre- 
cautions required  in  this  process,  and  for  the  slight  variations  required 
under  different  circumstances,  the  student  is  referred  to  Regnault's  Ele- 
ments of  Chemistry,  American  edition,  Vol.  II.  p.  408. 

(332.)  Volumes  of  Gases.  —  In  consequence  of  the  very  small 
density  of  gases,  their  volumes  can  be  determined  much  more 
accurately  by  measure  than  by  weight.  The  measurement  of  the 
volume  of  a  gas  is  effected  in  eudiometers,  or  graduated  tubes, 
Fig.  462,  which  are  generally  about  2  c.  m.  in  diameter  and  from 
25  c.  m.  to  80  c.  m.  long.  These  tubes  are  frequently  graduated 


Fig.  461. 


680  CHEMICAL   PHYSICS. 

into  cubic  centimetres,  but  it  is  more  accurate  to  divide  them 
into  millimetres  and  to  determine  afterwards  the  corresponding 
volumes  by  calibration.  The  graduation  is  easily  made,  with  the 
dividing  machine  before  described,  on  a  thin  coating  of  wax 


Fig.  462. 

spread  over  the  surface  of  the  tube,  and  the  divisions  are  after- 
wards etched  with  hydrofluoric  acid.  The  tube  is  then  calibrated 
by  pouring  into  it  repeatedly  the  same  measured  quantity  of 
mercury  through  a  long  funnel,  and  after  each  addition  accu- 
rately noting  the  division  to  which  it  rises  in  the  tube.  From 
these  data  it  is  easy  to  calculate  the  volume  corresponding  to 
each  graduation  ;  and  a  table  is  then  prepared,  from  which  these 
volumes  can  be  subsequently  ascertained  by  inspection.  The 
measurements  of  gases  are  best  performed  over  a  small  mercurial 
trough,  like  that  represented  in  Fig.  462,  which  was  contrived  by 
Bunsen,  and  is  admirably  adapted  to  the  purpose.  The  trough  has 
two  transparent  sides  of  plate-glass,  through  which  the  level  of  the 
mercury  is  easily  observed.  The  eudiometer  is  first  filled  with 
mercury  by  means  of  a  long  funnel  reaching  to  the  bottom  of  the 
tube ;  and  after  closing  its  mouth,  it  is  inverted  and  placed  in  the 
position  represented  in  the  figure,  when  the  gas  can  readily  be 
introduced  from  the  collecting  tubes.  When  practicable,  a  drop 
of  water  is  brought  into  the  head  of  the  eudiometer  before  filling 
it  with  mercury,  so  that  the  collected  gas  may  be  perfectly  satu- 
rated with  aqueous  vapor. 

Every  determination  of  the  volume  of  gases  requires  the  fol- 
lowing four  primary  observations  :  — 


WEIGHING   AND   MEASURING.  681 

1.  The  level  of  the  mercury  in  the  eudiometer. 

2.  The  level  of  the  mercury  in  the  trough  measured  on  the  etched 

divisions  of  the  eudiometer. 

3.  The  height  of  the  barometer. 

4.  The  temperature. 

The  eudiometer  is  first  brought  to  a  perpendicular  position  by 
means  of  a  plumb-line,  and  the  observations  are  then  made  by  the 
help  of  a  small  telescope  placed  at  a  distance  of  from  six  to  eleven 
feet.  The  axis  of  the  telescope  is  brought  to  a  horizontal  posi- 
tion, and  all  error  from  parallax  thus  avoided.  It  is  unneces- 
sary to  add,  that  the  heights  of  the  mercury  columns  must  always 
be  read  off  at  the  highest  point  of  the  meniscus. 

The  observed  volumes  of  gas  are  reduced  by  calculation  to  the 
volumes  in  a  dry  state  at  0°  and  under  a  pressure  of  76  c.  m.  by 
means  of  the  equation 

V  -     V       **°  —  ^°  —  ^ 

(1  +0.003660  76> 

which  is  easily  obtained  from  [107],  [184],  and  [203].     The 
following   measurements,   by  Bunsen,  of  a  volume  of  air  sat- 
urated with   aqueous  vapor,  may  serve  as   an  example  of  the 
calculation :  — 
Temperature  of  the  air,  20°.2 


Lower  level  of  mercury,  56.59 

Upper      "  "  31.73 

Difference  of  level,  24.86 

Reduced  height  A0,  24.78 


c.  m. 


Height  of  barometer,  74.69 

Correction  for  temperature,  0.25 

Reduced  height  If0,  74.44 

Tension  of  vapor,  §,  1.76 


;__Ao  — fl,  47.90 

The  division  317.3  corresponds  to  a  volume  by  table  of      292.7 
Correction  for  meniscus,      ......          0.4 

The  corrected  volume  F',  *'  :  »  .  .  .  293.1 
F',  ...  /  ,  log.  2.46701 
ff0  —  #0  —  $,  .  *  .  'v  log.  1.68033 
(1  -f-  0.003660  b7  Table  X1-*  •  ar-  co-  9.96902 
76,  .  .  '  .  .  V^  ar.  co.  8.11919 
Reduced  volume  V=  172.01,  .  log.  2.23555 

For  the  practical  details  of  the  methods  connected  with  the 
manipulation  and  measurement  of  gases,  we  would  refer  the 
student  to  Professor  Bunsen' s  work  on  Gasometry.  This  dis- 
tinguished experimentalist  has  very  greatly  improved  all  these 
processes,  and  has  given  them  an  accuracy  unsurpassed  by  any  of 
the  most  refined  methods  of  chemical  investigation. 


682  CHEMICAL   PHYSICS. 


PROBLEMS. 

Hygrometry. 

378.  A  glass  globe,  having  been  filled  at  0°  and  76  c.  m.  partly  with 
air  and  partly  with  water,  and  afterwards  sealed,  is  heated  to  100°.     Re- 
quired the  pressure  exerted  on  the  interior  surface  of  the  vessel,  provided 
that  there  is  an  excess  of  water  left  in  the  globe. 

379.  What  would  be  the  pressure,  if  ether  were  used  in  the  last  ex- 
ample instead  of  water  ? 

380.  Into  a  vacuous  vessel,  whose  capacity  equals  2.02  litres,  there 
were  introduced  one  litre  of  dry  air  and  sufficient  water  to  leave  after 
evaporation  20  cTm.8  in  the  liquid  state.      Required  the  tension  of  the 
mixture  of  air  and  vapor  in  the  interior  of  the  vessel  at  50°. 

381.  A  given  quantity  of  dry  air  weighs  5.2  grammes  at  0°  and  76 
c.  m.  pressure.     What  would  be  its  volume  at  30°  and  77  c.  m.  pressure 
when  saturated  with  vapor  ? 

382.  What  is  the  weight  of  a  cubic  metre  of  air  at  30°  and  77  c.  m. 
pressure  ?     The  relative  humidity  of  the  air  is  assumed  to  be  0.75. 

383.  The  volumes  of  air  given  in  the  table  below  were  measured  when 
saturated  with  vapor  at  the  temperatures  and  pressures  annexed.     It  is 
required  to  reduce  these  volumes  to  what  they  would  have  been  at  0°  and 
76  c.  m.  pressure,  had  the  gas  been  perfectly  dry. 


1.  250  t~^.3  H=  75.6  c.m.  t  =  15°. 

2.  120  "    #=25.4  "    t  =  20°. 

3.  75  "    //  =  5.6  "    t  =  10°. 


4.  500  Z~^?  H=  76.3  c.m.  t=  30°. 

5.  725  "   H  =  5.6  "   t  =  20°. 

6.  340  "    H=78   "   t  =  -20°. 


384.  The  volumes  of  air  given  in  the  following  table  were  measured 
at  0°  and  76  c.  m.  pressure  when  perfectly  dry.  It  is  required  to  deter- 
mine' what  would  have  been  the-  volume  at  the  temperature  and  pressure 
annexed  were  the  gas  saturated  with  moisture. 


1.  200  c^3    H=  75.4  c.m.    t=    15°. 

2.  500    "        H  =  45.5    "        t  =    10°. 

3.  25    "        H=  15.8    "        t  =    13°. 


4.  75  £T^T.3    H  =  77.2  c.  m.  t  =    -10°. 

5.  60     "        H  =  80.2    "      t  =      -4°. 

6.  140     "         H  =  79.4    "      t  =    -100. 


385.  In  the  following  problems  are  given,  first,  the  temperature  of  the 
atmosphere,  t°  ;  secondly,  the  dew-point,  t'  °.  It  is  required  to  determine 
in  each  case  the  relative  humidity  of  the  atmosphere  and  the  weight  of 
vapor  in  one  cubic  metre. 

1.  t  =  30°   t'  =  18°. 

2.  t  =  20°   t'  =  11°. 


3.   t  =  5°   t1  =  0°. 


4.  t  =  30°   t'  =  28°. 

5.  t  =  25°   t'  =  20°. 

6.  t  =  10°   t1  =  6°. 


7.  t  =  0°    t'  =  -4°. 

8.  t  =  6°    t1  =-10°. 

9.  t  =  41°    t'  =  39°. 


386.  In  the  following  problems  are  given,  first,  the  temperature  of  the 
dry-bulb  thermometer  ;  secondly,  that  of  the  wet-bulb.  Required  in  each 
case  the  relative  humidity  of  the  air. 


WEIGHING   AND   MEASURING.  683 


1.  t  =  30°   t'  =  28°. 

2.  t  =  20°   t'  =  12°. 

3.  t  =  10°   t'  =  2°. 


4.  t  =  28°  *'  =  26°.7. 

5.  f  =  15°  <'=12°.3. 

6.  t  =  12°  t'  =  8°. 


7.  t  —   0°  *'  =  -3°. 

8.  *  =  -5°  t'  =  -8°. 

9.  *  =  -20°  t'  =  -20°.8. 


387.  Assuming  that  the  air  is  four  fifths  saturated  with  aqueous  vapor 
at  the  temperature  of  20°,  how  much  water  would  fall  from  each  cubic 
metre  if  the  temperature  suddenly  fell  to  11°  ? 

388.  When  the  temperature  of  the  air  was  30°,  the  dew-point  was 
observed  to  be  at  28° ;  the  temperature  of  the  air  suddenly  fell  to  20°. 
How  much  rain  would  fall  on  a  square  kilometre  from  a  height  of  200 
metres,  assuming  that  the  atmosphere  were  of  uniform  density  and  hy- 
grornetric  condition  throughout  the  whole  height  ? 

Sources  of  Heat. 

389.  How  much  wood  charcoal  must  be  burnt  in  order  to  evaporate  50 
kilogrammes  of  water,  assuming  that  the  water  is  already  at  the  boiling- 
point,  and  that  all  the  heat  evolved  is  economized  in  the  process  ? 

390.  How  much  alcohol  must  be  burnt  in  order  to  melt  5  kilogrammes 
of  sulphur,  assuming  that  the  sulphur  is  already  at  the  melting-point,  and 
that  the  heat  is  all  economized  ? 

391.  How  much  coke  would  be  required  to  raise  the  temperature  of 
the  air  of  a  room  measuring  6  m.  X  7  m.  X  3.5  from  5°  to  25°,  assuming 
that  none  of  the  heat  evolved  was  lost  ? 

392.  How  many  cubic  metres  of  illuminating  gas  (marsh  gas)  must  be 
burnt  to  raise  the  temperature  of  40  kilogrammes  of  water  from  0°  to 
100°  ?     How  much,  in  order  to  convert  the  water  into  steam  ? 

Conduction  of  Heat. 

393.  It  is  required  to  make  a  copper  boiler  by  which  100  kilogrammes 
of  water  may  be  evaporated  each  hour.     "What  must  be  the  extent  of 
boiler  surface,  assuming  that  the  thickness  of  the  copper  is  2  m.  m.,  and 
that  the  difference  of  temperature  between  the  two  surfaces  of  the  copper 
plate  is  10°  ? 

394.  If  the  boiler  were  made  of  iron  5  m.  m.  thick,  what  must  be  the 
extent  of  the  boiler  surface  ? 

•WEIGHING  AND   MEASURING. 

Specific  Gravity  of  Solids. 

395.  The  specific  gravity  of  zinc  was  found  to  be  7.1582  when  the 
temperature  of  the  water  was  15°.     What  would  have  been  the  specific 
gravity  at  4°  ? 

396.  The  specific  gravity  of  antimony  was  found  to  be  6.681  when  the 
temperature  of  the  water  was  15°.     What  would  have  been  the  specific 
gravity  at  4°  ? 


684  CHEMICAL  PHYSICS. 

397.  The  specific  gravity  of  an  alloy  of  zinc  and  antimony  was  found 
from  the  following  data :  — 

Weight  of  the  alloy, 4.4106  grammes. 

"          "       specific-gravity  bottle,        .         .         .  9.0560         " 

"          "  "  "       full  of  water  at  4°,  19.0910         " 

"      bottle,  alloy,  and  water  at  14°.6,         .  22.8035 

398.  Find  the  specific  gravity  of  metallic   zinc   from   the  following 
data  :  — 

"Weight  of  the  zinc,       .        .        .        ,        .        .  .    12.4145  grammes. 

"      bottle, 9.0560 

"       full  of  water  at  18°,     .         .  .     19.0790 
"           "          "      zinc  and  water  at  12°.4,           .        29.7663         " 

Volume  of  Solids. 

399.  Gold-leaf  is  made  as  thin  as  one  ten-thousandth  of  a  millimetre. 
How  great  a  surface  could  be  covered  with  10  grammes  of  such  leaf  ? 

400.  A  cylinder  of  iron  weighing  21  kilogrammes  is  2.5  m.  high.    What 
is  its  diameter  ? 

401.  The  base  of  the  grand  pyramid  of  Egypt  measured  23.48  m.  on 
each  side ;  its  original  height  was  146.18  m.     Required  its  weight,  as- 
suming that  it  was  solid,  and  that  the  stone  of  which  it  is  constructed  has 
a  Sp.  Gr.  =  2.75. 

402.  Required  the  price  of  an  iron  pipe,  knowing  that  its  interior  di- 
ameter is  equal  to  0.254m.,  that  its  thickness  equals  0.014  m.  and  its 
length  213.4m.     The  specific  gravity  of  cast-iron  is  7.207,  and  its  price 
4  cents  a  pound. 

403.  A  silver  wire  1.5  m.  m.  in  diameter  weighs  3.2875  grammes.     It 
is  required  to  cover  it  with  a  coating  of  gold  0.4  m.  m.  in  thickness. 
What  will  be  the  weight  of  the  gold  ? 

Volume  of  Liquids. 

404.  What  is  the  volume  of  40  kilogrammes  of  mercury  at  100°  ?     If 
the  liquid  is  contained  in  a  cylindrical  vessel  6  c.  m.  in  diameter,  how  high 
would  it  stand  above  the  horizontal  base  ? 

405.  A  glass  flask  with  a  narrow  neck  was  weighed  full  of  mercury  at 
the  temperature  of  10°,  and  found  to  weigh  560.234  grammes.     The  flask 
itself  weighed  84.374  grammes.     Required  the  volume  of  the  flask. 

406.  Calculate  the  volume  at  0°  of  the  globe  employed  by  Regnault  in 
determining  the  absolute  weight  of  one  litre  of  air  and  of  other  gases  from 
the  following  data  (see  Fig.  454)  :  — 

Weight  of  the  glass  globe  at  4°.2  and  75.789  c.  m.,        .     .        .        .    1,258.55  gram. 

"  "          after  having  been  filled  with  water  at  0°,  .      11,126.05    ' 

Temperature  of  the  chamber  at  the  time  of  weighing,        ...  6° 

Height  of  the  barometer  at  the  same  time, 76.177  c.  m. 

Ans.  9,881.06  cT^.8 


I 

WEIGHING  AND   MEASURING.  685 

Weight  of  Gases. 

407.  Calculate  the  weight  of  one  litre  of  dry  air  at  0°  and  76  c.  m. 
from  the  following  determination  by  Regnault  (329).     The  globe  used 
was  the  same  as  in  the  last  example. 

Globe  full  of  Air  and  surrounded  by  Ice. 

Height  of  barometer  at  the  time  of  closing  the  stopcock,        .        .        .    76.119  c.m. 
Weight  added  to  globe  to  equipoise  it  in  balance  (Fig.  258),      .         .  1.487  gram. 

Globe  exhausted  of  Air  and  surrounded  by  Ice. 
Tension  of  air  remaining  in  globe  as  indicated  by  the  manometer  at 

the  moment  of  closing  the  stopcock, 0.843  c.  m. 

Weight  required  for  equipoise, 14.141  gram. 

Ans.  12.7744  gram. 

408.  Calculate  the  weight  of  one  litre  each  of  hydrogen  and  carbonic 
acid  at  0°  and  76  c.  m.  from  the  following  determinations  of  Regnault. 
The  data  are  given  in  the  same  order  as  in  the  last  problem. 

Hydrogen.  Carbonic  Acid. 

Globe  full  of  gas,     //o    =75.616    c.m.         Globe  full  of  gas,  H0    =76.304    c.m. 
W  =  13301    gram.  W  =    0.6335  gram. 

Globe  exhausted,     ha     =    0.340    c.  m.          Globe  exhausted,   ho     =    0.157    c.m. 

W"  =  14.1 785  gram.  W"  =20.211    gram. 

Ans.  0.88591  gram.  Ans.  19.5397  gram. 

409.  Reduce  the  weights  obtained  from  the  last  two  problems  to  the 
latitude  of  45°  and  the  sea-level.     See  page  670. 

410.  Reduce  the  weights  to  what  they  would  be  at  Quito.     Latitude, 
0°  13'.5.     Elevation  above  sea-level,  2,908  metres. 

411.  In  the  following  table  are  given,  first,  the  volume  of  the  gas; 
secondly,  the  pressure  to  which  it  is  exposed ;  thirdly,  its  temperature. 
Assuming  that  the  gas  is  saturated  with  vapor  of  water,  it  is  required  to 

calculate  the  weight  in  each  case. 

v.  H.  t. 

Air, 245  g~S?      76.12  c.m.       15°. 

Hydrogen, 564    "  64.32     "  12°. 

Carbonic  Acid, 202    "          45.20     "  4°. 

Chlorine, '     .          50    "          75.89     "          30°. 

Protoxide  of  Nitrogen,        .         .         .     465    "  66.23     "  8°. 

Steam,       .         .         .         .        .         .         500    "          76.54     "        213°. 

Alcohol  Vapor,    ....  1,500    "          54.22     "         152°. 

Ether  Vapor,    .         .         .        .        .        250    "          75.20     "         100°. 

412.  A  glass  globe  weighed,  when  open  to  the  air,  225.169  grammes ; 
filled  with  water  at  the  temperature  of  0°,  it  weighed  785.169  grammes. 
Required  the  weight  of  air  which  the  globe  would  contain  at  300°  and 
under  a  pressure  of  77  c.  m. 

413.  What  is  the  weight  of  one  cubic  metre  of  aqueous  vapor  at  its 
maximum  tension  at  the  following  temperatures  :   10°,  15°,  120°,  200°, 
and  250°? 

58 


686  CHEMICAL  PHYSICS. 

414.  What  is  the  weight  of  the  vapor  contained  in  one  cubic  metre  of 
the  atmosphere  under  the  conditions  given  in  problem  385  ? 

Specific  Gravity  of  Gases  and  Vapors. 

415.  Calculate  the  specific  gravity  of  hydrogen  and  carbonic  acid  at 
0°  from  the  data  given  in  problems  407,  408,  and  409. 

416.  Ascertain  the  specific  gravity  of  alcohol  vapor  from  the  following 
data :  — 

Weight  of  glass  globe,  TF', 50.8039  grammes. 

Height  of  barometer,  //', 74.754    c.  m. 

Temperature,  t', 18°. 

Weight  of  globe  and  vapor,'  TF,         ....  50.8245  grammes. 

Height  of  barometer,  H> 74.764    c.  m. 

Temperature,  t, 167°. 

Volume,  F, 351.5      cTnT3 

417.  Ascertain  the  specific  gravity  of  camphor  vapor  from  the  follow- 
ing data  :  — 

Weight  of  glass  globe,  TF', 50.1342  grammes. 

Height  of  barometer,  H1,          .        .   •     .        .        .  74.2        c.  m. 

Temperature,  t', 13°.5. 

Weight  of  globe  and  vapor,  TF,  50.8422  grammes. 

Height  of  barometer,  H, 74.2        c.  m. 

Temperature,  *, 244°. 

Volume,  F, 295         ^T.3 

Volume  of  Gases. 

418.  A  volume  of  air  saturated  with  moisture  gave  the  following  meas- 
urements.    Reduce  to  the  standard  temperature  and  pressure. 

Level  of  mercury  in  pneumatic  trough,        ....     52.34  c.  m. 

eudiometer, 24.25     " 

Volume  corresponding  to  24.25  division,     .         .        .  350     cTnf.3 

Temperature  of  the  air, 15°.4. 

Height  of  barometer, 76.54  c.  m. 

419.  A  volume  of  air  saturated  with  moisture  at  3°.l  and  57.59  c.  m. 
pressure,  was  found  to  measure  368.9  cTm.8-     After  absorbing  the  oxygen 
with  a  paper  ball  moistened  with  pyrogallate  of  potash,  and  drying  the 
residual  gas  with  a  ball  of  caustic  potash,  it  was  found  to  measure  313.8 
c.  m.8,  the  temperature  being  3°.l  and  the  pressure  53.58  c.  m.     Required 
the  percentage  composition  of  the  gas. 

420.  A  volume  of  gas  (choke-damp),  measured  moist  at  13.°5  and 
62.40  pressure,  was  found  to  be  171.2  cTln.8.     After  absorbing  the  car- 
bonic acid  with  a  ball  of  caustic  potash  and  drying  the  gas,  it  was  found 
to  measure  167.3  c.  m.3,  the  temperature  being  13.5°  and  the  pressure 
61.96  c.  m.     Finally,  after  absorbing  the  oxygen  with  pyrogallate  of  pot- 
ash, and  drying,  the  gas  was  found  to  measure,  at  13°.9  and  60.58  c.  m. 
pressure,  147  cTlu.8.     Required  the  percentage  composition  of  the  gas. 


APPENDIX 


LIST    OF    TABLES. 


Table  *Page 

I.  Weights  and  Measures        .        .        .        .        .        .        .        .11 

II.  Specific  Gravity  and  Weight  of  One  Litre  of  various  Gases 
and  Vapors,  calculated  for  Latitude  of  Washington  from  Reg- 
nault's  Experiments  ........  668 

III.  Specific  Gravity  of  Gases.     (Ann.  du  Bureau  des  Long.,  1855.) 

IV.  Specific  Gravity  of  Vapors.  "  "  " 
V.  Specific  Gravity  of  Liquids.            "                  "  " 

VI.  Specific  Gravity  of  Solids.              "  "  " 
VII.  Coefficients  of  Absorption  of  various  Gases  in  Water  and  Alco- 
hol.    (Bun?  n.) ...     392 

VIII.  Tension  of  the  Vapor  of  Alcohol.     (Regnault.)       ...        582 

IX.  Tension  of  Aqueous  Vapor  from — 32°  to  230°.     (Regnault.)    .     570 

X.  Tension  of  Aqueous  Vapor  from  —2°  to  35°.     (Regnault.)    .         570 

XL  Value  of  1  -}-  0.00366 1  between  — 2°  and  59°.     (Bunsen.)         .    528 

XII.  Value  of  1  -j-  0.00367  /  between  60°  and  299°.     (Gerhardt.)  528 

XIII.  Value  of  l-f  &(<'  —  *)  for  Glass.     (Gerhardt.)          .        .     493,695 

XIV.  Weight  of  One  Cubic  Centimetre  of  Air.     (Gerhardt.).        .        673 
XV.  Expansion  of  Solids.     (Miiller.) 496 

XVI.  Volume  of  Water  at  different  Temperatures.     (Kopp.)          526,  662 

XVII.  Reduction  of  Thermometer.     (Graham.) 436 

XVIII.  Reduction  of  Barometer 511 

XIX.  Reduction  of  Water  Column  to  Mercury.     (Bunsen.)  .     513 

XX.  Logarithms  of  Numbers. 

XXI.  Antilogarithms. 

*  These  numbers  indicate  the  pages  of  the  work  on  which  the  use  of  the  table  is  de- 
scribed. 


TABLES. 


TABLE    I. 


MEASURES    AND    WEIGHTS. 


ENGLISH    MEASURES. 
Measures  of  Length. 

THE  inch  is  the  smallest  lineal  integer  now  used.  For  mechanical 
purposes  it  is  divided  either  duodecimally  or  by  continual  bisection  ;  but 
for  scientific  purposes  it  is  most  convenient  to  divide  it  decimally.  The 
larger  units  are  thus  related  to  it :  — 


Mile.  Furlongs. 

Chains. 

Rods. 

Fathoms. 

Yards. 

Feet. 

Links. 

Inches. 

1=8  = 

80  = 

320 

=  880 

=  1760      = 

5280 

= 

8000 

=63360 

1   = 

10  = 

40 

=  110 

=    220     = 

660 

— 

1000 

= 

7920 

1  = 

4 

=    11 

=     22    = 

66 

= 

100 

= 

792 

1 

=      2.75 

=       5.5= 

16.5 

mm 

25 

= 

198 

1 

=       2    = 

6 

= 

9A 

— 

72 

.    * 

1    = 

3 

= 

4n 

= 

36 

1 

=      13S- 

12 

.000125=.001=.01=.04=     .11  = 


.22=      0.66= 


1  =        7.92 


Measures  of  Surface. 


Acre.  Roods.         Square  Chains. 

1       «       4       =       10 
1       =         2.5 
1 


Square  Yards.  Square  Feet. 

:     4840     =  43,560 

*     1210     =  10,865 

484     =  4,356 

1     =  9 


Measures  of  Volume, 

Cubic  Yard.  Cubic  Feet.  Cubic  Inches. 

1         =         27         =         46,656 
1  1,728 

58* 


690 


TABLES. 


Imperial  Measure. 

The  Imperial  Standard  Gallon  contains  ten  pounds  avoirdupois  weight 
of  distilled  water,  weighed  in  air  at  62°  Fahr.  and  30  in.  Barom.,  or  12 
pounds,  1  ounce,  16  pennyweights,  and  16  grains  Troy,  =  70,000  grains' 
weight  of  distilled  water.  A  cubic  inch  of  distilled  water  weighs 
252.458  grains,  and  the  imperial  gallon  contains  277,274  cubic  inches. 


Distilled  Water. 


Grains. 

8,750 
17,500 
70,000 
140,000 
560,000 
4,480,000 

Avoir.  Ib.        Cubic  Inches. 

=      1.25=        34.659 
=      2.5  =        69.318 
=    10      =      277.274 
=    20      =      554.548 
=    80      =  2,218.192 
=  640      =17,745.536 

Pint. 
=         1 
=         2 

=      8 
=    16 
=    64 
=  512 

Quart. 
=         1 

=      4 
=      8 
=    32 
=  256 

Galls 
i 

=    2 
=    8 
=  64 

.      Pecks.    E 
=      1 

=    4  = 
=  32  = 

us 

1 

8 

Qr. 


Apothecaries'  Measure. 

The  gallon  of  the  former  wine  measure  and  of  the  present  Apotheca- 
ries' measure  contains  58,333.31  grains'  weight  of  distilled  water,  or  231 
cubic  inches,  the  ratio  to  the  imperial  gallon  being  nearly  as  5  to  6,  or  as 
0.8331  to  1. 

Gr.  of  Dist.  Wat.     Cub.  Inch. 

58,333.31  =  231 

7,291.66  =  28.8 

455.72  =  1.8 

56.96  =  0.2 


Gallon. 

Pints. 

Ounces. 

Drachms. 

Minims. 

1 

=      8 

=    128 

=    1024 

= 

61,440 

1 

=       16 

=      128 

= 

7,680 

S  1 

=          8 

= 

480 

51 

= 

60 

Pound. 
1 


ENGLISH    WEIGHTS. 


Avoirdupois  Weight. 


Ounces. 

16 
1 


Drachms. 

256 

16 

1 


Grains. 

7000 
437.5 
27.34375 


Apothecaries'  Troy  Weight. 


Pound. 
1 


Ounces. 

12 
1 


Drachms. 

96 

8 

1 


Scruples. 

288 

24 

3 

1 


Grains. 
5760 

480 
60 
20 


TABLES. 


691 


FRENCH    MEASURES. 
Measures  of  Length. 


1 

Kilometre      = 

1000 

Metres. 

1 

Metre              = 

1.000  Metre. 

,1 

Hectometre    = 

100 

u 

1 

Decimetre       = 

0.100       « 

1 

Decametre      = 

10 

it 

1 

Centimetre     = 

0.010       « 

1 

Metre 

1 

a 

1 

Millimetre      = 

0.001       " 

1 

Kilometre 

0 

6214 

Mile. 

Logarithms. 

9.793  3712 

Ar.  Co.  Log. 

0.20G  6188 

L 

Metre 

3 

2809 

Feet. 

0.515  9930 

9.484  0070 

1 

Centimetre        = 

0.3937 

Inch. 

9.595  1742 

0.404  8258 

Measures  of  Volume. 


1   Cubic  Metre  = 

1   Cubic  Decimetre      = 
1   Cubic  Centimetre     = 


1   Cubic  Metre 
1   Cubic  Decimetre 
1   Cubic  Centimetre 
1  Litre 
1  Litre 
1  Litre 


35.31660  Cubic  Feet. 
61.02709  Cubic  Inches. 

0.06103      « 

0.22017  Gallon. 

0.88066  Quart. 

1.76133  Pints. 


1000.000  Litres. 

1.000      « 

0.001      « 

Logarithms. 

Ar.  Co.  Log. 

>et       1.547  9790 

8.452  0210 

ches.    1.7855226 

8.2144774 

«         8.785  5226 

1.2144774 

9.342  7581 

0.657  2419 

9.944  8083 

0.055  1917 

0.245  8407 

9.754  1593 

FRENCH  WEIGHTS. 


1  Kilogramme 
1  Hectogramme 
1  Decagramme 
1  Gramme 


=1000  Grammes. 
=  100         " 
=     10         « 
=       1 


1  Gramme         =  1.000  Gramme. 
1  Decigramme  =0.100        " 
1  Centigramme  =  0.010        " 
1  Milligramme  =  0.001        " 


1  Kilogramme  = 
1  "  = 

1  Gramme       = 


Logarithms.  Ar.  Co.  Log. 

2.20462  Pounds  Avoirdupois.     0.343  3337  9.656  6663 

2.67922       "       Troy.                 0.4280083  9.5719917 

15.43235  Grains.                           1.1884321  8.8115679 


TABLE  FOR   THE  REDUCTION  OF  THE  BAROMETRIC   SCALE. 


28  inch.  =  71. 1187  c.m. 

29  "     -73.6587    « 

30  "     =76.1986    « 

31  «     =78.7386    « 


71c.m.=  27.953  inch. 

72  «    =28.347    « 

73  «    =28.741    « 

74  "    =29.134   « 


75c.m.=  29.528  inch. 

76  "    =  29.922    " 

77  «    =30.315    « 

78  «    =30.709    « 


1  inch  =  2.539954  c.  m. 


1  c.  m.  =  0.3937  inch. 


692 


TABLES. 


LOGARITHMS 
FOR   REDUCING    THE    MOST    COMMON    WEIGHTS    AND    MEASURES. 

Measures  of  Length. 


Metre. 

Parisian  Foot. 

Austrian  Foot. 

Prussian  Foot. 

English  Foot. 

0, 

0.4S8  3313 

0.500  1723 

0.503  2730 

0.515  9929 

0.511  6687-1 

0. 

0.011  8410 

0.014  9417 

0.027  6616 

0.-199  8277-1 

0.988  1590-1 

0. 

0.003  1007 

0.0158206 

0.496  7270-1 

0.985  0583-1 

0.996  8993-1 

0, 

0.012  7199 

0.434  0071-1 

0.972  3384-1 

0.984  1794-1 

0.987  2801-1 

0. 

Measures  of  Surface. 


Square  Metre. 

Parisian  Sq.  Foot. 

Austrian  Sq.  Foot. 

Prussian  Sq.  Foot. 

English  Sq.  Foot. 

0. 

0.976  6625 

1.000  3445 

1.006  5459 

1.031  9857 

0.023  3375-1 

0. 

0.023  6820 

0.029  8834 

0.055  3232 

0.999  6555-2 

0.976  3180-1 

0. 

0.006  2014 

0.031  6412 

0.993  4540-2 

0.970  1166-1 

0.993  7986-1 

0. 

0.025  4398 

0.96S  0143-2 

0.944  6768-1 

0.968  3588-1 

0.974  5602-1 

0, 

Measures  of  Volume. 


Cubic  Metre. 

Parisian  Cub.  Foot.  Austrian  Cub  Foot. 

Prussian  Cub.  Foot. 

English  Cub  Foot. 

0. 

1.464  9938 

1.5005168 

1.509  8189 

1.5479786 

0.535  0062-2 

0. 

0.035  5230 

0.044  8251 

0.082  9848 

0.499  4832-2 

0.964  4770-1 

0. 

0.009  3021 

0.0474618 

0.490  1810-2 

0.955  1749-1 

0.990  6979-1 

0. 

0.038  1597 

0.452  0214-2 

0.9170152-1 

0.952  5382-1 

0.961  8403-1 

0. 

Weights. 


Kilogramme. 

Austrian  Pound. 

Prussian  Pound. 

Eng  Troy  Pound. 

English  Pound 
Avoirdupois. 

0. 

0.251  8027 

0.330  0224 

0.428  0208 

0.343  3453 

0.748  1973-1 

0. 

0.078  2197 

0.176  2182 

0.091  5426 

0.669  9776-1 

0.921  7803-1 

0, 

0.097  9984 

0.013  3229 

0.571  9792-1 

0.823  7818-1 

0.902  0016-1 

0. 

0.915  3244-1 

0.656  6547-1 

0.908  4574-1 

0.986  6771-1 

0.084  6756 

0, 

TABLES. 


693 


TABLE    II. 

SPECIFIC  GRAVITY  AND  ABSOLUTE  WEIGHT  OF  ONE  LITRE  OF 

SOME   OF   THE  MOST  IMPORTANT  GASES  AND   VAPORS. 

CALCULATED  FOR  THE  LATITUDE  OF  WASHINGTON. 


Names  of  Gases. 

•il 

«2 

Sp.  Or. 
Observed. 

Sp.  Or. 
Computed. 

Weight  of 
1  Litre  = 
l,OOOETm.3 

Logarithms. 

Ar.  Co. 
Logarithms. 

Air,  

1 

1.00000 

1.29206 

0.111282 

9.888718 

Alcohol, 

1.613 

1.58938 

2.05357 

0.312510 

9.687490 

Ammonia  gas,  . 

0.5967 

0.58738 

0.75893 

9.880201 

0.119799 

Antimony, 

16.90823 

21.84640 

1.339380 

8.660620 

Antimonide  of  hydrogen,  . 

4.33072 

5.59554 

0.747842 

9.252158 

Arsenic, 

10.65 

10.36553 

13.39285 

1.126873 

8.873127 

Arsenide  of  hydrogen, 

2.695 

2.69504 

3.48215 

0.541847 

9.458153 

Boron,    .... 

1.50646 

1.94643 

0.289238 

9.710762 

Bromine,  .... 

2 

5.54 

5.52827 

7.14285 

0.853872 

9.146128 

Bromohydric  acid, 

4 

2.79870 

3.61607 

0.558237 

9.441763 

Carbon,     .         .        .        . 

1 

0.8469* 

0.82924 

1.07143 

0.029963 

9.970037 

Carbonic  acid, 

2 

1.52908 

1.52131 

1.96433 

0.293215 

9.706785 

Carbonic  oxide, 

2 

0.96779 

0.96745 

1.25000 

0.096910 

9.903090 

Chlorine, 

2 

2.47 

2.45317 

3.16964 

0.501010 

9.498990 

Chloride  of  boron,     . 

4 

3.942 

4.05636 

5.24107 

0.719420 

9.280580 

Chloride  of  silicon, 

3 

5.939 

5.87380 

7.58928 

0.880201 

9.119799 

Chlorohydric  acid,     . 

4 

1.2474 

1.26114 

1.62947 

0.212045 

9.787955 

Cyanogen,     . 

2 

1.8064 

1.79669 

2.32143 

0.365755 

9.634245 

Cyanohydric  acid, 

4 

0.9476 

0.93290 

1.20536 

0.08  life 

9.918884 

Ether,     .... 

2 

2.586 

2.55689 

3.30365 

0.518994 

9.481006 

Fluorine,   .... 

2 

1.31297 

1.69643 

0.229536 

9.770464 

Fluoride  of  boron, 

4 

2.3124 

2.34608 

3.03127 

0.481625 

9-518375 

Fluoride  of  silicon,    . 

3 

3.600 

3.59338 

4.64287 

0.666786 

9.333214 

Fluohydric  acid,    . 

4 

0.69104 

0.89286 

9.950782 

0.049218 

Hydrogen, 

2 

0.06926 

0.06910 

0.08929 

8.950782 

1.049218 

Iodine,  .... 

2 

8.716 

8.77614 

11.33930 

1.054586 

8.945414 

lodohydric  acid, 

4 

4.443 

4.42262 

5.71429 

0.756962 

9.243038 

Marsh  gas,     . 

4 

0.5576 

0.55283 

0.71429 

9.853872 

0.146128 

Mercury,   .... 

2 

6.976 

6.91035 

8.92858 

0.950782 

9.049218 

Nitrogen, 

2 

0.97137 

0.96745 

1.25000 

0096910 

9.903090 

Nitrous  oxide,  . 

2 

1.5269 

1.52028 

1.96429 

0.293205 

9.706795 

Nitric  oxide, 

4 

1.0388 

1.03655 

1.33928 

0.126873 

,  9.873127 

Olefiant  gas, 

4 

0.9852 

0.96745 

1.25000 

0.096910 

9.903090 

Oxygen,        .        , 

1 

1.10563 

1.10566 

1.42857 

0.154902 

9.845098 

Phosphorus,       .  '   .  ,     .  ., 

1 

4.42 

4.28442 

5.53571 

0.743174 

9.256826 

Phosphide  of  hydrogen, 

4 

1.178 

1.17476 

1.51786 

0.181231 

9.818769 

Selenium,          •        .        », 

1 

5.52827 

7.14285 

0.853872 

9.146128 

Silicon,  .        .        .        »..." 

1 

2.90235 

3.75000 

0.574031 

9.425969 

Sulphur,    .        .        .        . 

1 

2.2 

2.21132 

2.85714 

0.455932 

9.544068 

Sulphide  of  hydrogen,  . 

2 

1.1912 

1.17476 

1.51786 

0.181231 

9.818769 

Sulphurous  acid,        .        . 

2 

2.247 

2.21131 

2.85714 

0.455932 

9.544068 

Water,  . 

2 

0.6235 

0.62193 

0.80357 

9.905025 

0.094975 

Computed  from  the  specific  gravity  of  carbonic  acid,  observed  by  Regnault. 


694 


TABLES. 


TABLE    III. 

SPECIFIC   GRAVITIES   OF   GASES  AT  0°  C. ;    BAROMETER,  76  c.  m. 


Names. 

Specific 
Gravity  by 
Observation. 

Specific 
Gravity  by 
Calculation. 

Observers. 

Air, 

1.000 

ferault. 

Oxygen,      

1.106 

.    . 

Lo 

Dumas  and  Boussin- 

0.0691 

«        «        « 

0.555 

0.559 

Thomson. 

Methyle,          .      ;.£.'!•     .*"_.'. 

0.490 

Olefiant  gas,        .... 

0.978 

0.980 

Th.  de  Saussure. 

Bicarbide  of   hydrogen    of   Fara- 

day, 

1.920 

1.960 

Faraday. 

Phosphide  of  hydrogen, 

1.214 

1.193 

Dumas. 

Arsenide  of  hydrogen, 

2.695 

2.695 

(( 

Chlorine,        .      "..•'• 

2.470 

.    . 

Gay-Lussac  &  The- 

Oxide  of  chlorine,  or  hypochloric 

[nard. 

acid,     

.    . 

2.340 

Hypochlorous  acid  of  Balard,     . 

.    . 

2.980 

0.972 

Dumas  and  Bonssin- 

Protoxide  of  nitrogen, 

1.520 

1.525 

Colin.              [gault. 

Deutoxide  of  nitrogen,  . 

1.0388 

1.036 

Berard. 

Cyanogen,         ,'>"','•• 

1.806 

1.818 

Gay-Lussac. 

Chloride  of  cyanogen,    .        '.        . 

.    . 

2.116 

u 

0.596 

0.591 

Biot  and  Arago. 

Oxide  of  carbon,    .         .      '  . 

0.957 

o 

Cruikshanck. 

Carbonic  acid,     .        .        .        .  * 

1.529 

.    . 

Dumas  and  Boussin- 

Chloro-carbonic  acid,      .        .        . 

.   . 

3.399 

[gault. 

Sulphurous  acid,     .... 

2.234 

.    . 

Thenard. 

Acid,  chlorohydric,      .      ''',•'*.'' 

1.247 

1.260 

Biot  and  Arago. 

bromohydric,  .        .        .         . 

.   . 

2.731 

iodohydric, 

4.413 

4.350 

Gay-Lussac. 

sulphohydric,          .         .         ;  :  '• 

1.191 

.    . 

Gay-Lussac  &  The- 

selenohydric,       .        .        . 

.   . 

2.795 

Bineau.            [nard. 

tellurohydric,          .        .      ;  . 

.    . 

4.490 

<( 

fluoboracic,          .        .  '     * 

2.371 

.   . 

John  Davy. 

fluosilicic,       .        .        '.       .  ,  •"'• 

3.573 

.   . 

a 

chloroboracic, 

3.420 

t 

Dumas. 

Monohydrate  of  methyle, 

1.617 

1.601 

Dumas  and  Peligot. 

Chlorohydrate  of  methyle,          l~r 

1.731 

1.737 

((        <(         « 

Fluohydrate  of  methyle, 

1.186 

1.170 

«                (C                   It 

TABLES. 


695 


TABLE    IY. 

SPECIFIC    GRAVITIES   OF   VAPORS    REDUCED    BY   CALCULATION 
TO   0°  C.,  AND   BAROMETER  76  c.  m. 


Names. 

Specific 
Gravity  by 
Observation. 

Specific 
Gravity  by 
Calculation. 

Observers. 

Air,          

1.000 

5.540 

5.390 

Mitscherlich. 

8.716 

8.700 

Dumas. 

Sulphur,      

6.617 

6.650 

4.420 

4.320 

c( 

Arsenic,      

10.600 

10.360 

Mitscherlich. 

6.976 

6.970 

Dumas. 

Acid,  arsenious,  .         .         .         . 

13.850 

13.300 

Mitscherlich. 

sulphuric  anhydrous, 

3.000 

2.760 

« 

selenious,    .... 

4.030 

.   . 

u 

hyponitrous,  .... 

1.720 

.   . 

« 

nitric  tetrahydrated,    . 

1.270 

.   . 

Binean. 

Yellow  chloride  of  sulphur,    . 

4.700 

4.650 

Dumas. 

Red  chloride  of  sulphur, 

3.700 

.   . 

M 

Protochloride  of  phosphorus, 

4.870 

4.790 

(t 

Chloride  of  arsenic,     . 

6.300 

6.250 

« 

Iodide  of  arsenic,   .... 

16.100 

15.640 

Mitscherlich. 

Protochloride  of  mercury,  . 

8.350 

8.200 

«c 

Bichloride  of  mercuiy,    . 

9.800 

9.420 

« 

Protobromide  of  mercury,  . 

10.1-10 

9.670 

M 

Deutobromide  of  mercury, 

12.1bO 

12.370 

U 

Deutoiodide  of  mercury,     . 

15.600 

15.680 

U 

Sulphide  of  mercury  (cinnabar),     . 

5.500 

5.400 

u 

Protochloride  of  antimony, 

7.800 

.    . 

u 

Protochloride  of  bismuth, 

11.100 

10.990 

Jacqnelain. 

Peroxichloride  of  chromium, 

(    5.520  ) 

5.500 

Bineau  and  Walter. 

I    5.900  J 

Bichloride  of  tin,    .... 

9.199 

8.990 

Dumas. 

Solid  chloride  of  cyanogen, 

6.390 

.   . 

Binean. 

Bromide  of  cyanogen,    . 

3.610 

.  . 

« 

Chloride  of  silicon, 

5.939 

5.959 

Dumas. 

Camphor,        

5.468 

5.314 

M 

Oil  of  turpentine, 

4.763 

4.765 

• 

o  770 

2.730 

Mitscherlich. 

Naphthaline, 

£i9    t    t\J 

4.528 

4.492 

Dumas. 

Chloride  of  elayle,      ..  ,  I^.H  . 

3.443 

3.450 

Gay-Lussac. 

Sulphide  of  carbon,    . 

2.644 

.   . 

M 

Alcohol,         .        .        .        .       • 

1.6133 

1.601 

14 

Ether,          .        .    •;  »  .  <.    *    :  „ 

2.586 

2.583 

ii 

3.067 

3.066 

Dumas  &  Boullay. 

oxalic,         .        .        •  \'tl'<»>v 

5.087 

5.081 

«            « 

5.409 

5.240 

«            « 

696 


TABLES. 


Names. 

Specific 
Gravity  by 
Observation. 

Specific 
Gravity  by 
Calculation. 

Observers. 

Methylic  alcohol,    .        ».  .     ^  _  ,  ,%.  I| 
Sulphate  of  methyle,  . 
Acetate  of  methyle,        »   "  .  »  ,      •  ""'' 
Fusel  oil,     .        .         .        »        .  . 

1.120 
4.565 
2.563 
3.147 
2.019 

1.110 
4.370 
2.570 
3.070 
2.020 

Dumas  and  Peligot. 
«              (( 

tt             tt 

Dumas. 
n 

Mercaptan,          .        .        . 
Aldehyde,       
Oil  of  bitter  almonds, 
Hydruret  of  salicyle,       •. 
Oil  of  cinnamon, 

2.326 
1.532 

4.270 
5.200 

2.160 
1.530 
3.708 
4.260 
4.620 
5.100 

Btinsen. 
Liebig. 
Wohler  and  Liebig. 
Pii-ia. 
Dumas  and  Peligot 
Gerhardt  and    Ca- 

2.770 

2.780 

Dumas.          [hours. 

4.270 

4.260 

«( 

valerian  ic,  .... 
cyanohydric,  .... 
Kakodyle     

3.680 
0.947 
7  100 

3.550 
0.936 
7  280 

Dumas  and  Stas. 
Gay-Lussac. 
Bunsen 

Oxide  of  kakodyle, 
Cyanuret  of  kakodyle, 
Chloride  of  kakodyle,     . 
Water,        ..... 

7.550 
4.630 
4.560 
0.6235 

7.830 
4.540 
4.800 
0.624 

« 
« 
ti 

Gay-Lussac. 

TABLE    Y. 

SPECIFIC  GRAVITY  OF  LIQUIDS  AT  4°  C. 


Name. 

Sp.  Gravity. 

Name. 

Sp.  Gravity. 

Water,  distilled, 

1.000 

Ether,    .... 

0.715 

Bromine,     . 

2.966 

chlorohydric, 

0.874 

Mercury  at  0°  C.,  . 

13.596 

acetic,  . 

0.868 

Acid,  sulphuric,  most  con- 

Methylic alcohol, 

0.798 

centrated,   . 

1.841 

Fusel  oil, 

0.818 

hyposulphuric,     . 

1.347 

Acetone,    . 

0.792 

nitric  fuming, 

1.451 

Mercaptan,    .        >  •     ;v 

0.840 

nitric  tetrahydrated, 

1.420 

Oil  of  turpentine, 

0.869 

nitric  of  commerce, 

1.220 

of  citron,         .        ••  •  !  '' 

0.847 

hyponitric,       .      *  ••  •  i 

1.451 

Aldehyde,  . 

0.790 

chlorohydric   concen- 

Oil of  bitter  almonds, 

.043 

trated  liquid,      i    • 

1.208 

of  spiraea,        .        .; 

.173 

acetic  monohydrated, 

1.068 

of  cumin,    .        . 

0.969 

acetic,  greatest  density, 

1.079 

of  cinnamon,  .       V  ' 

.010 

oleic,       .      ,•  •••;'      %  , 

0.898 

Sea-water,          .*    -f'i    • 

.026 

cyanohydric, 

0.696 

Milk,     .         .        v 

.030 

Sulphide  of  carbon,      8*    ] 

1.263 

Wine  of  Bordeaux,  . 

0.994 

Protochloride  of  sulphur, 

1.680 

of  Burgundy,      * 

0.991 

Alcohol,  absolute,   .      *%,>.< 

rrrO'ltoct"        /Jptl'Mt'Tr 

0.792 

Olive-oil,   .        .        t 

0.915 

08.47 

(hyd.of  Rudberg), 

0.927 

Naphtha,       •        •        . 

.847 

TABLES. 


697 


TABLE    VI. 

SPECIFIC  GRAVITY  OF  SOLIDS  AT  4°  C. 
1.   Simple  Bodies. 


Names. 

Specific  Gravity. 

Observers. 

4.948 

Gay-Lussac. 

2.086 

4.300 

Phosphorus,          

1  770 
5.670 

Herapath 

(Diamonds,                             .      j 
Carbon,  /                                                     ( 

(  Graphite,         .... 

3.530 
3.500 
2.500 
0.865 

Leroyer  &  Dumas. 
Gay-Lus.  and  Then. 

0.972 

«               « 

8.010 

7.788 

7.200 

7.810 

Zinc,    
Cadmium,  hammered,      .... 
Tin      

7.190 
8.690 
7.291 

7.812 

8.279 

8.666 

8.600 

17.600 

Freres  d'Echuyart. 

Chromium,  

5.900 
6.720 

Titanium,     

5.300 
6.240 

9  000 

Bucholz. 

9  822 

Freres  d'Echuyart. 

11  350 

8  850 

rolled  or  forged, 

8.950 
13.598 

Osmium,      
Indium  (cast  by  electric  battery),    . 

10.000  ? 
18.680 
11.300 

Children. 

rnllrd 

'11  son 

1  1  000  7 

10  470 

19  360 

19  260 

21.530 

rolled       .        .        . 

22.060 

59 


698 


TABLES. 


2.  Binary  Compounds. 


Names. 

Specific  Gravity. 

Observers. 

f  Quartz  hyalin., 
Acid,  silicic,  )  Agate,  .... 
(  Opal  (sil.  hyd.), 
hydrated  boracic  (sassoline), 

2.653 
2.615 
2.250 
1.480 
3.150 

M.* 
M. 
M. 
M. 
Boullay. 

Chloride  of  calcium,     .... 
Fluoride  of  calcium  (fluor-spar), 
Chloride  of  barium,     .... 
Chloride  of  potassium,    .... 
Iodide  of  potassium,    .... 
Chloride  of  sodium,         .... 

2.230 
3.200 
3.900 
1.836 
3.000 
2.100 

H 

M. 
Boullay. 
Wenzel. 
Boullay. 
Kirwan. 

Chloride  of  ammonium  (sal.  ammoniac), 
f  Corundum,  sapphire,  and  ori- 
Alumina,  )     ental  ruby, 

1.520 

4.160 
3.900 

M. 

M. 
M. 

Acid,  arsenious,       

3.700 

Leroyer  &  Dumas. 

Protoxide  of  antimony, 
Sulphide  of  antimony,    .... 
Oxide  of  silver,    

5.778 
4.334 
7.250 

Boullay.  - 
M. 
Boullay. 

Sulphide  of  silver,    

7.200 

M. 

Chloride  of  silver, 

5.548 

Boullay. 

Iodide  of  silver,       .... 

5.614 

tt 

Deutoxide  of  mercury, 
Protochloride  of  mercury, 
Bichloride  of  mercury, 
Deutoiodide  of  mercury,  .... 
Protoiodide  of  mercury, 
Bisulphide  of  mercury,    .... 
Oxide  of  bismuth, 

11.000 
7.140 
5.420 
6.320 
7.750 
8.124 
8.968 

(t 
tt 
tt 

(t 
tt 
it 

it                  , 

Sulphide  of  bismuth, 

6  540 

M. 

Sulphide  of  molybdenum,    . 
Tungstic  acid, 

4.600 
R  000 

M. 
M 

Protoxide  of  copper,    .... 
Deutoxide  of  copper, 

5.300 
6.130 

Boullay. 

(C 

Protosulphide  of  copper, 
Deutoxide  of  tin,     .... 

5.690 
6  700 

M. 
M. 

Protosulphide  of  tin,    .... 
Bisulphide  of  tin,    .        .        .        .        .  " 

5.267 
4  415 

Boullay. 

M 

Protoxide  of  lead  (cast), 
Peroxide  of  lead,     .        .        .-•'  c    .        . 

9.500 
9  200 

« 
tt 

Iodide  of  lead,      .        .        .        .       « 

fi  100 

tt 

Selenide  of  lead,      .        .        .   ""    *       , 

7  690 

M. 

Sulphide  of  lead  (Galena),  . 
Oxide  of  zinc,  .       %      •  .    '    .  *  .  .    ..'•«"• 

7.580 

K  C(\f) 

M. 

Boullay 

Sulphide  of  zinc  (blende),    .   ";.       » 

4.160 

M. 

*  M.  indicates  the  numbers  taken  from  the  "  Trait6  de  Mineralogie  »  of  Beudant.    The  mean  has 
generally  been  used. 


TABLES. 


699 


Names. 

Specific  Gravity. 

Observers. 

Peroxide  of  iron 

5.225 

Boullay. 

Magnetic  oxide  of 

iron, 

5.400 

tt 

Bisulphide    of    iron 

Sulphides  of  iron,  - 

(pyrites),  . 
Do.  (white  pyrites),. 

5.000 
4.840 

M. 
M. 

Magnetic  pyrites,  . 

4.620 

M. 

Peroxide  of  manganese,  .... 

4.480 

Boullay. 

Sesquioxide  of  manganese,  . 

4.810 

M. 

Red  oxide  of  manganese, 

4.722 

M. 

Protosulphide  of  manganese, 

3.950 

M. 

Peroxide  of  titanium  (rutile), 

4.250 

M. 

3.  Simple  Salts. 


Names. 

Specific  Gravity. 

Observers. 

(  Iceland  Spar, 
Carbonate  of  Lime,  <   . 
(  Arragomte, 

2.723 
2.946 

Malus. 
Thenard. 

Carbonate  of  magnesia  (giobertite), 

2.880 

M. 

Carbonate  of  iron  (iron  spar), 

3.850 

M. 

Carbonate  of  manganese, 

3.550 

M. 

Carbonate  of  zinc,        .... 

4.500 

M. 

Carbonate  of  barytes,       .... 

4.300 

M. 

Carbonate  of  strontia, 

3.650 

M. 

Carbonate  of  lead  (white  lead), 

6.730 

M. 

Sulphate  of  baryta  (heavy  spar),          . 

4.700 

M. 

Sulphate  of  strontia  (celestine), 

3.950 

M, 

Sulphate  of  lead,          .... 

6.300 

M. 

5.340 

Karstcn. 

(  Anhydrite,    . 
Sulphates  of  lime,  <  ~     J 
'  i  Gypsum,  . 

2.900 
2.330 

M. 

M. 

Sulphate  of  potash,      .        .        .        . 

2.400 

M. 

Anhydrous  sulphate  of  soda,  .        . 

2.630 

Karsten. 

Chromate  of  potash,     .... 

2.700 

Kopp. 

Chromate  of  lead  (native),      .        .        • 

6.600 

M. 

1.930 

M. 

3.185 

Karsten. 

Nitrate  of  strontia,       .... 

2.890 

M 

4.400 

tt 

6.700 

Gmelin. 

8.000 

M 

Tungstate  of  lime,        .        .        .      .  «• 

6.000 

Karsten. 

Aluminate  of  magnesia  (spinel),     .        » 

3.700 

M. 

Aluminate  of  zinc  (zinc  spinel),   .        •' 

4.700 

M. 

Silicate  of  zirconia  (zircon),     .        .      .  . 

4.400 

M. 

Borate  of  magnesia  (boracite),    . 

2.500 

M. 

703 


TABLES. 


tp—  i-»^ 

^-  —  OO 


050-.  0000 


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cocococoeoeococowcococoeoeoecwcococococo 
ddddoodddoddddooodddd 


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ooooooooooqoqqqqooco 
ooooodooodoooooocccoo 


iftOOS0C?}COOCtf^l'^CO^'O^'>»OOCOC00000^1*i*iC^f«00  ***•  O 

C5tO^DaecoOO<Nr-^fTtoOi~-»f-C»cocoo»;ocO(M**'O5 


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o  d  d  d  o 


^  s 


cocococococococococococococococccococoooco 
ooooaooocoooooooooooooo&QOoooooooocoooooao 

ddo'o'odo'oddooddddddddd 


•-lOO—  •   i-H  <M   •«*  «O  00  —  mOOCOQOCOOOTt  —  OOinCO 

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oooooooooqqoqooocqcoq 
ooooooooododo'oooo'oooo 


tOOcD^D^O^OCDtDCOCDcDtDcOCDCOCDCDCC^CtOCDtDCCCOCD 

oqqqoqoqqqqqqqqqqcqqccccq 
oddddddddddddddddddcddddd 


wco 


coeoeocococoeococcc^co^ec'e^eo 


CO  CO  CO   CO   CO 
Ci  C3^  C^  CJ5  Ci 

qqqoqqqqcqqqq 
dddodddddo'do'dddoooddddddd 


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TABLES. 


701 


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?  a! 


ooocoooooooocooococoo 
6ddddoo6oc5o6c>6ooooddd 


COOJOJOJOiOOOOOOOOQO 


r«~toQ4ao<«to«ono> 

t^t^VDtOtOtoSoSS 


c^oot^-oo  — 


00  ^*  kft 

•scgMoididialdioi 


—  dode4»rr^d'*CJ'^'deoc'-< 
OOit-i-tOifi-TCOW'.N.—  --  OCO 


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oo  O  —  co »-' 

tf)  1C 


t^»  irtCO— *O>OOO*1iCOp—   CiOO^OinCO^CO^t^CO'fCO^I*-* 

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II 
II 


»t  O  oo  i-  i-  o»  o<  c;  IM  o  i-  i-  oo  c  er  oo  «n  c>i  —  — 

i7i«ooico*^^-«oo»no>»»io>'*o»no<oiMQo^ 


r*meo 

—  —  <M 


oococx)t-.i-.i^<ooo«Dift«n»«krt»ft«n-f'tt'*-t« 
ooooooooooqooqoqccooo 
ddo'o'oddooddodo'dddddoo 


8na«e«giot0«gQ«MMe«9*o;aw<NO«M9i9i« 
oooqqqqqqqqqoqqqcocq 
dooodddddddddoddddood 


C>1C^C»1(N(>I?3CT(N  —  —  —  —  ^-  —  —  — —  —  — ' 

ddddddddddodddocdco  oo 


i'-- 
oooooooqooqqqqsqooccq 

do'ddddoddoddddodooooo 


59* 


702 


TABLES. 


TABLE    VIII. 

TABLE  OF  THE  TENSION  OF  THE  VAPOR  OF  ABSOLUTE  ALCOHOL, 
ACCORDING  TO  REGNAULT.* 


0  C. 

Tension. 

°C. 

Tension. 

°C. 

Tension. 

°C. 

Tension. 

o 
0.0 

in.  in. 
12.73 

o 
4.0 

m.m. 
16.62 

0 

8.0 

in.  in. 

21.31 

o 
12.0 

m.m. 
27.19 

0.1 

12.82 

4.1 

16.73 

8.1 

21.45 

12.1 

27.36 

0.2 

12.91 

4.2 

16.84 

8.2 

21.53 

12.2 

27.53 

0.3 

13.01 

4.3 

16.95 

8.3 

21.72 

12.3 

27.70 

0.4 

13.10 

4.4 

17.05 

8.4 

21.85 

12.4 

27.87 

0.5 

13.19 

4.5 

17.16 

8.5 

21.99 

12.5 

28.04 

0.6 

13.28 

4.6 

17.27 

8.6 

22.12 

12.6 

28.21 

0.7 

13.37 

4.7 

17.38 

8.7 

22.25 

12.7 

28.38 

0.8 

13.46 

4.8 

17.48 

8.8 

22.39 

12.8 

28.55 

0.9 

13.56 

4.9 

17.59 

8.9 

22.52 

12.9 

28.72 

1.0 

13.65 

5.0 

17.70 

9.0 

22.66 

13.0 

28.89 

1.1 

13.74 

5.1 

17.82 

9.1 

22.80 

13.1 

29.07 

1.2 

13.81 

5.2 

17.93 

9.2 

22.94 

13.2 

29.25 

1.3 

13.93 

5.3 

18.04 

9.3 

23.03 

13.3 

29.43 

1.4 

1  4.03 

5.4 

18.16 

9.4 

23.23 

13.4 

29.61 

1.3 

14.12 

5.5 

18.27 

9.5 

23.37 

13.5 

29.79 

1.6 

14.22 

5.6 

18.38 

9.6 

23.51 

13.6 

29.97 

1.7 

14.31 

5.7 

18.50 

9.7 

23.65 

13.7 

30.15 

1.8 

14.41 

5.8 

18.61 

9.8 

23.79 

13.8 

30.23 

1.9 

14.50 

5.9 

18.73 

9.9 

23.94 

13.9 

30.51 

2.0 

14.60 

6.0 

18.84 

10.0 

24.08 

14.0 

30.69 

2.1 

14.70 

6.1 

18.96 

10.1 

24.23 

14.1 

30.88 

2.2 

14.79 

6.2 

19.08 

10.2 

24.38 

14.2 

31.07 

2.3 

14.89 

6.3 

19.20 

10.3 

24.53 

14.3 

31.26 

2.4 

14.99 

6.4 

19.32 

10.4 

24.68 

14.4 

31.45 

2.5 

15.09 

6.5 

19.44 

10.5 

24.83 

14.5 

31.64 

2.6 

15.19 

6.6 

19.56 

10-6 

24.99 

14.6 

31.84 

2.7 

15.29 

6.7 

19.68 

10.7 

25.14 

14.7 

32.03 

2.8 

15.39 

6.8 

19.80 

10.8 

25.29 

14.8 

32.22 

2.9 

15.49 

6.9 

19.92 

10.9 

25.44 

14.9 

32.41 

3.0 

15.59 

7.0 

20.04 

11.0 

25.59 

15.0 

32.60 

3.1 

15.69 

7.1 

20.17 

11.1 

25.75 

15.1 

32.80 

3.2 

15.79 

7.2 

20.30 

11.2 

25.91 

15.2 

33.01 

3.3 

15.90 

7.3 

20.43 

11.3 

26.07 

15.3 

33.21 

3.4 

16.00 

7.4 

20.55 

11.4 

26.23 

15.4 

33.41 

3.5 

16.10 

7.5 

20.68 

11.5 

26.39 

15.5 

33.61 

3.6 

16.21 

7.6 

20.81 

11.6 

26.55 

15.6 

33.82 

3.7 

16.31 

7.7 

20.93 

11.7 

26.71 

15.7 

34.02 

38 

16.41 

7.8 

21.06 

11.8 

26.87 

15.8 

31.22 

3.9 

16.52 

7.9 

21.19 

11.9 

27.03 

15.9 

34.42 

*  This  table  is  calculated  from  recent  experiments  of  Regnault. 


TABLES. 


703 


°c. 

Tension. 

QC. 

Tension. 

oc. 

Tension. 

oc. 

Tension. 

0 

in  .  in  • 

o 

m.  m. 

0 

m.m. 

0 

m.m. 

16.0 

34.62 

20.0 

44.00 

24.0 

55.70 

2tf.O 

70.02 

16.1 

34.84 

20.1 

44.27 

24.1 

56.04 

2S.1 

70.49 

16.2 

35.05 

20.2 

44.54 

24.2 

56.37 

28.2 

70.89 

16.3 

35.27 

20.3 

44.81 

24.3 

56.70 

28.3 

7  1  .29 

16.4 

35.48 

20.4 

45.08 

24.4 

57.03 

28.4 

71.69 

16.5 

35.70 

20.5 

45.35 

24.5 

57.37 

28.5 

72.09 

16.6 

35.91 

20.6 

45.61 

24.6 

57.70 

2S.6 

7249 

16.7 

36.13 

20.7 

45.88 

24.7 

58.03 

2S.7 

72.69 

16.8 

36.34 

20.8 

46.15 

24.8 

58.36 

23.8 

'3.29 

16.9 

36.56 

20.9 

46.42 

24.9 

58.70 

28.9 

7:j.69 

17.0 

36.77 

21.0 

46.69 

25.0 

59.03 

29.0 

74.09 

17.1 

37.00 

21.1 

46.98 

25.1 

59.38 

29.1 

71.53 

17.2 

37.23 

21.2 

47.26 

25.2 

59.73 

23.2 

71.96 

17.3 

37.45 

21.3 

47.55 

25.3 

60.08 

29.3 

7.3.39 

17.4 

37.68 

21.4 

47.63 

25.4 

60.43 

29.4 

7'».82 

17.5 

37.91 

21.5 

48.12 

25.5 

60.78 

29.5 

76  25 

17.6 

38.14 

21.6 

48.40 

25.6 

61.13 

29.6 

76-68 

17.7 

38.36 

21.7 

48.69 

25.7 

61.48 

29.7 

77.12 

17.8 

38.59 

21.8 

48.97 

25.8 

61.83 

29.3 

77.55 

17.9 

38.82 

21.9 

49.26 

25.9 

62.18 

29.9 

77.98 

30.0 

78.41 

18.0 

39.05 

22.0 

49.54 

26.0 

62.53 

18.1 

39.29 

22.1 

49.84 

26.1 

62.90 

18.2 

39.53 

22.2 

50.14 

26.2 

63.27 

18.3 

39.77 

22.3 

50.44 

26.3 

63.64 

18.4 

40.01 

22.4 

50.74 

26.4 

64.01 

18.5 

40.25 

22.5 

51.04 

26.5 

64.37 

18.6 

40.49 

22.6 

51.34 

26.6 

64.74 

18.7 

40.73 

22.7 

51.64 

26.7 

65.11 

18.8 

40-97 

22.8 

51.94 

26.8 

65.48 

18.9 

41.21 

22.9 

52.24 

26.9 

65.85 

19.0 

41.45 

23.0 

52.54 

27.0 

66.22 

19.1 

41.71 

23.1 

52.86 

27.1 

66.60 

19.2 

41.96 

23.2 

53.17 

27.2 

66.99 

19.3 

42.22 

23.3 

53.49 

27.3 

67.38 

19.4 

42.47 

23.4 

53.81 

27.4 

67.77 

19.5 

42.73 

23.5 

54.12 

27.5 

63.15 

19.6 

42.98 

23.6 

54.44 

27.6 

68  54 

19.7 

43.2  1 

23.7 

54.75 

27.7 

6S.93 

19.8 

43.49 

23.8 

55.07 

27.8 

69.31 

19.9 

43.75 

23.9 

55.38 

27.9 

69.70 

1 

704 


TABLES. 


TABLE    IX. 

TABLE  FOR   THE   TENSION  OF  AQUEOUS  VAPOE  FOR  TEMPERA- 
TURES  FROM  —32°    TO   +230°,   BY  REGNAULT. 


Temperature. 

Tension  in 
Centimetres. 

Temperature. 

Tension  in 
Centimetres. 

Temperature. 

Tension  in 
Centimetres. 

o 
—82 

0.0320 

o 
-H9 

1.6346 

+105° 

90.6410 

30 

0.0386 

20 

1.7391 

110 

107.5370 

25 

0.0605 

21 

1.8495 

115 

1269410 

20 

0.0927 

22 

1.9659 

120 

149.1280 

15 

0.1400 

23 

2.0888 

125 

174.388 

10 

0.2093 

24 

2.2184 

130 

203.028 

—  5 

0.3113 

25 

2.3550 

135 

235.373 

0 

0.4600 

26 

2.4988 

140 

271.763 

+  1 

0.4940 

27 

2.6505 

145 

312.555 

2 

0.5302 

28 

2.8101 

150 

358.123 

3 

0.5687 

29 

2.9782 

155 

408.856 

4 

0.6097 

30 

3.1548 

160 

465.162 

5 

0.6534 

35 

4.1827 

165 

527.454 

6 

0.6998 

40 

5.4906 

170 

596.166 

7 

0.7492 

45 

7.1391 

175 

671.743 

8 

0.8017 

50 

9.1982 

180 

754.639 

9 

0.8574 

55 

11.7478 

185 

845.323 

10 

0.9165 

60 

14.8791 

190 

944.270 

11 

0.9792 

65 

18.6945 

195 

1051.963 

12 

.0457 

70 

23.3093 

200 

1168.896 

13 

.1162 

75 

28.8517 

205 

1295.566 

14 

.1908 

80 

35.4643 

210 

1432.480 

15 

.2699 

85 

43.3041 

215 

1580.133 

16 

.3586 

90 

52.5450 

220 

1739.036 

17 

.4421 

95 

63.3778 

225 

1909.704 

18 

.5357 

100 

76.0000 

230 

2092.640 

Tension  of  Vapor  of  Water -,  according  to  Dulong  and  Arago. 


Temperature. 

Tension  in 
Atmospheres. 

Pressure  in 
Kilogrammes 
onl^Tm.8 

Temperature. 

Tension  in 
Atmospheres. 

Pressure  in 
Kilogrammes 
onl^THr:* 

o 
100 

1 

1.033 

226.3 

25 

25.825 

121.4 

2 

2.066 

265.89 

50 

51.650 

135.1 

3 

3.099 

311.36 

100 

103.3 

145.4 

4 

4.106 

363.58 

200 

206.6 

160.2 

6 

6.198 

423.57 

400 

413.2 

172.1 

8 

8.264 

462.71 

600 

619.8 

190.0 

12 

12.396 

492.47 

800 

826.4 

203.6 

16 

16.528 

516.75 

1000 

1033.0 

214.7 

23 

20.660 

TABLES 


705 


TABLE    X. 

TABLE  FOR  THE  TENSION  OF  AQUEOUS  VAPOR  FOR  TEMPERA- 
TURES FROM  —2°  TO  +35°  C ,  ACCORDING  TO  REGNAULT. 


00. 

Tension. 

00. 

Tension. 

°C 

Tension. 

oo. 

Tension. 

O 

—2.0 

m.  m. 
3.955 

0 

+2.0 

m.  m. 
5.302 

o 
+6.0 

m.  m. 
6.993 

+10.0 

m.  m. 
9.165 

1.9 

3.985 

2.1 

5.340 

6.1 

7.047 

10.  1 

9.227 

1.8 

.016 

2.2 

5.378 

6.2 

7.095 

10.2 

9.288 

1.7 

.047 

2.3 

5.416 

6.3 

7.144 

10.3 

9.350 

1.6 

.078 

2.4 

5.454 

6.1 

7.193 

10.4 

9.412 

1.5 

.109 

2.5 

5.491 

6.5 

7.242 

10.5 

9.474 

1.4 

.140 

2.6 

5.530 

6.6 

7.292 

10-6 

9.537 

1.3 

4.171 

2.7 

5.599 

6.7 

7.342 

10.7 

9.601 

1.2 

4.203 

2.8 

5.603 

6.8 

7.392 

10.8 

9.665 

1.1 

4.235 

2.9 

5.617 

6.9 

7.442 

10.9 

9.728 

1.0 

4.267 

3.0 

5.687 

7.0 

7.492 

11.0 

9.792 

0.9 

4.299 

3.1 

5.727 

7.1 

7.544 

11.1 

9.857 

0.8 

4.331 

3.2 

5.767 

7.2 

7.595 

11.2 

9.923 

0.7 

4  364 

3.3 

5.807 

7.3 

7.617 

11.3 

9.9S9 

0.6 

4.397 

3.4 

5.848 

7.4 

7.699 

11.4 

10.054 

0.5 

4.430 

3.5 

5.889 

7.5 

7.751 

.    11.5 

10.120 

0.4 

4.163 

3.6 

5.930 

7.6 

7.804 

11.6 

10.187 

0.3 

4.497 

3.7 

5.972 

7.7 

7.S57 

11.7 

10.255 

0.2 

4.531 

38 

6.014 

7.8 

7.910 

11.8 

10.322 

—O.I 

4.565 

3.9 

6.055 

7.9 

7.9GI 

11.9 

10.389 

0.0 

4.600 

4.0 

6.097 

8.0 

8.017 

12.0 

10.457 

+0.1 

4.63* 

4.1 

6.140 

8.1 

8.072 

12.1 

10.526 

0.2 

4.6f>7 

4.2 

6.183 

8.2 

8.126 

12.2 

10.596 

0.3 

4.700 

4.3 

6.226 

8.3 

8.181 

12.3 

10.665 

0.4 

4.733 

4.4 

6.270 

8.4 

8.236 

12.4 

10.734 

0.5 

4.767 

4.5 

6.313 

8.5 

8.291 

125 

10.804 

0.6 

4.801 

4.6 

6.357 

8.6 

8.347 

12.6 

10.875 

0.7 

4.836 

4.7 

6.401 

8.7 

8.404 

12  7 

10.947 

0.8 

4.871 

4.8 

6.445 

8.8 

8.461 

12.8 

11.019 

0-9 

4.905 

4.9 

6.490 

8.9 

8.517 

12.9 

11.090 

1.0 

4  9  JO 

5.0 

6.534 

9.0 

8.574 

13.0 

11.162 

1.1 

4.975 

5.1 

6.580 

9.1 

8.632 

13.1 

11.235 

1.2 

5.011 

5.2 

6.625 

9.2 

8.690 

13.2 

11.309 

1.3 

5.047 

5.3 

6.671 

9.3 

8.748 

13.3 

11.383 

1.4 

5.082 

5.4 

6.717 

9.4 

8.807 

13.4 

11.456 

1.5 

5.118 

5.5 

6.763 

9.5 

8.865 

13.5 

11.530 

1.6 

5.155 

5.6 

6.810 

9.6 

8.925 

13.6 

11.605 

1.7 

5.191 

5.7 

6.857 

9.7 

8.985 

13.7 

11.681 

1.8 

5.228 

5.8 

6.904 

9.8 

9.045 

13.8 

11.757 

1.9 

5.265 

5.9 

6.951 

9.9 

9.105 

13.9 

11.832 

706 


TABLES. 


°c. 

Tension. 

oC. 

Tension. 

oC. 

Tension. 

OC. 

Tension. 

o 

111.  in. 

o 

m.m. 

o 

m.m. 

o 

m.m. 

+14.0 

11.908 

+18.0 

15.357 

+22.0 

19.659 

+26.0 

24.988 

14.1 

11.986 

18.1 

15.454 

22.1 

19.780 

26.1 

25.138 

14.2 

12.064 

18.2 

15.552 

22.2 

19.901 

26.2 

25.288 

14.3 

12.142 

18.3 

15.650 

22.3 

20.022 

26.3 

25.  -138 

14.4 

12.220 

18.4 

15.747 

22.4 

20.143 

26.4 

25.58S 

14.5 

12.298 

18.5 

15.845 

22.5 

20.265 

26.5 

25.738 

14.6 

12.378 

18.6 

15.945 

22.6 

20.389 

26.6 

25.891 

14.7 

12.458 

18.7 

16.045 

22.7 

20.514 

26.7 

26.015 

14.8 

12.538 

18.8 

16.145 

22.8 

20.639 

2i>.8 

26.198 

14.9 

12.619 

18.9 

16.246 

22.9 

20.763 

26.9 

26.351 

15.0 

12.699 

19.0 

16.346 

23.0 

20.888 

27.0 

26.505 

15  1 

12.781 

19.1 

16.449 

23.1 

21.016 

27.1 

26.663 

15.2 

12.S6I 

19.2 

16.552 

23.2 

21.144 

27.2 

26.820 

15.3 

12.947 

19.3 

16.655 

23.3 

21.272 

27.3 

26.978 

15.4 

13.029 

19.4 

16.758 

23.4 

21.400 

27.4 

27.136 

15.5 

13.112 

19.5 

16.861 

23.5 

21.528 

27.5 

27.294 

15.6 

13.197 

19.6 

16.967 

23.6 

21-659 

27.6 

27.455 

15.7 

13.281 

19.7 

17.073 

23.7 

21.790 

27.7 

27.617 

15.8 

13.366 

19.8 

17.179 

23.8 

21.921 

27.8 

27.778 

15.9 

13.451 

19.9 

17.285 

23.9 

22.053 

27.9 

27.939 

16.0 

13.536 

20.0 

17.391 

24.0 

22.184 

28.0 

28.101 

16.1 

13.623 

20.1 

17.500 

24.1 

22.319 

28.1 

28.267 

16.2 

13.710 

20.2   , 

17.608 

24.2 

22.453 

28.2 

23.433 

16.3 

13.797 

20.3 

17.717 

24.3 

22.588 

28.3 

28.599 

16.4 

13.885 

20.4 

17.826 

24.4 

22.723 

28.4 

28.765 

16.5 

13.972 

20.5 

17.935 

24.5 

22.858 

28.5 

28.931 

16.6 

14.062 

20.6 

18.047 

24.6 

22.996 

28.6 

29.101 

16.7 

14.151 

20.7 

18.159 

24.7 

23.135 

28.7 

29.271 

16.8 

14.241 

20.8 

18.271 

24.8 

23.273 

28.8 

29.441 

16.9 

14.331 

20.9 

18.383 

24.9 

23.411 

28.9 

29.612 

17.0 

14.421 

21.0 

18.495 

25.0 

23.550 

29.0 

29.782 

17.1 

14.513 

21.1 

18.610 

25.1 

23.692 

29.1 

29.956 

17.2 

14.605 

21.2 

18.724 

25.2 

23.834 

29.2 

30.131 

17.3 

14.697 

21.3 

18.839 

25.3 

23.976 

29.3 

30.303 

17.4 

14.790 

21.4 

18.954 

25.4 

24.119 

29.4 

30.479 

17.5 

14.882 

21.5 

19.069 

25.5 

24.261 

29.5 

30.654 

17.6 

14.977 

21.6 

19.187 

25.6 

24.406 

29.6 

30.833 

17.7 

15.072 

21.7 

19.305 

25.7 

24.552 

29.7 

31.011 

17.8 

15.167 

21.8 

19.423 

25.8 

24.697 

29.8 

31.190 

17.9 

15.262 

21.9 

19.541 

21.9 

24.842 

29.9 

31.369 

TABLES. 


707 


°c. 

Tension. 

oc. 

Tension. 

oc. 

Tension. 

OC. 

Tension. 

m.  in. 

0 

m.  m. 

0 

m.  m. 

o 

m.  m. 

+30.0 

31.543 

+31.0 

33.405 

+32.0 

35.359 

+33.0 

37.410 

30.1 

31.729 

31.1 

33.596 

32.1 

35.559 

33.1 

37.621 

30.2 

31.911 

31.2 

33.787 

32.2 

35.760 

33.2 

37.832 

30.3 

32.094 

31.3 

33.980 

32.3 

35.962 

33.3 

38.045 

30.4 

32.278 

31.4 

34.174 

32.4 

36.165 

33.4 

38.258 

30.5 

32.463 

31.5 

34.368 

32.5 

36.370 

33.5 

38.473 

30.6 

32.6-30 

31.6 

34.564 

32.6 

36.576 

33.6 

38.689 

30.7 

32.337 

31.7 

34.761 

32.7 

36.783 

33.7 

38.906 

30.8 

33.026 

31.8 

34.959 

32.8 

36.991 

3:1.8 

39.124 

309 

33215 

31.9 

35.159 

32.9 

37.200 

33.9 

39.344 

34.0 

39.565 

34.3 

40.230 

31.6 

40.907 

34.9 

41.595 

34.1 

39.786 

34.4 

40.455 

34.7 

41.135 

35.0 

41.827 

34.2 

40.007 

34.5 

40.680 

34.8 

41.364 

TABLE    XI. 

TABLE  FOR  THE  CALCULATION  OF  THE  VALUE  OF  1  +  0.00366  t. 


t. 

Number. 

Log. 

t. 

Number. 

Log. 

o 
—2.0 

0.99268 

9.99681 

o 
0.0 

.00000 

0.00000 

1.9 

0.99305 

9.99697 

+0.1 

.00037 

0.00016 

1.8 

0.99341 

9.99713 

0.2 

.00073 

0.00032 

1.7 

0.99378 

9.99729 

0.3 

.00110 

0.00048 

1.6 

0.99414 

9.99745 

0.4 

.00146 

0.00063 

1.5 

0.99451 

9.99761 

0.5 

.00183 

0.00079 

1.4 

0.99488 

9.99777 

0.6 

.00220 

0.00095 

1.8 

0.99524 

9.99793 

0.7 

.00256 

0.00111 

1.2 

0.99561 

9.99809 

0.8 

.00293 

0.00127 

1.1 

0.99597 

9.99825 

0.9 

.00329 

0.00143 

1.0 

0.99634 

9.99841 

1.0 

.00366 

0.00159 

0.9 

0.99671 

9.99857 

1.1 

.00403 

0.00175 

0.8 

0.99707 

9.99873 

1.2 

.00439 

0.00191 

0.7 

0.99744 

9.99888 

1.3 

.00476 

0.00207 

0.6 

0.99780 

9.99904 

1.4 

.00512 

0.00222 

0.5 

0.99817 

9.99920 

1.5 

.00549 

0.00238 

0.4 

0.99854 

9.99937 

1.6 

.00586 

0.00254 

0.3 

0.99890 

9.99952 

1.7 

.00622 

0.00270 

0.2 

0.99927 

9.99968 

1.8 

.00659 

0.00285 

—0.1 

0.99963 

9.99984 

1.9 

.00695 

0.00301 

708 


TABLES. 


*. 

Number. 

Log. 

R 

Number. 

Log. 

o 
-4-2.0 

1.00732 

0.00317 

0 

H-6.0 

1.02196 

0.00943 

2.1 

1.00769 

0.00333 

6.1 

1.02233 

0.00959 

2.2 

1.00805 

0.00349 

6.2 

1.02269 

0.00975 

2.3 

1.00842 

0-00365 

6.3 

1.02306 

0.00991 

2.4 

1.00878 

0.00381 

6.4 

1.023-12 

0.01006 

2.5 

1.00915 

0.00397 

6.5 

1.02379 

0.01022 

2.6 

1.00952 

0.00412 

6.6 

1.02416 

0.01038 

2.7 

1.00988 

0.00428 

6.7 

1.02452 

0.01054 

2.8 

1.01025 

0.00444 

6.8 

1.02489 

0.01069 

2.9 

1.01061 

0.00459 

6.9 

1.02525 

0.01084 

3.0 

1.01098 

0.00474 

7.0 

1.02562 

0.01099 

3.1 

1.01135 

0.00490 

7.1 

1.02599 

0.01115 

3.2 

1.01171 

0.00506 

7.2 

1  .02635 

0.01131 

3.3 

1.01208 

0.00521 

7.3 

1.02672 

0.01147 

3.4 

1.01244 

0.00537 

7.4 

1.02708 

0.01162 

3.5 

1.01281 

0.00553 

7.5 

1.02745 

0.01177 

3.6 

1.01318 

0.00568 

7.6 

1.02782 

0.01193 

3.7 

1.01354 

0.00584 

7.7 

1.02818 

0.01208 

3.8 

1.01391 

0.00600 

7.8 

1.02855 

0.01223 

3.9 

1.01427 

0.00615 

7.9 

1.02891 

0.01238 

4.0 

1.01464 

0.00631 

8.0 

1  .02928 

0.01253 

4.1 

1.01501 

0.00647  * 

8.1 

1.02965 

0.01269 

4.2 

1.01537 

0.00663 

8.2 

1  .03001 

0.01284 

4.3 

1.01574 

0.00678 

8.3 

1.03038 

0.01300 

4.4 

1.01610 

0.00694 

8.4 

1.03074 

0.01315 

4.5 

1.01647 

0.00710 

8.5 

1.03111 

0.01330 

4.6 

1.01684 

0.00725 

8.6 

1.03148 

0.01346 

4.7 

1.01720 

0.00741 

8.7 

1.03184 

0.01361 

4.8 

1.01757 

0.00756 

8.8 

1.03221 

0.01377 

4.9 

1.01793 

0.00772 

8.9 

1.03257 

0.01S92 

5.0 

.01830 

0.00788 

9.0 

1.03294 

0.01407 

5.1 

1.01867 

0.00803 

9.1 

1.03331 

0.01423 

5.2 

.01903 

0.00819 

9.2 

1.03367 

0.01438 

5.3 

.01940 

0.00834 

9.3 

1.03404 

0.01454 

5.4 

.01976 

0  00850 

9.4 

1.03440 

0.01469 

5.5 

.02013 

0.00865 

9.5 

1.03477 

0.01484 

5.6 

.02050 

0.00881 

9.6 

1.03514 

0.01500 

5.7 

.02086 

Q.00896 

9.7 

1.03550 

0.01515 

5.8 

.02123 

0.00912 

9.8 

1.03587 

0.01530 

5.9 

1.02159 

0.00927 

9.9 

1.03623 

0.01545 

TABLES. 


709 


t. 

Number. 

Log. 

t. 

Number. 

Log. 

+10°.0 

1.03660 

0.01561 

o 
H-14.0 

1.05124 

0.02170 

10.1 

1.03697 

0.01577 

14.1 

1.05161 

0.02185 

10.2 

.03733 

0.01592 

14.2 

1.05197 

0.02200 

10.3 

.03770 

0.01607 

14.3 

1.05234 

0.02215 

10.4 

.03806 

0.01623 

14.4 

1.05270 

0.02230 

10.5 

.03843 

0.01639 

14.5 

1.05307 

0.02246 

10.6 

.03880 

0.01653 

14.6 

1.05344 

0.02261 

10.7 

.03916 

0.01669 

14.7 

1  05360 

0.02276 

10.8 

.03953 

0.01683 

14.8 

1.05417 

0.02291 

10.9 

.03989 

0.01698 

14.9 

1.05453 

0.02306 

11.0 

.04026 

0.01714 

15.0 

1.05490 

0.02321 

11.1 

.04063 

0.01729 

15.1 

1  .03527 

0.02336 

11.2 

.04099 

0.01744 

15.2 

1.05563 

0.02351 

11.3 

.04136 

0.01759 

15.3 

1.05600 

0.02366 

11.4 

.04172 

0.01775 

15.4 

1.05636 

0.02381 

11.5 

.04209 

0.01790 

15.5 

1.05673 

0.02396 

11.6 

.04246 

0.01805 

13.6 

1.05710 

0.02411 

11.7 

.04282 

0.01820 

15.7 

1.05746 

0.02426 

11.8 

.04319 

0.01836 

15.8 

1.05783 

0.02441 

11.9 

.04355 

0.01851 

15.9 

1.05819 

0.02456 

12.0 

1.04392 

0.01867 

16.0 

1.05856 

0.02471 

12.1 

1.04429 

0.01882 

16.1 

1.05893 

0.02486 

12.2 

1.04465 

0.01897 

16.2 

1.05929 

0.02501 

12.3 

1.04502 

0.01912 

16.3 

1.05966 

0.02516 

12.4 

1.04538 

0.01928 

16.4 

1.06002 

0.02531 

12.5 

1.04575 

0.01943 

16.5 

1.06039 

0.02546 

12.6 

1.04612 

0.01958 

16.6 

1.06076 

0.02561 

12.7 

1.04648 

0.01973 

16.7 

1.06112 

0.02576 

12.8 

1.04685 

0.01989 

16.8 

1.06149 

0.02591 

12.9 

1.04721 

0.02004 

16.9 

1.06185 

0.02606 

13.0 

1.04758 

0.02019 

17.0 

1.06222 

0.02621 

13.1 

1.04795 

0.02034 

17.1 

1.06259 

0.02636 

13.2 

1.04831 

0.02049 

17.2 

.06295 

0.02651 

13.3 

1.04868 

0.02064 

17.3 

.06332 

0.02666 

13.4 

1.04904 

0.02079 

17.4 

.06368 

0.02681 

13.5 

1.04941 

0.02095 

17.5 

.06405 

0.02696 

13.6 

1.04978 

0.02110 

17.6 

.06442 

0.02711 

13.7 

1.05014 

0.02125 

17.7 

.06478 

0.02726 

13.8 

1.05051 

0.02140 

17.8 

.06515 

0.02741 

13.9 

1.05037 

0.02155 

17.9 

.06551 

0.02756 

60 


710 


TABLES. 


t. 

Number. 

Log. 

t. 

Number. 

Log. 

4-18°.0 

1.06588 

0.02771 

o 
+22.0 

1.08052 

0.03363 

18.1 

1.06625 

0.02786 

22.1 

1.08089 

0.03378 

18.2 

1.06661 

0.02801 

22.2 

1.08125 

0.03393 

18.3 

1.06698 

0.02816 

22.3 

1.08162 

0.03408 

18.4 

1.06734 

0.02831 

22.4 

1.08198 

0.03422 

18.5 

1.06771 

0.02846 

22.5 

1.0S235 

0.03437 

18.6 

1.06808 

0.02861 

22.6 

1.08272 

0.03452 

18.7 

1.06844 

0.02876 

22.7 

1.08308 

0.03466 

18.8 

1.06881 

0.02891 

22.8 

1.08345 

0.03481 

18.9 

1.06917 

0.02906 

22.9 

1.08381 

0.03496 

19.0 

1.06954 

0.02921 

23.0 

1.08418 

0.03510 

19.1 

1.06991 

0.02936 

23.1 

1.08455 

0.03525 

19.2 

1.07027 

0.02951 

23.2 

1.08491 

0.03539 

19.3 

1.07064 

0.02965 

23.3 

1.08528 

0.03554 

19.4 

1.07100 

0.02980 

23.4 

1.08564 

0.03568 

19.5 

1.07137 

0.02995 

23.5 

1.08601 

0.03583 

19.6 

1.07174 

0.03009 

23.6 

1.0S638 

0.03598 

19.7 

1.07210 

0.03024 

23.7 

1.08674 

0.03612 

19.8 

1.07247 

0.03039 

23.8 

1.03711 

0.03627 

19.9 

1.07283 

0.03053 

23.9 

1.08747 

0.03642 

20.0 

1.07320 

0.03068 

24.0 

1.08784 

0.03656 

20.1 

1.07357 

0.03083 

24.1 

1.08821 

0.03671 

20.2 

1.07393 

0.03098 

24.2 

1.08857 

0.03685 

20.3 

1.07430 

0.03113 

24.3 

1.08894 

0.03700 

20.4 

1.07466 

0.03128 

24.4 

1.08930 

0.03714 

20.5 

1.07503 

0.03142 

24.5 

1.08967 

0.03729 

20.6 

1.07540 

0.03157 

24.6 

1.09004 

0.03744 

20.7 

1.07576 

0.03172 

24.7 

1.09040 

0.03758 

20.8 

1.07613 

0.03187 

24.8 

1.09077 

0.03772 

20.9 

1.07649 

0.03201 

24.9 

1.09113 

0.03787 

21.0 

1.07686 

0.03216 

25.0 

1.09150 

0.03802 

21.1 

.07723 

0.03231 

25.1 

1.09187 

0.03817 

21.2 

.07759 

0.03246 

25.2 

1.09223 

0.03831 

21.3 

.07796 

0.03261 

25.3 

1.09260 

0.03846 

21.4 

.07832 

0.03275 

25.4 

1.09296 

0.03860 

21.5 

.07869 

0.03290 

25.5 

1.09333 

0.03875 

21.6 

.07906 

0.03305 

25.6 

1.09370 

0.03889 

21.7 

.07942 

0.03320 

25.7 

1.09406 

0.03904 

21.8 

.07979 

0.03334 

25.8 

1.09443 

0.03918 

21.9 

.08015 

0.03349 

25.9 

1.09479 

0.03933 

TABLES. 


711 


t. 

Number. 

Log. 

t. 

Number. 

Log. 

o 
4-26.0 

1.09516 

0.03948 

o 
-K30.0 

1.10980 

0.04524 

26.1 

1.09553 

0.03963 

30.1 

1.11017 

0.04538 

26.2 

.09589 

0.03977 

30.2 

1.11053 

0.04552 

26.3 

.09626 

0.03992 

30.3 

1.11090 

0.04567 

26.4 

.09662 

0.04006 

30.4 

1.11126 

0.04581 

26.5 

.09699 

0.04021 

30.5 

1.11163 

0.04595 

26.6 

.09736 

0.04035 

30.6 

1.11200 

0.04610 

26.7 

.09772 

0.01050 

30.7 

1  11236 

0.04624 

26.8 

.09809 

0.04064 

30.8 

1.11273 

0.04638 

26.9 

1.09845 

0.04079 

30.9 

1.11309 

0.04653 

27.0 

1.09882 

0.04093 

31.0 

1.11346 

0.04667 

27.1 

1.09919 

0.04107 

31.1 

1.11383 

0.04681 

27.2 

1.09955 

0.04122 

31.2 

1.11419 

0.04695 

27.3 

1.09992 

0.04136 

31.3 

1.11456 

0.04710 

27.4 

1.10023 

0.04150 

31.4 

1.11492 

0.04724 

27.5 

1.10065 

0.04165 

31.5 

1.11529 

0.04738 

27.6 

1.10102 

0.04179 

31.6 

1.11566 

0.04753 

27.7 

1.10138 

0.04193 

31.7 

1.11602 

0.04767 

27.8 

1.10175 

0.04208 

31.8 

1.11639 

0.04781 

27.9 

1.10211 

0.04222 

31.9 

1.11675 

0.04796 

28.0 

1.10248 

0.04237 

32.0 

1.11712 

0.04810 

28.1 

1.10285 

0.04251 

32.1 

1.11749 

0.04824 

23.2 

1.10321 

0.04266 

32.2 

1.11785 

0.04838 

23.a 

1.10358 

0.04280 

32.3 

1.11822 

0.04852 

28.4 

1.10394 

0.04295 

32.4 

1.11858 

0.04866 

28.5 

1.10431 

0.04309 

32.5 

1.11895 

0.04S81 

28.6 

1.10468 

0.04323 

32.6 

1.11932 

0.04895 

28.7 

1.10504 

0.04338 

32.7 

1.119H8 

0.04909 

28.8 

1.10541 

0.04352 

32.8 

1.12005 

0.04923 

2S.9 

1.10577 

0.04367 

32.9 

1.12041 

0.04938 

29.0 

1.10614 

0.04381 

33.0 

1.12078 

0.04952 

29.1 

1.10651 

0.04395 

33.1 

1.12115 

0.04966 

29.2 

1.10687 

0.04410 

33.2 

1.12151 

0.04980 

29.3 

1.10724 

0.04424 

33.3 

1.12138 

0.04994 

29.4 

1.10760 

00143S 

33.4 

1.12224 

0.05008 

29.5 

1.10797 

0.04453 

33.5 

1.12261 

0.05022 

29.6 

1.10334 

0.04467 

33.6 

1.12298 

0.05036 

29.7 

1.10870 

0.04482 

33.7 

1.12334 

0.05050 

29.8 

1.10907 

0.01196 

33.8 

1.12371 

0.05065 

29.9 

1.10943 

0.04510 

33.9 

1.12407 

0.05079 

712 


TABLES. 


t. 

Number. 

Log. 

t. 

Number. 

Log. 

o 
+34.0 

.12444 

0.05094 

o 
-1-37.0 

.13542 

0.05516 

34.1 

.12481 

0.05108 

37.1 

.13579 

0.05530 

34.2 

.12517 

0.05122 

37.2 

.13615 

0.05544 

34.3 

.12554 

0.05136 

37.3 

.13652 

0.05558 

34.4 

.12590 

0.05150 

37.4 

.13688 

0.05572 

34.5 

.12627 

0.05164 

37.5 

.13725 

0.05585 

34,6 

.12664 

0.05178 

37.6 

.13762 

0.05599 

34.7 

.12700 

0.05193 

37.7 

.13798 

0.05613 

34.8 

.12737 

0.05207 

37.8 

.13835 

0.05627 

34.9 

1.12773 

0.05221 

37.9 

.13871 

0.05641 

35.0 

1  12810 

0.05235 

38.0 

.13908 

0.05655 

351 

1-12847 

0.05249 

38.1 

.13945 

0.05669 

35.2 

1.12883 

0.05263 

38.2 

.13981 

0.05683 

35.3 

1  12920 

0.05277 

38.3 

.14018 

0.05697 

35.4 

1.12956 

0.05291 

38.4 

.14054 

0.05711 

35.5 

1.12993 

0.05305 

38.5 

.14091 

0.05725 

35.6 

1.13030 

0.05319 

88.6 

.14128 

0.05739 

35.7 

1.13066 

0.05333 

38.7 

.14164 

OX)5753 

35.8 

1.13103 

0.05347 

38.8 

.14201 

0.05767 

35.9 

1.13139 

0.05361 

38.9 

.14237 

0.05781 

36.0 

1.13176 

0.03375 

39.0 

1.14274 

0.05795 

36.1 

1.13213 

0.05389 

39.1 

1.14311 

0.05809 

36.2 

1.13249 

0.05403 

39.2 

1.14347 

0.05823 

36.3 

1.13286 

0.05417 

39.3 

1.14384 

0.05837 

36.4 

1.13322 

0.05431 

39.4 

1.14420 

0.05850 

36.5 

1.13359 

0.05446 

39.5 

1.14457 

0.05864 

36.6 

1.13396 

0.05460 

39.6 

1.14494 

0.05878 

36.7 

1.13432 

0.05474 

39.7 

1.14530 

0.05892 

36.8 

1.13469 

0.05488 

39.8 

1.14567 

0.05905 

36.9 

1.13505 

0.05502 

39.9 

1.14603 

0.05919 

40 

1.14640 

0.05934 

50 

1.18300 

0.07298 

41 

1.15006 

0.06072 

51 

1.18666 

0.07433 

42 

1.15372 

0.06210 

52 

1.19032 

0.07566 

43 

.15738 

0.06318 

53 

1.19398 

0.07700 

44 

.16104 

0.06485 

54 

1.19764 

0.07833 

45 

.16470 

0.06621 

55 

1.20130 

0.07965 

46 

.16836 

0.06758 

56 

1.20496 

0.08097 

47 

.17202 

0.06893 

57 

1.20862 

0.08229 

48 

1.17568 

0.07029 

58 

1.21228 

0.08360 

49 

1.17934 

0.07164 

59 

1.21594 

0.08491 

TABLES. 


713 


TABLE    XII. 

TABLE  FOR  THE   CALCULATION  OF  THE   VALUE   OF  1  +  0.00367  t. 


t. 

log. 

Diff. 

t. 

lof. 

Diff. 

t. 

log. 

Diff. 

60 

0.08643 

131 

100 

0.13577 

117 

140 

0.18007 

105 

61 

0.03772 

131 

101 

0.13693 

116 

141 

0.18112 

105 

62 

0.08903 

131 

102 

0.13809 

116 

142 

O.J82I7 

105 

63 

0.09033 

130 

103 

0.13925 

116 

143 

0.1S322 

105 

64 

0.09162 

129 

104 

0.14011 

116 

144 

0.18426 

104 

65 

0.09291 

129 

105 

0.1415G 

115 

115 

0.18530 

104 

66 

0.09120 

129 

106 

0.14271 

115 

116 

0.18634 

104 

67 

0.09518 

123 

107 

0.14385 

114 

147 

0.18738 

104 

68 

0.09676 

128 

108 

0.14499 

114 

148 

0.18841 

103 

69 

0.09803 

127 

109 

0.14613 

114 

149 

0.18944 

103 

70 

0.09930 

127 

110 

0.14727 

114 

150 

0.19017 

103 

71 

0.10057 

127 

111 

0.14841 

114 

151 

0.19150 

102 

72 

0.10183 

126 

112 

0.14954 

113 

152 

0.19252 

102 

73 

0.10309 

126 

113 

0.15067 

113 

153 

0.19354 

102 

74 

0.10434 

125 

114 

0.15179 

112 

154 

0.19456 

102 

75 

0.10559 

125 

115 

0.15291 

112 

155 

0.19558 

102 

76 

0.10684 

125 

116 

0.15103 

112 

156 

0.19fi60 

102 

77 

0.10309 

125 

117 

0.15515 

112 

157 

0.19761 

101 

73 

0.10933 

124 

118 

0.15626 

111 

158 

0.19862 

101 

79 

0.11057 

124 

119 

0.15737 

111 

159 

0.19963 

101 

60 

0.11180 

123 

120 

0.15S48 

111 

160 

0.20063 

100 

81 

0.11303 

123 

121 

0.15959 

111 

161 

0.20163 

100 

82 

0.11426 

123 

122 

0.160K9 

110 

162 

0.20263 

100 

83 

0.11548 

122 

123 

0.16179 

110 

163 

0.20363 

100 

84 

0.11670 

122 

124 

0.16289 

110 

164 

0.20463 

100 

85 

0.11792 

122 

125 

0.16398 

109 

165 

0.20562 

99 

86 

0.11913 

121 

126 

0.16507 

109 

166 

0.20661 

99 

87 

0.12034 

121 

127 

0.16616 

109 

167 

0.20760 

99 

88 

0.12155 

121 

128 

0.16725 

109 

163 

0.20859 

99 

89 

0.12275 

120 

129 

0.16833 

108 

169 

0.20958 

99 

90 

0.12395 

120 

130 

0.16941 

108 

170 

0.21056 

93 

91 

0.12515 

120 

131 

0.17049 

108 

171 

0.21154 

93 

92 

0.12634 

,.119 

132 

0.17156 

107 

172 

0.21252 

98 

93 

0.12753 

119 

133 

0.17263 

107 

173 

0.21350 

98 

94 

0.12872 

119 

134 

0.17370 

107 

174 

0.21417 

97 

95 

0.12990 

118 

135 

0.17477 

107 

175 

0.21544 

97 

96 

0.13108 

118 

136 

0.17584 

107 

176 

0.21611 

97 

97 

0.13226 

118 

137 

0.17690 

106 

177 

0.21738 

97 

98 

0.13343 

117 

138 

0.17796 

106 

173 

0.21834 

9G 

99 

0.13460 

117 

139 

0.17902 

106 

179 

0.21930 

96 

60' 


714 


TABLES. 


t. 

log. 

Diff. 

t. 

log. 

Diff. 

t. 

log. 

i 
Diff. 

180 

0.22026 

96 

220 

0.25705 

88 

260 

0.29027 

82 

181 

0.22122 

96 

221 

0.25793 

88 

261 

0.29178 

81  ! 

182 

0.22218 

96 

222 

0.25881 

88 

262 

0.29260 

82 

183 

0.22314 

96 

223 

0.25969 

88 

263 

0/29341 

81 

184 

0.22  109 

95 

224 

0.26057 

88 

264 

0.29-122 

81 

185 

0.22504 

95 

225 

0.26144 

87 

265 

0.29:03 

81 

186 

0.22599 

95 

226 

0.26231 

87 

266 

0.29584 

81 

187 

0.22H93 

94 

227 

0.26318 

87 

267 

0.29664 

80 

188 

0.227S7 

94 

228 

0.26405 

87 

268 

0.29745 

81 

189 

0.22882 

95 

229 

0.26492 

87 

269 

0.29825 

80 

190 

0.22976 

94 

230 

0.26578 

86 

270 

0.29905 

80 

191 

0.23070 

94 

231 

0.26665 

87 

271 

0.29985 

80 

192 

0.23163 

93 

232 

0.26751 

86 

272 

0.30064 

79 

193 

0.23257 

94 

233 

0.26837 

86 

273 

0.30144 

80 

194 

0.23350 

93 

234 

0.26922 

85 

274 

0.30224 

80 

195 

0.23143 

93 

235 

0.27008 

86 

275 

0.30303 

79 

196 

0.23536 

93 

236 

0.27094 

86 

276 

0.30383 

80 

197 

0.23628 

92 

237 

0.27179 

85 

277 

0.30462 

79 

193 

0.23721 

93 

238 

0.27264 

85 

278 

0.30541 

79 

199 

0.23813 

92 

239 

0.27349 

85 

279 

0.30620 

79 

200 

0.23905 

92 

240 

0.27434 

85 

280 

0.30698 

78 

201 

0.23997 

91 

241 

0.27519 

85 

281 

0.30776 

78 

202 

0.24088 

92 

212 

0.27603 

84 

282 

0.30855 

79 

203 

0.2(180 

91 

243 

0.27688 

85 

283 

0.30933 

78 

204 

0.24271 

91 

244 

0.27772 

84 

284 

0.31011 

78 

205 

0.24362 

91 

245 

0.27856 

84 

285 

0.31089 

78 

206 

0.24153 

91 

216 

0.27910 

84 

2S6 

0.31167 

78 

207 

0.24544 

90 

247 

0.28023 

83 

287 

0.31245 

78 

208 

0.24634 

92 

248 

0.28107 

84 

288 

0.31323 

78 

209 

0.24724 

90 

249 

0.28190 

83 

289 

0.31400 

77 

210 

0.24814 

90 

250 

0.28274 

84 

290 

0.31477 

77 

211 

0.24904 

90 

251 

0.28357 

83 

291 

0.31554 

77 

212 

0.24994 

90 

252 

0.28439 

82 

292 

0.31631 

77 

213 

0.25084 

90 

253 

0.28522 

83 

293 

0.31708 

77 

214 

0.25173 

89 

254 

0.28605 

83 

294 

0.31785 

77 

215 

0.25262 

89 

255 

0.28687 

82 

295 

0.31862 

77 

216 

0.25351 

89 

256 

0.28769 

82 

296 

0.31938 

76 

217 

0.25440 

89 

257 

0.28851 

82 

297 

0.32014 

76 

213 

0.25529 

89 

258 

0.28933 

82 

298 

0.32091 

77 

219 

0.25617 

88 

259 

0.29015 

82 

299 

0.32167 

76 

TABLES. 


715 


TABLE    XIII. 

Expansion  of  Glass. 
TABLE  FOR   THE    CALCULATION  OF  THE  VALUE  OF   l+K(f  —  t). 


t'—t. 

log. 

Diff. 

t'  —  t. 

l«g. 

Diff. 

100° 

0.00117 

200 

0.00234 

12 

110 

0.00129 

12 

210 

0.00216 

12 

120 

0.00140 

11 

220 

0.00257 

11 

130 

0.00152 

12 

230 

0.00269 

12 

140 

0.00164 

12 

240 

0.00281 

12 

150 

0.00176 

12 

250 

0.00293 

12 

160 

0.00187 

11 

260 

0.00304 

11 

170 

0.00199 

12 

270 

0.00316 

12 

180 

0.00211 

12 

280 

0.00328 

12 

190 

0.00222 

11 

290 

0.00339 

11 

TABLE    XIV. 

TABLE  FOR  THE  CALCULATION  OF  THE  WEIGHT  OF  ONE  CUBIC 
CENTIMETRE    OF   AIR. 

Weight  at  0°  =  0.0012932.  HQ  =  76  c.  m. 


t. 

log. 

Ditt 

t. 

log. 

Diff. 

0 

0 

7.11166 

0 

15 

7.08739 

151 

1 

7.11007 

159 

16 

7.08688 

151 

2 

7.10848 

159 

17 

7.08538 

150 

3 

7.10690 

158 

18 

7.08388 

150 

4 

7.10333 

157 

19 

7.09239 

149 

5 

7.10376 

157 

20 

7.08090 

149 

6 

7.10220 

156 

21 

7.07942 

148 

7 

7.10064 

156 

22 

7.07794 

148 

8 

7.09909 

155 

23 

7.07647 

147 

9 

7.09755 

154 

24 

7.07500 

147 

10 

7.09601 

154 

25 

7.07354 

146 

11 

7.09447 

154 

26 

7.07208 

146 

12 

7.09294 

153 

27 

7.07063 

145 

13 

7.09142 

152 

28 

7.06918 

145 

14 

7.08990 

152 

29 

7.06774 

144 

The  following  corrections  must  be  added  to  the  above  logarithms  when  the  barometer 
stands  higher  than  76  c.  m.,  and  subtracted  from   them  when  it  stands  lower.     The 
correction  for  tenths  and  hundredths  of  centimetres  is  found  by  moving  the  decimal 
point  one  or  two  figures  to  the  left. 
Diff.  in  c.  m.  Corr.  Diff.  in  c.  m.  Corr.  Diff.  in  c.  m.  Coir. 


0.0057 
0.0114 
0.0171 


0.0228 
0.0285 
0.0342 


0.0399 
0.0456 
0.0313 


716 


TABLES. 


TABLE    XV. 

EXPANSION    OF    SOLIDS. 


Interval  of 

Amount  of  Expansion. 

Nnii  16  of  Substuncc. 

Temperature. 

Decimal  Fractions. 

Vulgar  Fract. 

Linear  Expansion  determined  by  Lavoisier  and  Laplace. 

English  Flint-Glass, 

0°  to  100° 

0.00081166 

T*W 

Glass  tube  (without  lead), 

«    «      « 

0.00087572 

T&fS 

Steel  (not  hardened),     . 

ti    tt      (t 

0.00107880 

¥^T 

Steel  (hardened), 

a    «      « 

0.00123956 

FffT 

Soft  Iron,       .... 

a    «      it 

0.00122045 

wi» 

Gold  

«    «      « 

0.00146606 

i 

Copper,          .        .        ... 

a    a      <t  -    '« 

0.00171220 

3"  81" 

Brass,          .... 

«    «      « 

0.00186760 

vfe 

Silver             .... 

(C        tt           (( 

0.00190868 

5k 

Tin,   

({     ft        11 

0.00193765 

5T^ 

Lead      

ft       tf 

C\  AAOC  fC9£? 

1 

ty  Dulong  and  Petit 

U.UU^o4ooO 

rifT 

Platinum,       . 

CO0  to   100° 

0.00088420 

nVr 

|  0     to  300 

0.00275482 

-g-^-j 

Glass,          .... 

(o   to  100 

•<0     to  200 

0.00086133 
0.00184502 

TT^T 

¥5"¥ 

(o     to  300 

0.00303252 

^J-^. 

Iron,       

(  0     to  100 

0.00118210 

^ 

j  0     to  300 

0.00440528 

S"vT 

Copper,      .... 

f  0     to  100 
(0     to  300 

0.00171820 
0.00564972 

s 

By  Wollaston. 

Palladium,     .... 

0°  to  100° 

0.00100000       1       T<y\nr 

By  Brunner.  —  Expansion  for  one  Degree. 

Ice,        .        *  .       • 

—6°  to  0° 

0.0000375         |        -rfy 

Cubic  Expansion  determined  by  Kopp 


Substance. 

Formula.  ^E^n. 

Substance. 

Formula. 

Cub.Expan. 
for  1°  C. 

Copper, 

Cu 

0.000051 

Fluor-spar, 

CaF 

0.000062 

Lead, 

Pb 

0.000089 

Aragonite, 

CaO,  C02 

0.000065 

Tin, 

Sn 

0.000069 

Calc-spar, 

CaO,  COa 

0.000018 

Iron, 
Zinc, 

Fe 
Zn 

0.000037 
0.000089 

Bitter-spar, 

(        CaO,  COa      ) 
}   -l-MgO,  C0«      J 

0.000035 

Cadmium, 
Bismuth, 

Cd 
Bi 

0.000094 
0.000040 

Iron-spar, 

jFe(Mn,Mg)0,  i 
1            COa            f 

0.000035 

Antimony, 

Sb 

0.000033 

Heavy-spar, 

BaO,  SO3 

0.000058 

Sulphur, 

s 

0.000183 

Celestine, 

SrO,  SO3 

0.000061 

Galena, 
Zinc-blende, 

PbS 
ZnS 

0.000068 
0.000036 

Quartz, 

Si03           | 

0.000042 
0.000039 

Iron  pyrites, 
Rutilc, 

FeSa 

TiO> 

0.000034 
0.000032 

Orthoclase, 

(       KO,  SiOs       { 
\  +Al,03,3Si03( 

0.000026 
0.000017 

Tin  stone, 

Sn02 

0.000016 

Soft  soda  glass, 

0000026 

Iron-s.:  lance, 

Fea03 

0.000040 

Another  sort, 

. 

O.OU0024 

Magnetic  iron 

Hard    potash- 

I 

ore, 

FesO4 

0.000029 

glass, 

.     1  0.000021 

TABLES. 


717 


TABLE    XYI. 

VOLUME  AND  DENSITY  OF  WATER.  —  BY  KOPP. 


Tempera- 
ture. 

Volume  of  Water 
(atO°  =  l). 

Sp.  Gr.  of  Water 
(at  0°  =-  1). 

Volume  of  Water 
(at4°  =  l). 

Sp.  Gr.  of  Water 

(at  4°  =  1). 

0 

0 

1.00000 

.000000 

.00012 

0.999877 

1 

0.99995 

.000053 

.00007 

0.999930 

2 

0.99991 

.000092 

.00003 

0.999969 

3 

0.99989 

.000115 

.00001 

0.999992 

4 

0.99988 

.000123 

.00000 

1.000000 

5 

0.99988 

.000117 

.00001 

0.999994 

6 

0.99990 

.000097 

.00003 

0.999973 

7 

0.99994 

.000062 

.00006 

0.999939 

8 

0.99999 

.000014 

.00011 

0.999890 

9 

1.00005 

0.999952 

.00017 

0.999329 

10 

1.00012 

0.999876 

.00025 

0.999753 

f    11 

.00021 

0.999785 

.00034 

0.999664 

12 

.00031 

0.999636 

.00044 

0.999562 

13 

.00043 

0.999572 

.00055 

0.999449 

14 

.00036 

0.999445 

.00068 

0.999322 

15 

.00070 

0.999306 

.00082 

0.999183 

16 

.00085 

0.999155 

.00097 

0.999032 

17 

.00101 

0.998992 

.00113 

0.998869 

18 

.00113 

0.993817 

.00131 

0.998695 

19 

.00137 

0.998631 

.00149 

0.99S509 

20 

.00157 

0.998435 

.00169 

0.998312 

21 

.00178 

0.998228 

.00190 

0.998104 

22 

.00200 

0.998010 

.00212 

0.997886 

23 

.00223 

0.997780 

.00235 

0.997657 

24 

.00247 

0.997541 

.00259 

0.997419 

25 

.00271 

0.997293 

.00284 

0.997170 

26 

.00295 

0.997035 

.00310 

0.996912 

27 

.00319 

0.996767 

.00337 

0.996644 

28 

.00347 

0.996489 

.00365 

0.996367 

29 

.00376 

0.996202 

.00393 

0.996082 

30 

.00406 

0.995908 

.00423 

0.995787 

35 

.00570 

40 

.00753 

45 

.00954 

50 

.01177 

55 

.014,10 

60 

.01659 

65 

.01930 

70 

.02225 

75 

.02541 

80 

.02858 

• 

85 

1.03189 

90 

1.03540 

95 

1.03909 

100 

1.04299 

718 


TABLES. 


TABLE     XVII. 

FOR  CONVERTING  DEGREES   OF  THE   CENTIGRADE   THERMOME- 
TER INTO  DEGREES   OF  FAHRENHEIT'S   SCALE. 


Gent. 

Fahr. 

Cent. 

Fahr. 

Cent. 

Fahr. 

Cent. 

Fahr. 

Cent. 

Fahr. 

—100° 

—  14S.O 

—58 

—  72°.4 

0 

—16 

4-3.2 

4-26 

4-78°.8 

+68 

4-154°.4 

99 

146.2 

57 

70.6 

15 

5.0 

27 

80.6 

66 

156.2 

98 

144.4 

56 

68.8 

14 

6.8 

28 

82.4 

70 

158.0 

97 

142.6 

55 

67.0 

13 

8.6 

29 

84.2 

71 

159.8 

96 

140.3 

54 

65.2 

12 

10.4 

30 

86.0 

72 

161.6 

95 

139.0 

53 

63.4 

11 

12.2 

31 

87.8 

73 

163.4 

94 

137.2 

52 

61.6 

10 

14.0 

32 

89.6 

74 

165.2 

93 

135.4 

51 

59.8 

9 

15.8 

33 

91.4 

75 

167.0 

92 

133.6 

50 

58.0 

8 

17.6 

34 

93.2 

76 

168.8 

91 

131.8 

49 

56.2 

7 

19.4 

35 

95.0 

77 

170.6 

90 

130.0 

48 

51.4 

6 

21.2 

36 

96.8 

78 

172.4 

89 

12S.2 

47 

52.6 

5 

23.0 

37 

98.6 

79 

174.2 

88 

126.4 

46 

50.8 

4 

24.8 

38 

100.4 

80 

176.0 

87 

124.6 

45 

49.0 

3 

26.6 

39 

102.2 

81 

177.8 

86 

122.8 

44 

47.2 

2 

28.4 

40 

104.0 

82 

179.6 

85 

121.0 

43 

45.4 

—  1 

30.2 

41 

105.8 

83 

181.4 

84 

119.2 

42 

43.6 

0 

32.0 

42 

107.6 

84 

183.2 

83 

117.4 

41 

41.8 

+  I 

33.8 

43 

109.4 

85 

185.0 

82 

115.6 

40 

40.0 

2 

35.6 

44 

111.2 

86 

1868 

81 

113.8 

39 

38.2 

3 

37.4 

45 

113.0 

87 

188.6 

80 

112.0 

38 

36.4 

4 

39.2 

46 

114.8 

88 

190.4 

79 

110.2 

37 

34.6 

5 

41.0 

47 

116.6 

89 

192.2 

78 

108.4 

36 

32.8 

6 

42.8 

48 

118.4 

90 

194.0 

77 

106.6 

35 

31.0 

7 

44.6 

49 

120.2 

91 

195.8 

76 

104.8 

34 

29.2 

8 

46.4 

50 

122.0 

92 

197.6 

75 

103.0 

33 

27.4 

9 

48.2 

51 

123.8 

93 

199.4 

74 

101.2 

32 

25.6 

10 

50.0 

52 

125.6 

94 

201.2 

73 

99.4 

31 

23.8 

11 

51.8 

53 

127.4 

95 

203.0 

72 

97.6 

30 

22.0 

12 

53.6 

54 

129.2 

96 

204.8 

71 

95.8 

29 

20.2 

13 

55.4 

55 

131.0 

97 

206.6 

70 

94.0 

28 

18.4 

14 

57.2 

56 

132.8 

98 

208.4 

69 

92.2 

27 

16.6 

15 

59.0 

57 

134.6 

99 

210.2 

68 

90.4 

26 

14.8 

16 

60.8 

58 

136.4 

100 

212.0 

67 

88.6 

25 

13.0 

17 

62.6 

59 

138.2 

101 

213.8 

66 

86.8 

24 

11.2 

18 

64.4 

60 

140.0 

102 

215.6 

65 

85.0 

23 

9.4 

19 

66.2 

61 

141.8 

103 

217.4 

64 

83.2 

22 

7.6 

20 

68.0 

62 

143.6 

104 

219.2 

63 

81.4 

21 

5.8 

21 

69.8 

63 

145.4 

105 

221.0 

62 

79.6 

20 

4.0 

22 

71.6 

64 

147.2 

106 

222.8 

61 

77.8 

19 

2.2 

23 

73.4 

65 

149.0 

107 

224.6 

60 

76.0 

18 

—0.4 

24 

75.2 

66 

150.8 

108 

226.4 

59 

74.2 

17 

4-1.4 

25 

77.0 

67 

152.6 

109 

228.2 

TABLES. 


719 


Cent. 

Fahr. 

Cent. 

Fahr. 

Cent. 

Fahr. 

Cent. 

Fahr. 

Cent. 

Fahr. 

0 

0 

0 

0 

0 

0 

o 

0 

0 

o 

+  110 

+230.0 

+  158 

+316.4 

+206 

+402.8 

+254 

+489.2 

+302 

+575.6 

111 

231.8 

159 

318.2 

207 

404.6 

255 

491.0 

303 

577.4 

112 

233.6 

160 

320.0 

208 

406.4 

256 

492.8 

304 

579.2 

113 

235.4 

161 

321.8 

209 

408.2 

257 

494.6 

305 

581.0 

114 

237.2 

162 

323.6 

210 

410.0 

258 

496.4 

306 

582.8 

115 

239.0 

163 

325.4 

211 

411.8 

259 

498.2 

307 

584.6 

116 

240.8 

164 

327.2 

212 

413.6 

260 

500.0 

308 

586.4 

117 

242.6 

165 

329.0 

213 

415.4 

261 

501.8 

309 

588.2 

118 

244.4 

166 

330.8 

214 

417.2 

262 

503.6 

310 

590.0 

119 

246.2 

167 

332.6 

215 

419.0 

263 

505.4 

311 

591.8 

120 

248.0 

168 

334.4 

216 

420.8 

264 

507.2 

312 

593.6 

121 

249.8 

169 

336.2 

217 

422.6 

265 

509.0 

313 

595.4 

122 

251.6 

170 

338.0 

218 

424.4 

266 

510.8 

314 

597.2 

123 

253.4 

171 

339.8 

219 

426.2 

267 

512.6 

315 

599.0 

124 

255.2 

172 

341.6 

220 

428.0 

268 

514.4 

316 

600.8 

125 

257.0 

173 

343.4 

221 

429.8 

269 

516.2 

317 

602.6 

126 

258.8 

174 

345.2 

222 

431.6 

270 

518.0 

318 

604.4 

127 

260.6 

175 

347.0 

223 

433.4 

271 

519.8 

319 

606.2 

128 

262.4 

176 

348.8 

224 

435.2 

272 

521.6 

320 

608.0 

129 

264.2 

177 

350.6 

225 

437.0 

273 

523.4 

321 

609.8 

130 

266.0 

178 

352.4 

226 

438.8 

274 

525.2 

322 

611.6 

131 

267.8 

179 

354.2 

227 

440.6 

275 

5270 

323 

613.4 

132 

269.6 

180 

356.0 

228 

442.4 

276 

528.8 

324 

615.2 

133 

271.4 

181 

357.8 

229 

444.2 

277 

530.6 

325 

617.0 

134 

273.2 

182 

359.6 

230 

446.0 

278 

532.4 

326 

618.8 

135 

275.0 

183 

361.4 

231 

447.8 

279 

534.2 

327 

620.6 

136 

276.8 

184 

363.2 

232 

449.6 

280 

536.0 

328 

622.4 

137 

278.6 

185 

365.0 

233 

451.4 

281 

537.8 

329 

624.2 

138 

280.4 

186 

366.8 

234 

453.2 

282 

539.6 

330 

626.0 

139 

282.2 

187 

368.6 

235 

455.0 

283 

541.4 

331 

627.8 

140 

284.0 

188 

370.4 

236 

456.8 

284 

543.2 

332 

629.6 

141 

285.8 

189 

372.2 

237 

458.6 

285 

545.0 

333 

631.4 

142 

287.6 

190 

374.0 

238 

460.4 

286 

546.8 

334 

633.2 

143 

289.4 

191 

375.8 

239 

462.2 

287 

548.6 

335 

635.0 

144 

291.2 

192 

377.6 

240 

464.0 

288 

550.4 

336 

636.8 

145 

293.0 

193   379.4 

241 

465.8 

289 

552.2 

337 

638.6 

146 

294.8 

194   381.2 

242 

467.6 

290 

554.0 

338 

640.4 

147 

296.6 

195  1  383.0 

243 

469.4 

291 

555.8 

339 

642.2 

148 

298.4 

196   384.8 

244 

471.2 

292 

557.6 

340 

644.0 

149 

300.2 

197   386.6 

245 

473.0 

293 

559.4 

341 

645.8 

150 

302.0 

198   388.4 

246 

474.8 

294 

561.2 

342 

647.6 

151 

303.8 

199   390.2 

247 

476  6 

295 

563.0 

343 

649.4 

152 

305.6 

200   392.0 

218 

478.4 

296 

564.8 

344 

651.2 

153 

307.4 

201   393.8 

249 

480.2 

297 

566.6 

345 

653.0 

154, 

309.2 

202   395.6 

250 

482.0 

298 

568.4 

346 

654.8 

165 

311.0 

203   397.4 

251 

483.8 

299 

570.2 

347 

606.6 

156 

312.8 

204   399.2 

252 

485.6 

300 

572.0 

348 

658.4 

157 

314.6 

205   401.0 

253 

487.4 

301 

573.8 

349 

660.2 

720 


TABLES. 


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ffi  giMCOCOCOCOCOCOCOCOCO  COCOeO-Tt-fT-TTT  "*     -* 

J    ^OOOOOOOOOO  OOOOOOOOOO  00 

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B  

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l^J(       *Z  t^  ^O"-^i— lC<IC*icOCO"*'*flO  lOCOCOt^t'-QOOOCiCiO  61^ 

rH  \~\        c?  ^o  10  10  10  in  in  in  in  in  in  in  in  in  in  in  in  in  o  in  co  co  co 

p 
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^?  1  d'~f~'<-f-1<"*"*"1'-1<^'1<  1">O»OiOlOiOlOlOlOiO  l« 

.^•Kj  g  "OOOOOOOOOO  OOOOOOOOOO  O 

P^H    £   ^oooooooooo  oooooooooo  q 

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si 

CO  <NOOit»CO»OCO(MO 

aoS3S333S§§  lil 111 I 1 " 

PR    3   c0.0.0.0.0.0.0.®0.0.  0.0.0.P,°.9^® 

O        6666666666  6666666666  66 

O 

S    ..   a^^^^'^^^oio©  »o©ioqioqioqioq  ^P, 

6666666666  6666666666  66 

22222°°°oo  ooooooooo©  oo 

.RRR^^^oqq  ©qoqqqqqqq  oq 

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g»O©lO©»O©lO©iO©  !O©lf5©»O©lO©»O©  »O© 

•  ©'H^oioieoeorfTrio  iococot*>t*>o6oDO5o*»6  ©i^ 


TABLES. 


721 


CO  rH    Oi     t**     lO     ~t     CM    ©     X 

CO  T}«-T»OCCl-^35Ci 


©qqqqqqq   qqqcqqqqqq   qqqqqoqqqo 
dddddodd   dddododddd   dddddodddd 


OX*^CO-fCOi-i©          CO     - 
COX»Or-<^CO-r  T1?^? 


>-i©x*^io-tCMi-i 
to  to  <e  IN.  ce  o>  ©  M 

CO      —     COCOCCCOI^t^ 

©qqqqqqq   qqqqqoqqqo   qqoqqqcooo 
©ddddddd   dddododddd   dooddddddd 


lO-tCO     —     OXt^lO  T     CM     i-i 

y     Si    O    O     f*     Cvl  CC     ~r     i1**     CO     s£ 

o   o   «o        inoioioiooiocococo        co   co   co    _    co   co   cc    co    i^- 


iftovoq»oq*oq 

cci^t^coxoisid 
coxxxxxxss 


»O©»O©»O©iO©iO© 


»O©iO©iO©lO©lO© 


VS     —     Sit^'On     —     Ci  t"»OJO~O3t*CO-f'N©  XCO-^OTOCOCO-f'M© 

SOO     —     <MCO-T-r  iftCOt^TOXCr.     O     —     <NCO  CO-TlOCO«-4--'XSiO     — 

r.  00  =  0000   ©ooooo^«  —  —   —_,-  -  ,~  —  ^  ^  ^  ^ 


qqoqooqq 
©ddddddd 


qqqqqqqqqq 
©ddddddd©© 


qqqqqqqqqq 
dddddodddd 


CM     —     SiXCOlOCOSM  « 

lOCOCOI^-GCSiO-N  CM 

©0    =    OOO^rH          ^ 


lOCOCMOSit^COiOCO 

i-ideo    —   ^f'ocor-oo 

OJ     CM     C*l    CM     OJ     CM     *^     OI     TJ 


qqqqqqqq 
©ddddddd 


q  qqqqqqqq© 
©ddddddd©© 


qoqcocqqqq 
©dddodddd© 


io©>o©»o©if5q       io©io©ioq 
S  co   S   co   co   s 


q  10  © 


10  q  10  q  10  q  »o  q  10  q 

:  >*  -t  10 


l-»  lO  CO  -*  Si  ^  CO 

O  O  ^  CM  CM  CO  T 


©  X  CO  — 


e»i©xco  -t  01  ©   x   »^   «o   eo   —  si»^ 

_____   o    -•   —   c*l  co    i*   10    '^   co    t»   x   ss   s:   o 

Ooooo©   ©0000=0  =  0©  00  =  0000  =  00 

^qqqqqq   ©qqqqqqqq©  qqqqqqqqqq 

©ddddddd   ©ddddo'do'd©  o'do'c'ddddo'd 


xt^ce  —  co  —  ©xt»io 


0000  =  000   ©©000  =  0000   ccoc"  =  do  =  =  = 
©000  =  0  =  0   ooooooooo©   oc  =  oooooo© 


©©©0000©    ©©©©00©©©©    ©©©OO©©©©0 


©   >o  ©   10  ©   »o  © 


ioqioqioq»o©io©       ioqioq»o©io© 

©^^CMCMCOCO^f-riO  lOCO'-Cf^^-^'XSS 

^T^I'^I'TTTTT^T  ^'^I^14'^*T^1**T'*T 


<O~*'MOXCe-4'O1  ©XCO'^'MOOOJ^JOOJ  ^-Sit»'"1^i-*Sit>->'^^ 

COT:©   —   —   fico-*1  »ta»»»gg*«©^«  co«—   >oce»^»^<n: 

_  -H  <M  <M  ci  (M  ^>  CM  <M  01  <M  01  -M  C*l  -M  CO  ~*  CO  CO  "*  W  CO  ' :  CO  CC 

§00  =  0  =  00  oooooooooo  co©  =  = 

^qqqqqqq-  qqqqqqqqqq  ©0  =  0  =  00000 

©dddddd©  ©©©dddddd©  ©dddddddoo 


S:O    —    OicO'T-'iO 

§  I  i  i  i  i  1  i 

©dddddd© 


CM     01     CM     01     ?1     -     CO     CO     ^     TO 

§000  =  0  =  000 
^qqqqoqqqq 

©©ddddddd© 


a  a  g  »  x  g  «  e  e  e 

q  q  q  q'q  q  q  q  q  c 

©d©*dddd©©o 


»o  q  10  q  »o  ©  10  q 
i«  oi  CM  co   co   -r   -f   \n 


10  ©   10  q   >o  q   «  ©       10  q   us  q   10  q   >o  q   10  c 
cot^i^ocTrsisi©       d^^oi^jco';':-';-';''' 


CM     07     CM     CM     CM     CM 


61 


722 


TABLES. 


TABLE    XIX. 

TABLE  FOR  THE  REDUCTION  OF  THE  PRESSURE   OF  A  COLUMN 
OF   WATER   TO   A   COLUMN   OF   MERCURY. 


Pressure  of 
U'ater, 
in  Millimetres. 

Pressure  of 
Men-urv, 
in  Millimetres. 

Pressure  of 
Water, 
in  Millimetres. 

Pressure  of 
Mercury, 
in  Millimetres. 

Pressure  of 
Wafer, 
in  Millimetres 

Pressure  of 
Mercury, 
in  Millimetres. 

1 

0.07 

41 

3.03 

81 

5  98 

2 

0.15 

42 

3.10 

82 

6.05 

3 

0.22 

43 

3.17 

83 

6  13 

4 

0.30 

44 

3.25 

84 

6.20 

5 

0.37 

45 

3.32 

85 

6.27 

6 

0.14 

46 

3.39 

86 

6.35 

7 

0.52 

47 

3.47 

87 

6.12 

8 

0.53 

48 

3.54 

88 

6.49 

9 

0.63 

49 

3.62 

89 

6.57 

10 

0.74 

50 

3.69 

90 

6.64 

11 

0.81 

51 

3.76 

91 

6.72 

12 

O.S9 

52 

3.84 

92 

6.79 

13 

0.<)6 

53 

3.91 

93 

6.86 

14 

1.03 

54 

3.99 

94 

6.94 

15 

1.12 

55 

4.06 

95 

7.01 

16 

1.18 

56 

4.13 

96 

7.  OS 

17 

1.26 

57 

4.21 

97 

7.16 

18 

1.33 

58 

4.28 

98 

7.23 

19 

1.40 

59 

4.33 

99 

7.31 

20 

1.48 

60 

4.43 

100 

7.38 

21 

1.55 

61 

4.50 

200 

14.76 

22 

1.62 

62 

4.58 

300 

22.14 

23 

1.70 

63 

4.65 

400 

29.52 

24 

1.77 

64 

4.72 

500 

36.90 

25 

1.84 

65 

4.80 

600 

44.28 

26 

1.92 

66 

4.87 

700 

51.66 

27 

1.98 

67 

4.94 

800 

59.04 

28 

2.07 

68 

5.02 

900 

66.42 

29 

2.14 

69 

5.09 

1000 

73.80 

30 

2.21 

70 

5.17 

31 

2.29 

71 

5.24 

32 

2.36 

72 

5.31 

33 

2.44 

73 

5.39 

34 

2.51 

74 

5.46 

35 

2.58 

75 

5.54 

36 

2.66 

76 

5.61 

37 

2.73 

77 

5.68 

38 

2.80 

78 

5.76 

39 

2.88 

79 

5.83 

40 

2.95 

80 

5.90 

,     j 

LOGARITHMS  AND  ANTI-LOGARITHMS, 


LOGARITHMS  OF  NUMBERS. 

•3  S3 

Proportional  Parts, 

2J 
3  H 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

il 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0000 

0043 

0086 

0128 

0170 

0212 

0253 

0294 

0334 

0374 

4 

8 

12 

17 

21 

25 

29 

33 

37 

11 

0414 

0453 

0492 

0531 

0569 

0607 

0645 

0682 

0719 

0755 

4 

a 

11 

15 

19 

23 

26 

30  34 

12 

0792 

0828 

0864 

0899 

0934 

0969 

1004 

1038 

1072 

1106 

3 

7 

10 

14 

17 

21 

24 

28  31 

13 

1139 

1173 

1206 

1239 

1271 

1303 

1335 

1367 

1399 

1430 

3 

6 

10 

13 

16 

19 

23 

26  29 

14 

1461 

1492 

1523 

1553 

1584 

1614 

1644 

1673 

1703 

1732 

3 

« 

9 

12 

15 

18 

21 

24 

27 

15 

1761 

1790 

1818 

1847 

1875 

1903 

1931 

1959 

1987 

2014 

3 

6 

8 

11 

14 

17 

20 

22 

25 

16 

2041 

2068 

2095 

2122 

2148 

2175 

2201 

2227 

2253 

2279 

1 

5 

8 

11 

13 

16 

18 

21  24 

17 

2304 

2330 

2355 

2380 

2405 

2430 

2455 

2480 

2504 

2529 

2 

5 

7 

10 

12 

15 

17 

20  22 

18 

2553 

2577 

2601 

2625 

264S 

2672 

2695 

2718 

2742 

2765 

2 

5 

7 

9 

12 

14 

16 

19  21 

19 

2788 

2810 

2833 

2856 

2878 

2900 

2923 

2945 

2967 

2989 

2 

4 

7 

9 

11 

13 

16 

18 

20 

20 

3010 

3032 

3054 

3075 

3096 

3118 

3139 

3160 

3181 

3201 

2 

4 

6 

8 

11 

13 

15 

17 

19 

21 

3222 

3243 

3263 

3284 

3304 

3324 

3345 

3365 

3385 

3404 

2 

4 

6 

8 

10 

12 

14 

16 

18 

22 

3424 

3444 

3464 

3483 

3502 

3522 

3541 

3560 

3579 

3598 

2 

4 

6 

8 

10 

12 

14 

15 

17 

23 

3617 

3636 

3655 

3674 

3692 

3711 

3729 

3747 

3766 

3784 

2 

4 

6 

7 

9 

11 

13 

15 

17 

24 

3802 

3820 

3838 

3856 

3874 

3892 

3909 

3927 

3945 

3962 

2 

4 

5 

7 

9 

11 

12 

14 

16 

25 

3979 

3997 

4014 

4031 

4048 

4065 

4082 

4099 

4116 

4133 

•  2 

3 

5 

7 

9 

10 

12 

14 

15 

26 

4150 

4166 

4183 

4200 

4216 

4232 

4249 

4265 

4281 

4298 

2 

3 

5 

7 

8 

10 

11 

13 

15 

27 

4314 

4330 

4346 

4362 

4378 

4393 

4409 

4425 

4440 

4456 

2 

3 

5 

6 

8 

9 

11 

13 

14 

28 

4472 

4487 

4502 

4518 

4533 

4548 

4564 

4579 

4594 

4609 

2 

3 

5 

6 

8 

9 

11 

12 

14 

29 

4624 

4639 

4654 

4669 

4683 

4698 

4713 

4728 

4742 

4757 

1 

3 

4 

6 

7 

9 

10 

12 

13 

30 

4771 

4786 

4800 

4814 

4829 

4843 

4857 

4871 

4886 

4900 

1 

3 

4 

6 

7 

9 

10 

11 

13 

31 

4914 

4928 

4942 

4955 

4969 

4983 

4997 

5011 

5024 

5038 

1 

3 

4 

6 

7 

8 

10 

11 

12 

32 

5051 

5065 

5079 

5092 

5105 

5119 

5132 

5145 

5159 

5172 

J  I 

3 

4 

5 

7 

8 

9 

11 

12 

33 

5185 

5198 

5211 

5224 

5237 

5250 

5263 

5276 

5289 

5302 

1 

3 

4 

5 

6 

8 

9 

10 

12 

34 

5315 

5328 

5340 

5353 

5366 

5378 

5391 

5403 

5416 

5428 

1 

3 

4 

5 

6 

8 

9 

10 

11 

35 

5441 

5453 

5465 

5478 

5490 

5502 

5514 

5527 

5539 

5551 

1 

2 

4 

5 

6 

7 

9 

10 

11 

36 

5563 

5575 

5587 

5599 

5611 

5623 

5635 

5647 

5658 

5670 

1 

2 

4 

5 

6 

7 

8 

10 

11 

37 

5682 

5694 

5705 

5717 

5729 

5740 

5752 

5763 

5775 

5786 

1 

2 

3 

5 

6 

7 

8 

9 

10 

38 

5798 

5809 

5821 

5832 

5843 

5855 

5866 

5877 

5888 

5899 

I 

2 

3 

5 

6 

7 

8 

9 

10 

39 

5911 

5922 

5933 

5944 

5955 

5966 

5977 

5988 

5999 

6010 

1 

2 

3 

4 

5 

7 

8 

9 

10 

40 

6021 

6031 

6042 

6053 

6064 

6075 

6085 

6096 

6107 

6117 

1 

2 

3 

4 

5 

6 

8 

9 

10 

41 

6128 

6138 

6149 

6160 

6170 

6180 

6191 

6201 

6212 

6222 

1 

2 

3 

4 

5 

6 

7 

8 

9 

42 

6232 

6243 

6253 

6263 

6274 

6284 

6294 

6304 

6314 

6325 

1 

2 

3 

4 

5 

6 

7 

8 

9 

43 

6335 

6345 

6355 

6365 

6375 

6385 

6395 

6405 

6415 

6425 

1 

2 

3 

4 

5 

6 

7 

8 

9 

44 

6435 

6444 

6454 

6464 

6474 

6484 

6493 

6503 

6513 

6522 

1 

2 

3 

4 

5 

6 

7 

8 

9 

45 

6532 

6542 

6551 

6561 

6571 

6580 

6590 

6599 

6609 

6618 

1 

2 

3 

4 

5 

6 

7 

8 

9 

46 

6628 

6637 

6646 

6656 

6665 

6675 

6684 

6693 

6702 

6712 

1 

2 

3 

4 

5 

6 

7 

7 

8 

47 

6721 

6730 

6739 

6749 

6758 

6767 

6776 

6785 

6794 

6803 

1 

2 

3 

4 

5 

5 

6 

7 

8 

48 

6812 

6821 

6830 

6839 

6848 

6857 

6866 

6875 

6884 

6893 

1 

2 

3 

4 

4 

5 

6 

7 

8 

49 

6902 

6911 

6920 

6928 

6937 

6946 

6955 

6964 

6972 

6981 

1 

2 

3 

4 

4 

5 

6 

7 

8 

50 

6990 

6998 

7007 

7016 

7024 

7033 

7042 

7050 

7059 

7067 

1 

2 

3 

3 

4 

5 

6 

7 

8 

51 

7076 

7034 

7093 

7101 

7110 

7118 

7126 

7135 

7143 

7152 

1 

2 

3 

3 

4 

5 

6 

7 

8 

52 

7160 

7168 

7177 

7185 

7193 

7202 

7210 

7218 

7226 

7235 

1 

2 

2 

3 

4 

5 

6 

7 

7 

53 

7243 

7251 

7259 

7267 

7275 

7284 

7292 

7300 

7308 

7316 

1 

2 

2 

3 

4 

5 

6 

6 

7 

54 

7324 

7332 

7340 

7348 

7356 

7364 

7372 

7380 

7388 

7396 

1 

2 

2!  3 

41  5 

6  6|  7 

LOGARITHMS  OF  NUMBERS. 

Natural 
Numbers. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Proportional  Parts. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

55 

7404 

7412 

7419 

7427 

7435 

7443 

7451 

7459 

7466 

7474 

i 

2 

2 

3 

4 

5 

5 

6 

7 

56 

7482 

7490 

7497 

7505 

7513 

7520 

7528 

7536 

7543 

7551 

i 

9 

2 

3 

4 

5 

5 

6 

7 

57 

7559 

7566 

7574 

7582 

7589 

7597 

7604 

7612 

7619 

7627 

i 

2 

2 

3 

4 

5 

5 

6 

7 

58 

7634 

7642 

7649 

7657 

7664 

7672 

7679 

7686 

7694 

7701 

i 

1 

2 

3 

4 

4 

5 

6 

7 

59 

7709 

7716 

7723 

7731 

7738 

7745 

7752 

7760 

7767 

7774 

i 

1 

2 

3 

4 

4 

5 

6 

7 

60 

7782 

7789 

7796 

7803 

7810 

7818 

7825 

7832 

7839 

7846 

i 

1 

2 

3 

4 

4 

5 

6 

6 

61 

7853 

7860 

7868 

7875 

7882 

7889 

7896 

7903 

7910 

7917 

i 

1 

2 

3 

4 

4 

5 

6 

6 

62 

7924 

7931 

7938 

7945 

7952 

7959 

7966 

7973 

7980 

7987 

i 

1 

2 

3 

3 

4 

5 

6 

6 

63 

7993 

8000 

8007 

8014 

8021 

8028 

8035 

8041 

8048 

8055 

i 

1 

2 

3 

3 

4 

5 

5 

6 

64 

8062 

8069 

8075 

8082 

8089 

8096 

8102 

8109 

8116 

8122 

i 

1 

2 

3 

3 

4 

5 

5 

6 

65 

8129 

8136 

8142 

8149 

8156 

8162 

8169 

8176 

8182 

8189 

i 

1 

2 

3 

3 

4 

5 

5 

6 

66 

8195 

8202 

8209 

8215 

8222 

8228 

8235 

8241 

8248 

8254 

i 

1 

2 

3 

3 

4 

5 

5 

6 

67 

8261 

8267 

8274 

8280 

8287 

8293 

8299 

8306 

8312 

8319 

i 

1 

2 

3 

3 

4 

5 

5 

6 

68 

8325 

8331 

.8338 

8344 

8351 

8357 

8363 

8370 

8376 

8382 

i 

1 

2 

3 

3 

4 

4 

5 

6 

69 

8388 

8395 

8401 

8407 

8414 

8420 

8426 

8432 

8439 

8445 

i 

1 

2 

2 

3 

4 

4 

5 

6 

70 

8451 

8457 

8463 

8470 

8476 

8482 

8488 

8494 

8500 

8506 

i 

1 

2 

2 

3 

4 

4 

6 

6 

71 

8513 

8519 

8525 

8531 

8537 

8543 

8549 

8555 

8561 

8567 

i 

1 

2 

2 

3 

4 

4 

5 

5 

72 

8573 

8579 

8585 

8591 

8597 

8603 

8609 

8615 

8621 

8627 

i 

1 

2 

2 

3 

4 

4 

5 

5 

73 

8633 

8639 

8645 

8651 

8657 

8663 

8669 

8675 

8681 

8686 

i 

1 

2 

2 

3 

4 

4 

5 

5 

74 

8692 

8698 

8704 

8710 

8716 

8722 

8727 

8733 

8739 

8745 

i 

1 

2 

2 

3 

4 

4 

5 

5 

75 

8751 

8756 

8762 

8768 

8774 

8779 

8785 

8791 

8797 

8802 

i 

1 

2 

2 

3 

3 

4 

5 

5 

76 

8808 

8814 

8820 

8825 

8831 

8837 

8842 

8848 

8854 

8859 

i 

1 

2 

2 

3 

3 

4 

5 

5 

77 

8865 

8871 

8876 

8882 

8887 

8893 

8899 

8904 

8910 

8915 

i 

1 

2 

2 

3 

3 

4 

4 

5 

78 

8921 

8927 

8932 

8938 

8943 

8949 

8954 

8960 

8965 

8971 

i 

1 

2 

2 

3 

3 

4 

4 

5 

79 

8976 

8982 

8937 

8993 

8998 

9004 

9009 

9015 

9020 

9025 

i 

1 

2 

2 

3 

3 

4 

4 

5 

80 

9031 

9036 

9042 

9047 

9053 

9058 

9063 

9069 

9074 

9079 

i 

,.I 

2 

2 

3 

3 

4 

4 

5 

81 

9085 

9090 

9096 

9101 

9106 

9112 

9117 

9122 

9128 

9133 

i 

1 

2 

2 

3 

3 

4 

4 

5 

82 

9138 

9143 

9149 

9154 

9159 

9165 

9170 

9175 

9180 

9186 

i 

1 

2 

2 

3 

3 

4 

4 

5 

83 

9191 

9196 

9201 

9206 

9212 

9217 

9222 

9227 

9232 

9238 

i 

i 

2 

2 

3 

3 

4 

4 

5 

84 

9243 

9248 

9253 

9258 

9263 

9269 

9274 

9279 

9284 

9289 

i 

1 

2 

2 

3 

3 

4 

4 

5 

85 

9294 

9299 

9304 

9309 

9315 

9320 

9325 

9330 

9335 

9340 

i 

i 

2 

2 

3 

3 

4 

4 

5 

86 

9345 

9350 

9355 

9360 

9365 

9370 

9375 

9380 

9385 

9390 

1 

"i 

2 

2 

3 

3 

4 

4 

5 

87 

9395 

9400 

9405 

9410 

9415 

9420 

9425 

9430 

9435 

9440 

0 

1 

1 

2 

2 

3 

3 

4 

4 

88 

9445 

9450 

9455 

9460 

9465 

9469 

9474 

9479 

9484 

9489 

0 

t 

1 

2 

2 

3 

3 

4 

4 

89 

9494 

9499 

9504 

9509 

9513 

9518 

9523 

9528 

9533 

9538 

0 

1 

1 

2 

2 

3 

3 

4 

4 

90 

9542 

9547 

9552 

9557 

9562 

9566 

9571 

9576 

9581 

9586 

0 

1 

1 

2 

2 

3 

3 

4 

4 

91 

9590 

9595 

9600 

9605 

9609 

9614 

9619 

9624 

9628 

9633 

0 

1 

1 

2 

2 

3 

3 

4 

4 

92 

9638 

9643 

9647 

9652 

9657 

9661 

9666 

9671 

9675 

9680 

0 

1 

1 

2 

2 

3 

3 

4 

4 

93 

9685 

9689 

9694 

9699 

9703 

9708 

9713 

9717 

9722 

9727 

0 

1 

1 

2 

2 

3 

3 

4 

4 

94 

9731 

9736 

9741 

9745 

9750 

9754 

9759 

9763 

9768 

9773 

0 

1 

1 

2 

2 

3 

I 

4 

4 

95 

9777 

9782 

9786 

9791 

9795 

9800 

9805 

9809 

9814 

9818 

0 

1 

1 

2 

2 

3 

1 

4 

4 

96 

9823 

9827 

9832 

9836 

9841 

9845 

9850 

9854 

9859 

9863 

0 

1 

1 

2 

2 

3 

3 

4 

4 

97 

9868 

9872 

9877 

9S81 

9886 

9890 

9894 

9899 

9903 

9908 

0 

1 

1 

2 

2 

?, 

:j 

4 

4 

98 

99^2 

9917 

9921 

9926 

9930 

9934 

9939 

9943 

9948 

9952 

0 

1 

1 

2 

2 

3 

^ 

4 

4 

99 

995  S 

9961 

9965 

9969 

9974 

9978 

9983 

9987 

9991 

9996 

0 

1 

1  2 

2 

3 

3 

3 

4 

ANTILOGARITHMS. 

ts 

Proportional  Parts, 

I 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

•c 

1 

2 

1 

4 

5 

6 

7 

8 

9 

.00 

1000 

1002 

1005 

1007 

1009 

1012 

1014 

1016 

1019 

1021 

0 

0 

1 

i 

1 

2 

2 

2 

.01 

1023 

1026 

1028 

1030 

1033 

1035 

1038 

1040 

1042 

1045 

0 

0 

ll  1 

1  2 

2 

2 

.02 

1047 

1050 

1052 

1054 

1057 

1059 

1062 

1064 

1067 

1069 

0 

0 

1 

i 

1 

2 

1 

2 

.03 

1072 

1074 

1076 

1079 

1081 

1084 

1086 

1089 

1091 

1094 

0 

0 

1 

i 

1 

2 

2 

2 

.04 

1096 

1099 

1102 

1104 

1107 

1109 

1112 

1114 

1117 

1119 

0 

1 

1 

i 

2 

2 

2 

2 

.05 

1122 

1125 

1127 

1130 

1132 

1135 

1138 

1140 

1143 

1146 

0 

1 

1 

i 

2 

2 

2 

2 

.06 

1148 

1151 

1153 

1156 

1159 

1161 

1164 

1167 

1169 

1172 

0 

1 

i 

2 

2 

2 

2 

.07 

1175 

1178 

1180 

1183 

1186 

1189 

1191 

1194 

1197 

1199 

0 

1 

i 

2 

2 

2 

2 

.03 

1202 

1205 

1208 

1211 

1213 

1216 

1219 

1222 

1225 

1227 

0 

I 

i 

2 

2 

2 

3 

.09 

1230 

1233 

1236 

1239 

1242 

1245 

1247 

1250 

1253 

1256 

0 

1 

1 

2 

2 

2 

3 

.10 

1259 

1262 

1265 

1268 

1271 

1274 

1276 

1279 

1282 

1285 

0 

1 

i 

%1 

2 

2 

2 

3 

.11 

1288 

1291 

1294 

1297 

1300 

1303 

1306 

1309 

1312 

1315 

0 

1 

i 

2 

2 

2 

2 

3 

.12 

1318 

1321 

1324 

1327 

1330 

1334 

1337 

1340 

1343 

1346 

0 

1 

i 

2 

.2 

2 

2 

3  i 

.13 

1349 

1352 

1355 

1358 

1361 

1365 

1368 

1371 

1374 

1377 

0 

1 

i 

2 

2 

2 

3 

3  ! 

.14 

1380 

1384 

1387 

1390 

1393 

1396 

1400 

1403 

1406 

1409 

0 

1 

i 

2 

2 

2 

« 

3 

.15 

1413 

1416 

1419 

1422 

1426 

1429 

1432 

1435 

1439 

1442 

0 

1 

i 

2 

2 

2 

3 

3 

.16 

1445 

1449 

1452 

1455 

1459 

1462 

1466 

1469 

1472 

1476 

0 

1 

i 

2 

2 

2|  3 

3 

.17 

1479 

1483 

1486 

1489 

1493 

1496 

1500 

1503 

1507 

1510 

0 

1 

i 

2 

2 

21  3 

3 

.18 

1514 

1517 

1521 

1524 

1528 

1531 

1535 

1538 

1542 

1545 

0 

1 

i 

2 

2 

2  3 

3 

.19 

1549 

1552 

1556 

1560 

1563 

1567 

1570 

1574 

1578 

1581 

0 

1 

i 

2 

2 

3 

3 

3 

.20 

1585 

1589 

1592 

1596 

1600 

1603 

1607 

1611 

1614 

1618 

0 

1 

i 

2 

2 

3 

3 

3 

.21 

1622 

1626 

1629 

1633 

1637 

1641 

1644 

1648 

1652 

1656 

0 

1 

2 

2 

2 

3  3 

3 

.22 

1660 

1663 

1667 

1671 

1675 

1679 

1683 

1687 

1690 

1694 

0 

1 

2 

2 

2 

3;  3 

3 

.23 

1698 

1702 

1706 

1710 

1714 

1718 

1722 

1726 

1730 

1734 

0 

1 

2 

2 

2 

3 

9 

4 

.24 

1738 

1742 

1746 

1750 

1754 

1758 

1762 

1766 

1770 

1774 

0 

1 

2 

2 

2 

3 

o 

4 

.25 

1778 

1782 

1786 

1791 

1795 

1799 

1803 

1807 

1811 

1816 

0 

1 

2 

2 

2 

3 

3 

4 

.26 

1820 

1824 

1828 

1832 

1837 

1841 

1845 

1849 

1854  1858 

0 

1 

2 

2 

3 

8  3 

4 

.27 

1862 

1866 

1871 

1875 

1879 

1884 

1888 

1892 

1897  1901 

0 

1 

2 

2 

3 

3|  3 

4 

.28 

1905 

1910 

1914 

1919 

1923 

1928 

1932 

1936 

1941  1945 

0 

1 

2 

2 

3 

S|  4j  4 

.29 

1950 

1954 

1959 

19&3 

1968 

1972 

1977 

1982 

1986  1991 

1 

0 

1 

2 

2 

3 

3 

4 

4 

.30 

1995 

2000 

2004 

2009 

2014 

2018 

2023 

2028 

2032 

2037 

0 

1 

2 

2 

0 

3 

4 

* 

.31 

2042 

2046 

2051 

2056 

2061 

2065 

2070  2075 

2080 

2084 

0 

1 

2 

2 

3 

3  4;  4 

•32 

2089 

2094 

2099 

2104 

2109 

2113 

2118  2123 

2128 

2133 

0 

1 

2 

2 

•  3 

3  4|  4 

.33 

2138 

2143 

2148 

2153 

2158 

2163 

2168  2173 

2178 

2183 

0 

1 

2 

2 

3 

3  4 

4 

.34 

2188 

2193 

2198 

2203 

2208 

2213 

2218 

2223 

2228 

2234 

1 

2 

2 

3 

3 

4  4 

5 

.35 

2239 

2244 

2249 

2254 

2259 

2265 

2270 

2275 

2280 

2286 

2 

2 

3 

3 

4  4 

K 

.36 

2291 

2296 

2301 

2307 

2312 

2317 

2323  2328 

2333 

2339 

2 

2 

3 

3 

4 

4 

5 

.37 

2344 

2350 

2355 

2360  2366 

2371 

2377  2382 

2388 

2393 

2 

2 

3 

3 

4 

4 

5 

.38 

2399 

2404 

2410 

2415  2421 

2427 

2432  2438 

2443 

2449 

2 

2 

3 

3 

4 

4 

5 

.39 

2455 

2460 

2466 

2472 

2477 

2483 

2489 

2495 

2500 

2506 

2 

2 

3 

3 

4 

5 

5 

.40 

2512 

2518 

2523 

2529 

2535 

2541 

2547 

2553 

2559 

2564 

2 

2 

a 

4 

4 

5 

5 

.41 

2570 

2576 

2582 

2588 

2594 

2600 

2606 

2612 

2618 

2624 

2 

2 

9 

4 

4 

» 

5 

.42 

2630 

2636 

2642 

2649 

2655 

2661 

2667 

2673 

2679 

2685 

2 

2 

9 

4 

4 

5 

6 

.43 

2692 

2698 

2704 

2710 

2716 

2723 

2729 

2735 

2742 

2748 

2 

3 

3 

4 

4 

5 

6  I 

.44 

2754 

2761 

2767 

2773 

2780 

2786 

2793 

2799 

2805 

2812 

2 

3 

3 

4 

4 

5 

6 

.45 

2818 

2825 

2831 

2838 

2844 

2851 

2858 

2864 

2871 

2877 

2 

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2884 

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2911 

2917 

2924 

2931 

2938 

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3 

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4 

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5 

6 

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2951 

2958 

2965 

2972 

2979 

2985 

2992 

2999 

3006 

3013 

2 

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5 

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3020 

3027 

3034 

3041 

3048 

3055 

3062 

3069 

3076 

3083 

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6 

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.49 

3090 

3097 

3105 

3112 

3119 

3126 

3133 

3141 

3148 

3155 

2 

3 

4 

4 

5 

6 

6 

ANTILOGARITHMS. 

•  » 

Proportional  Paris. 

II 

0 

1 

2 

3 

4 

5 

G 

7 

8 

9 

i 

,     f 

Hi  *£ 

12  8 

4 

5 

6  7 

8 

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1 

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3170 

3177 

3184 

3192 

3199 

3206 

3214 

3221 

3228 

i 

1 

2 

3 

4 

4 

5 

6 

7 

.51 

32.36 

3243 

3251 

3258  3266 

3273 

3281 

3289 

3296  3304 

2 

2 

3 

4 

5 

5 

6 

7  i 

.52 

3311 

3319 

3327 

3334 

3342 

3350 

3357 

3365 

3373  3381 

2 

2 

3 

4 

5 

5 

6 

7 

.53 

3388 

3396 

3404 

3412 

3420 

3428 

3436 

3443 

3451 

3459 

2 

2 

3 

4 

5 

6 

6 

7 

.54 

3467 

3475 

3483 

3491 

3499 

3508 

3516 

3524 

3532 

3540 

2 

2 

3 

4 

5 

6 

6 

7  1 

.55 

3548 

3556 

3565 

3573 

3581 

3589 

3597 

3606 

3614 

3622 

2 

2 

3 

4 

5 

G 

7 

7  , 

.56 

3631 

3639  3648 

3656 

3664 

3673 

3681 

3690 

3698 

3707 

2 

3 

3 

4 

5 

6 

7 

8 

.57 

3715 

3724!  3733 

3741 

3750 

3758 

3767 

3776 

3784  3793 

2 

3 

3 

4 

5 

6  7 

8 

.58 

3802 

3811 

3819 

3828  3837 

3846 

3855 

3864 

3873  3882 

2 

3 

4 

4 

5 

6'  7 

8 

.59 

3890 

3899 

3908 

3917 

3926 

3936 

3945 

3954 

3963^972 

2 

3 

4 

5 

5 

6j  7 

8 

.60 

3981 

3990 

3999 

4009 

4018 

4027 

4036 

4046 

4055  4064 

2 

3 

4 

5 

6 

6  7 

8 

.61 

4074 

4083 

4093 

4102 

4111 

4121 

4130 

4140 

4150  4159 

2 

3 

4 

5 

6 

7 

8 

9 

.62 

4169 

4178 

4188 

4198 

4207 

4217 

4227 

4236 

4246  4256 

2 

3 

4 

5 

6 

7 

8 

9 

.63 

4266 

4276 

4285 

4295 

4305 

4315 

4325 

4335 

4345  4355 

2 

3 

4 

5 

6 

7 

8 

9 

.64 

4365 

4375 

4385 

4395 

4406 

4416 

4426 

4436 

4446 

4457 

2 

3 

A 

5 

6 

7 

8 

9 

.65 

4467 

4477 

4487 

4498 

4508 

4519 

4529 

4539 

4550 

4560 

2 

3 

4 

5 

6 

7 

S 

9 

.66 

4571 

4581 

4592 

4603 

4613 

4624 

4634 

4645 

4656  4667 

2 

3  4 

5 

G 

7  9 

10 

.67 

4677 

4688 

4699 

4710 

4721 

4732 

4742 

4753 

4764  4775 

2 

3  4 

5 

7 

8 

9 

10 

.68 

4786 

4797 

4808 

4819 

4831 

4842 

4853 

4864 

4875  4887 

2 

3  4 

6 

7 

8  9 

10 

.69 

4898 

4909 

4920 

4932 

4943 

4955 

4966 

4977 

4989  5000 

2 

3 

5 

6 

7 

8  9 

10 

.70 

5012 

5023 

5035 

5047 

5058 

5070 

5082 

5093 

5105 

5117 

2 

4i  5 

6 

7 

8  9 

11 

.71 

5129 

5140 

5152 

5164 

5176 

5188 

5200 

5212 

5224  5236 

2 

4  5 

6 

7 

8  10!  11 

.72 

5248 

5260 

5272 

5284 

5297 

5309 

5321 

5333 

5346  5358 

2 

4 

5 

6 

7 

9  10;  11  i 

.73 

5370 

5383 

5395 

5408 

5420 

5433 

5445 

5458 

5470  5483 

3 

4 

t 

G 

8 

9  10 

11  1 

.74 

5495 

5508 

5521 

5534 

5546 

5559 

5572 

5585 

5598  5610 

3  4 

5 

6 

8 

9  10 

12 

.75 

5623 

5636 

5649 

5662 

5675 

5689 

5702 

5715 

5728  5741 

3 

4 

5 

7 

8 

9  10 

12 

.76 

5754 

5768 

5781 

5794 

5808 

5821 

5834 

5848 

5861  5875 

8 

4  5 

7 

8  9  11 

12 

.77 

5888 

5902 

5916 

5929 

5943 

5957 

5970 

5984 

5998  6012 

3 

4  5 

7 

8  10;  n 

12 

.73 

G026 

6039 

6053 

6067 

6081 

6095 

6109 

6124 

6138  6152 

3 

4  6 

7 

8  lo'll 

13 

.79 

6166 

6180 

6194 

6209 

6223 

6237 

6252 

6266 

6281  6295 

3 

4  .6 

7 

9 

10  11 

13 

.80 

6310 

6324 

6339 

6353 

6368 

6383 

6397 

6412 

6427 

6442 

i 

3 

4  6 

7 

9 

10  12 

13 

.81 

6457 

6471 

6486 

6501 

6516 

6531 

6546 

C561 

6577 

6592 

v 

3 

5!  6 

8  9  11  12 

14 

•82 

6607 

662  •• 

6637 

6653 

6668 

6683 

6699 

6714 

6730 

6745 

2 

3 

5 

6 

8  9  11  12 

14 

.83 

6761 

6776 

6792 

6808 

6823 

6839 

6855 

6871 

6887 

6902 

2 

a 

5  6 

g 

9;  11   13 

14 

.84 

6918 

6934 

6950 

6966 

6982 

6998 

7015 

7031 

7047 

7063 

2 

3 

5  6 

8  10;  11,  is 

15 

1 

.85 

7079 

7096 

7112 

7129 

7145 

7161 

7178 

7194 

7211 

7228 

2 

3 

5  7 

8  10  12  13 

15 

.86 

7244 

7261 

7278 

7295 

7311 

7328 

7345 

7362 

7379 

7396 

2 

3 

5  7 

8  10,  12  13 

15 

.87 

7413 

7430 

7447 

7464 

7482 

7499 

7516 

7534 

7551 

7568 

2 

3 

5 

7 

9  10J12 

14 

16 

.88 

7586 

7603 

7621 

7638 

7656 

7674 

7691 

7709 

7727 

7745 

2 

4 

5 

•  7 

9  11  12 

14 

16 

.89 

7762 

7780 

7798 

7816 

7834 

7852 

7870 

7889 

7907 

7925 

2 

4 

5 

7 

9  11 

13 

14 

16 

.90 

7943 

7962 

7980 

7998 

8017 

8035 

8054 

8072 

8091 

8110 

2 

6 

7 

9 

11 

13 

15 

17 

.91 

8128  8147 

8166 

8185 

8204 

8222 

8241 

8260 

8279 

8299 

s 

e 

8 

9j  11  13 

15 

17 

.92 

8318  8337 

8356 

8375  8395 

8414 

8433 

8453 

8472 

8492 

2 

6 

8 

10  12  14 

15 

17 

.93 

8511  8531 

8551 

8570  8590 

8610 

8630 

8650 

8670 

8690 

2 

6 

8 

10  12  14 

16 

18 

.94 

8710 

8V30 

8750 

8770  8790 

8810 

8831 

8851 

8872 

8892 

s 

6 

8 

10  12 

14 

16 

18 

.95 

8913 

8933 

8954 

8974 

8995 

9016 

9036 

9057 

9078 

9099 

2 

4 

6 

8 

10  12  15 

17 

19 

.96 

9120 

9141 

9162 

9183  9204 

9226 

9247 

9268  9290 

9311 

2 

468 

ll|  IS!  15 

17 

19  i 

.97 

9333 

9354 

9376 

9397  9419 

^141 

9462 

9484  9506 

9528 

2 

479 

11  13'l5 

17J  20 

.98 

9550 

9572 

9594 

9616  9638 

9661 

9683 

9705 

9727 

9750 

2 

4 

7  9 

11  13i  16 

18, 

20 

.99 

9772 

9795 

9817 

9840  9863 

9886 

9908 

9931 

9954  9977 

2579 

11.'  14  16  18 

20 

CONSTANT  LOGARITHMS. 

Ar.  Co. 

Logarithms.         Logarithms. 

Circumf.  of  circle  when  R  =  1,     (|     =    1.5708)  0.1961199  9.8038801 

«       «      «         «      D  =  if     (ff     —    3.1416)  0.4971499  9.5028501 

Area  of  circle  when  R*  =  1,          (TT     =    3.1416)  0.4971499  9.5028501 

"    "      "         "     Z>2=1,          (^     =   0.7854)  9.8950899  0.1049101 

«     "      «         «     <72=1,           (i-  =    0.0796)  8.9007901  1.0992099 

Surface  of  sphere  when  R2  =  1,    (4  TT  =  12.5664)  1.0992099  8.9007901 

"      "       «         "     Z>2=1,    (TT    =   3.1416)  0.4971499  9.5028501 

"      «       «         "     0«=1,    (i     =   0.3183)  9.5028501  0.4971499 

7T 

Solidity  of  sphere  when  J?3  =  1,    (^TT=    4.1888)  0.6220886  9.3779114 

o 

«       «      •«         "      1^=1,    (5     =    0.5236)  9.7189986  0.2810014 

o 

» 

"       "      ".       "       (73=1,    (^=   0.0169)  8.2275490  1.7724510 

OTT 

Log.  ofTr2,                                       (7T2    =9.86960)  0.9942997  9.0057003 

Intensity  of  gravity  at  Paris,          (g     =  9.80960)  0.991  6513  9.008  3487 

«        "       "      in  Lat.  45°,      (g     =  9.80604)  0.991 4937  9.008  5063 

"         "       «      on  Equator,     (g     =9.78062)  0.9903664  9.0096336 

Length  of  seconds  pendulum  at  Paris,  (I  =  0.99392)  9.997  3515  0.002  6485 

No.  of  seconds  in  a  day,                                (86400)  4936  5137  5.063  4863 

Specific  Gravity  of  Mercury,                       (13.596)  1.1334112  8.8665888 

Mean  height  of  Barometer,                        (76c.m.)  1.8808136  8.1191864 

Corresponding  air  pressure  on  £~5r.2,       (1,033.296)  3.014  2248  6.985  7752 


INDEX, 


ABSOLUTE  WEIGHT.    (See  Weight.) 
Absorption  of  gases  by  solids,  379. 

"  ?'  "  laws  of,  381. 

"  "        by  liquids.     (See  Solu- 

"  of  liquids  by  solids,  363.  [bility.) 

Absorption-Meter,  402.     Analysis  of  mixed 

gases  by,  409. 
Acceleration,  definition  of,  23. 

of  gravity,  65. 

Action  and  reaction,  law  of,  49. 
Adhesion,  342.     (And see  Osmose.) 
"         between  gases,  412. 
"  "        liquids,  383. 

"  *'      and  gases,  391. 

"        solids,  342. 
"  "    and  gases,  379, 383. 

"  «  "      "     liquids,  344. 

"         phenomena  of,  classified,  342. 
Air.    (See  Atmosphere.) 
Air-Pump,  with  valves,  329. 

without  valves,  325. 
degree  of  exhaustion,  327. 
Air-Thermometer,  533.   (See  Thermoscope.) 

"  Regnault's,  534. 

Alcoometer,  Gay-Lussac's,  264. 
Alloys,  expansion  in  solidifying,  553. 

"       melting-point  of,  550. 
Alumina,  crystallization  of,  120. 
Analogies  of  Nature,  9. 
Annealing,  207,  211. 

"         of  glass,  212. 

Antimony,  ratio  of  crystalline  axes  of,  122. 
Arago  and  Dulong,  experiments  on   Mari- 

otte's  law,  293. 

"'  "          experiments  on  tension 

of  aqueous  vapor,  575. 
Archimedes's  Law,  235. 

"      demonstration  of,  237. 
"      illustration  of,  236. 
Arsenic,  crystallization  of,  120. 
Arsenious  Acid,  crystallization  of,  120. 
Artesian  Wells,  233,  647. 
Aspirator,  325,  392. 
Atmosphere,  buoyancy  of,  268. 
dew-point  of,  641. 
effects  of  expansion  of,  540. 
pressure  of,  266,  279. 
probable  limit  of,  307. 
relative  humidity  of,  640. 
waves  of,  286. 
Atomic  Theory,  110. 
Atoms,  size  of,  Boscovisch's  opinion  of,  110. 

"  "       Newton's  opinion  of,  110. 

Attraction  of  Earth.    (See  Gravity.) 

62 


Axes  of  crystals,  121, 123. 
"    lateral  and  vertical,  122. 
"    ratio  in  crystals  of  antimony,  122. 
"          "  "          bichromate  of  pot- 

ash,  124.       [122. 

"          "  "  carbonate  of  lime, 

gypsum,  123.  [124. 

"          "  "  sulphate  of  copper, 

"          "  "  "        iron,  123. 

"          "  "  sulphur,  123. 

"          "  "  tin,  122. 

"    similar,  125. 

BABINET,  formula  of,  305. 
Balance,  accuracy  and  sensibility  of,  102. 
"        centre  of  gravity  of,  how  adjusted, 
"        degree  of  sensibility  of,  105.    [101. 
"        description  of,  100. 
"        hydrostatic,  248. 
"        regarded  as  a  lever,  101. 

"    pendulum,  102.    [94. 
"        spring,  indicates  absolute  weight, 
Balloons,  270. 

"        ascensional  force  of,  271. 
Barometer,  Aneroid,  285. 

"  Bourdon's  metallic,  190. 

"  common,  284. 

"  Fortin's,  232. 

"  history  of,  275. 

"  oscillations  of,  286. 

"  Regnault's,  280. 

"  theory  of,  278. 

"  used  in  measuring  heights,  304. 

"      meteorology,  287. 
"  various  uses  of,  285. 

Barometrical  Observations,  corrected  for  ca- 
pillarity, 284, 355. 

"  "          corrected  for  tem- 

perature, 284, 511. 
Bevelling,  181. 
Bichromate  of  potash,   ratio  of  crystalline 

axes  of,  124. 

Billiards,  illustrative  of  elasticity,  201. 
Bodies,  collision  of  unelastic,  49. 

"  "         elastic,  196. 

Body,  definition  of,  3. 
Boiler.    (See  Steam- Boiler. ) 
Boiling-Point,  determination  of,  569. 

"  influenced  by  pressure,  566, 

«  table  of,  566.  [577. 

"  of  water,  565. 

«  "        effect  of  salts  on,  568. 

»  "        influenced    by  con- 

taining vessel,  568. 


730 


INDEX. 


Boiling-Point,  use  in  measuring  heights,  567. 
Boracic  Acid,  how  used  in  crystallizing,  120. 
Boscovisch's  opinion  of  atom'ic  theory,  110. 
Bourdon.   (See  Barometer  and  Manometer.) 
Buoyancy  of  gases,  268. 

"          "   liquids,  235,  247. 
Bramah's  Press,  220. 
Breguet's  Metallic  Thermometer,  504. 
Britannia  Bridge,  expansion  of,  503. 
Brittleness,  definition  of,  205. 
Brix,  latent  heat  of  vapors,  604. 
Bronze,  tempering  of,  212. 
Bunsen,   absorption-meter,  402. 

solution  of  gases  in  liquids,  393. 

"        specific  gravity  of  gases,  671.     By 

effusion,  414. 
tension  of  condensed  gases,  593. 

"        volume  of  gases,  679. 

CAGNIARD  DE  LA.  TOUR,  experiments  on 

dense  vapors,  601. 
Calcite,  hardness  of  faces  of,  210. 

"       ratio  of  crystalline  axes  of,  122. 
"       rhombohedrons  of,  152. 
Capillarity,  346. 

"          absorption  of  liquids  by  porous 

solids,  363. 

amount  of  pressure,  351. 
effects  of  pressure,  352. 
form  of  meniscus,  347,  349. 
"          general  phenomena  of,  346,  354. 

illustrations  of,  353,  362. 
"          influence  of  temperature  on,  360. 
u          numerical  laws  of,  355. 
"          pressure  resulting  from  molecu- 
lar forces,  349. 

"          verification  of  laws  of,  357. 
Capillary  Tubes,  height  of   liquid  in,  354, 
"         Plates,  357,  359.  [358,  360. 

Carbonate  of  soda,  laws  of  its  solubility,  376. 

"          "  lime.     (See  Calcite.) 
Carbonic  Acid,  condensation  of,  596,  609. 
Cathetometer,  185, 281. 
Cements,  343. 
Centre  of  Gravity,  properties  of,  60. 

"    '    position  of,  61. 
"         oscillation,  definition  and  proper- 
ties of,  70. 

"         pressure,  220,  240. 
Centigrade  Thermometric  Scale,  436. 
Centrifugal  force,  79. 

"      at  equator,  82. 
"  "      measure  of,  80. 

"       modifying  gravity,  81. 
Centripetal  force,  78. 
Charcoal,  absorption  of  gases  by,  380. 
Chemical  Change,  distinguished  from  solu- 
tion, 371. 

"         Physics,  definition  of,  6. 
Chemistry,  how  distinguished  from  Physics, 
"  the  three  questions  of,  5.          [5. 

Chimney,  theory  of.  541. 
Cleavage,  laws  of,  205. 

"         planes  of,  119,  204. 
Clock,  description  of,  72. 
Coefficient  of  absorption  of  gases.  392. 

"   compressibility  of  liquids,  217. 
"   conduction  of  heat,  659. 
"         "  cubic  expansion,  492. 

"  elasticity,  186. 
"         "  expansion  of  gases,  528. 


Coefficient  of  expansion  of  water,  527. 

"        of  mercury,  510,514. 
"         "  linear  expansion,  491. 
Cohesion,  119,  342. 
Coinage,  208. 
Collision  of  elastic  bodies,  196. 

"        "   unelastic  bodies,  49. 
Column.     (See  Mercury  Column.) 
Combustion,  heat  from,  649. 
Components  and  Resultants,  38. 
Compressibility  of  gases,  115,  273,  648. 
"  "         laws  of,  2^7. 

«*  "         limit  to,  301. 

"  "    (SeeMariotte'sLaw.) 

''  of  liquids,  215. 

"  of  matter,  illustrations   of, 

Condensation  of  gases,  592.  [113. 

"  "        apparatus  of  Katte- 

rer,  598. 
"  "        apparatus   of  Thilo- 

rier,  596. 

"         by  cold,  593. 
"        by  pressure,  594. 
'*  "        Faraday's       experi- 

ments on,  599. 

"  "        Faraday's      method, 

595.  [648. 

"  "        heat   resulting  from, 

Condensed  Gases,  boiling-points  of,  592, 


"       freezing-points  of,  599. 
u       latent  heat  of,  609. 


[610. 

low  temperature  from, 
maximum  tension  of,  593, 
table  of,  595.  [595. 

Condensing-Pump,  333. 
Conduction  of  Heat,  coefficients  of,  659. 
"  "•         illustrations  of,  655. 

"  "         in  crystals,  656. 

"  "        in  gases,  657. 

"  "  "     Grove's  experi- 

ments on,  657. 

"  "         in  liquids,  657. 

"  "  *•      Despretz's  ex- 

periments on,  657. 

"  "        in   liquids,    Eumford's 

experiments  on,  657. 

"  "        in    solids,    conductors 

good  and  bad,  654. 

"  "        in  solids,  experiments 

of    Wiedmann    and 
Franz,  656. 
"  "        in  solids,  Ingenhousz's 

apparatus,  655. 

"  "         in  solids,  laws  of,  655. 

"  "        in  various  metals,  656. 

Co-ordinates,  definition  of,  20 
Copper,  tempering  of,  212. 
Cornish  Boiler,  616. 
Coulomb,  laws  of  elasticity,  192. 
Couples,  definition  of  mechanical,  47. 
Cryophorus,  609. 
Crystal,  axes  of,  121. 
centre  of,  124. 
definition  of,  121. 
parameters  of  planes  of,  124. 
planes  of,  121. 
similar  axes  of,  125. 

"       planes  of,  126. 
size  of,  121. 
(See  Form.) 
Crystalline  form,  119. 


INDEX. 


731 


Crystalline  form,  identify  of,  defined,  183. 

"          structure,  119. 
Crystallization,  process  of,  119. 

water  of,  372. 
Crystallography,  119. 

terms  of,  121. 
Crystals,  cleavage  of,  lly,  204. 

"        conduction  of  heat  in,  656. 

"        determination  of,  175. 

"        expansion  of,  498. 

"        groups  of,  173. 

"        irregularities  of,  170. 

"        models  of,  132. 

"        modifications  of,  131,  175. 

"  laws    governing, 

"        simple  and  compound,  129.     [132. 

"        symbols  of,  128. 

"        systems  of,  121,  175. 

"        twin,  173. 

"        (See  Form.) 

D  ALTON'S  Apparatus  for  tension  of  vapors, 

572. 

"         Laws,  638. 
Daniell's  Hygrometer,  643. 
Densimeter,'  252. 
Density,  definition  of,  18.    (See  Mass.; 

"  "     how  related  to  weight,  91. 
Despretz,  conduction  of  heat  in  liquids,  657. 
expansion  of  water.  523,  626,  549. 
"        experiments  on  Mariotte's   Law, 

291. 

Dew,  theory  of,  653. 
Diffusion  bottles,  419. 

"        tube  of  Graham,  420. 
"        of  gases,  419. 

"        Dalton's  theory  of,  422. 
"         illustrations  of,  423. 
"        of  liquids,  383.  [384. 

"      Graham's  experiments  on, 
"      illustrations  of,  384. 
"  "      laws  of,  385. 

"  "      (See  Osmose). 

Dimorphism,  184. 
Distillation,  process  of,  588. 
Dividing  engine,  443. 
Divisibility  of  matter.     (See  Matter.) 
Ductility,  205. 

"         order  of,  207. 
Dulong  and  Petit,  experiments  on  expansion 

of  mercury,  508,  514. 
"      specific  heat  of  gases,  483,  489. 
"      (See  Arago.) 
Dynamics,  definition  of,  34. 

EARTH,  centre  of  gravity  of,  84. 
"        eccentricity  of,  83. 
"       origin  of  form  of,  85. 
"       spheroidal  figure  of,  83. 
Effusion  of  gases,  412.  [413. 

"        "      "      experiments  of  Graham, 

"      law  of,  414. 
"        "      "      use    in    determining  Sp. 

Gr..  414. 

Elastic  bodies,  collision  of,  196. 
Elasticity,  coefficient  of,  186. 
definition  of,  115. 
limits  of,  115, 193. 
limited  and  unlimited,  115. 
"         of  compression,  187. 
"          "  crystals,  195. 


Elasticity  of  flexxire,  187. 

"          "       "        applications  of,  189. 

"          "  liquids,  115,  215. 

"          "  solids,  185. 

"          "  tension,  laws  of,  185. 

"  torsion,  191. 

"          "        "        applications  of,  193. 
"          «        «        laws  of,  192. 
"        perfect  and  imperfect,  115. 
"        varieties  of,  115. 
Elements,  chemical  definition  of,  3. 
Engine,  dividing,  443. 

"       steam,  615  et  seq. 
Equilibrium,  mechanical,  definition  of,  34. 
of  floating  bodies,  242. 
of  liquids,  228.  [62. 

stable,  unstable,  and  neutral, 
Expansion,  coefficient  of,  491. 
"        force  of,  499. 
"        by  heat,  430. 
"          "       "      cubic,  431, 492. 
"          "       "      linear,  431,  491. 
"        heat  absorbed  in,  475,  480. 
"         of  gases,  528. 
"         "      "      expansion  of  air,  540. 
"         "      "      air-thermometer,  533. 
"          "       "       air-pyrometer,  539. 
"         "      "      coefficients  of,  628. 
"         "      "      general  laws  of,  532. 
"         "      "      methods    of   determin- 
ing, 530. 

"          "    liquids,  607. 
"          "        "      above     the     boiling- 
point,  519. 

"          "        "      absolute    and   appar- 
ent, 507. 
"          "        "      change   of  rate  with 

temperature,  517. 
"          "        "      experiments  of  Drion, 

619. 
"          "        "      experiments  of  Kopp, 

516. 
"          "        "      experiments  of  Pierre, 

516. 

"          "        "      formula    for    alcohol, 
ether,    and    oil    of 
turpentine,  518. 
"          "        "      represented  by  curves, 

518. 

"         "  solids,  494. 
"         "      "      applications  of,  504. 
•'         "      "      determination  of  cubic, 
495,  515.  [494. 

"         "      "      determination  of  linear, 
«         «'      "      case  of  crystals,  498. 
"          "       ''  "      glass,  497,  498. 

"         "      "      experiments  of  Kopp, 

496. 
•"         "      "      experiments  of  La  Place 

and  Lavoisier,  494. 
"          "      "       illustrations  of,  500. 
"         «      "      order  of  compressibili- 
ty and  expansibility, 
497. 

"         «      «      related  to  fusibility, 497. 
"         "      "      variation  with  temper- 
ature, 497. 

"         «  mercury,  508. 
«         «        "      coefficients  of,  510. 
"         "        "      correction    of  barom- 
eter, 511. 


732 


INDEX. 


Expansion  of  mercury,  determination  of  ab- 
solute, 508. 

"  "  "  determination  of  ap- 
parent, 513.  [510. 

"         "        "      empirical  formula  of, 

4<  "  "  method  of  determin- 
ing absolute,  Dulong 
and  Petit,  508.  Reg- 
nault,  509. 

"  "  "  Relation  between  ap- 
parent and  absolute, 
515. 

"         "  water,  520. 

«          "       u      curve  of,  521, 524. 

"         "      "      coefficient  of,  527. 

"  "  "  determination  of  maxi- 
mum density,  522. 

"  "  "  empirical  formulas  for, 
526. 

"  "  "  experiments  of  Des- 
pretz,  523. 

"  "  "  experiments  of  Pliicker 
and  Geissler,  523. 

"  "  "  point  of  maximum  den- 
sity, 520. 

"  "  "  (See  Maximum  Density.) 
Extension,  definition  of,  10. 

44        how  measured,  11. 

FAHRENHEIT,  thermometric  scale  of,  435. 
Faraday,  experiments  on  condensed  gases, 

595,  599. 

Floating  bodies,  laws  of,  241. 
Fluidity,  definition  of,  215. 
Force,  change  of  point  of  application,  38. 
"      definition  of  mechanical,  32. 
"      intensity  and  quantity  of,  37,  53. 
"      laws  governing  direction  of,  32. 
"      living,  52. 
"      measure  of,  34. 
"     moving,  37.     (See  Momentum.) 
"      origin  of  idea  of,  6. 
"      synonymous  with  volition,  7. 
"      unit  of,  36,  93. 
Forces,  centre  of  parallel,  48 

"      centrifugal  and  centripetal,  77. 
"      composition  of,  38,  42. 

"  "  parallel,  43,  47. 

"      decomposition  of,  40. 

illustration  of  parallel,  46. 
parallelogram  of,  39. 
"      represented  by  lines,  38. 
"      acting  in  the  same  direction,  result- 
ant of,  39. 

Forces,  Molecular,  117,  342.  [351,  352. 

"  "        pressure  exerted  by,  349, 

Form,  crystalline,  119,  127. 

dominant  and  secondary,  130. 
essential  and  accidental,  119. 
hemihedral,  128. 
holohedral,  127. 
principal,  143, 151,  153,  159. 
"      tetartohedral,  129,  156.  - 
"      (See  Hemihedral  and  Holohedral.) 
Forms  of  crystals.    Dimetric,  142.    Hexago- 
nal, 147.     Monoclinic,  163.     Monometric, 
132.     Triclinic,  168.     Trimetric,  158. 
Formulae :  — 

Absolute  expansion  of  mercury,  509. 

"         weight,  87. 
Air-thermometer,  536  -  539. 


Formulae :  — 


Air-pump,  327,  328. 

Analysis  of  gases  by  absorption,  411. 

Apparent    expansion    of    mercury, 

513,  514. 
Apparent  and  absolute  coefficient  of 

expansion,  515. 

Ascensional  force  of  balloon,  272. 
Barometrical  observations  corrected 

for  temperature,  511,  512. 
Capillarity,  357,  358. 
Centrifugal  force.  80-83. 
Coefficient  of  expansion  and  specific 
gravity,  496.  [516. 

Coefficient  of   expansion  of  solids, 
Collision  of  elastic  bodies,  196-198. 
"          unelastic  bodies,  49-51. 
Compensating  pendulum,  506. 
Conduction  of  heat,  659. 
Correction  of  thermometric  observa- 
tions, 449. 
Couples,  47. 

Decomposition  of  forces,  41. 
Density  and  weight,  91. 
Dimensions  of  safety-valve,  620. 
Effusion  of  gases,  415. 
Elasticity  of  flexure,  188. 
tension,  186. 
"  torsion.  192. 

Expansion  by  heat,  492,  493. 
"         of  gases,  529. 

"       determination  of, 
Heat  of  fusion,  560.  [531,  532. 

Hydrometer,  251,  252. 
Intensity  of  gravity,  65. 

"  "     *    at  different  lati- 

tudes, 77. 

La  Place's  and  Babinet's,  305. 
Latent  heat  of  steam.  607. 
Mariotte's  flask,  323,  324. 
"  ,       law,  287,  288. 
Mass  and  density,  18. 
Measure  of  forces,  36. 
Measurement  of  height  by  barome- 

eter,  304,  305. 
Momentum,  37. 
Parallel  forces,  45. 
Parallelogram  of  forces,  40. 
Pendulum,  68,  69,  73,  75,  76. 
Person's  law,  561,  563. 
Power  or  quantity  of  a  force,  53. 
Pressure  of  atmosphere,  279. 

"  liquids,  219,  227,  232. 

Psychrometer,  644. 
Reduction  of  thermometric   scales, 

436,  446. 

"          of  volumes  of  gases  to 

standard  pressure,  314. 

"          of  volume  of  moist  gases, 

637. 

Relative  and  absolute  weight,  95.  [96. 
Relative  specific  weight  and  density, 
Relative  specific  weight  and  relative 

weight,  96. 

Relative  weight  and  mass,  95,  96. 
Safety-tubes,  316,  317. 
Size  of  thermometer-bulb,  446. 
Solution  of  gases,  394. 

"      of  mixed  gases,  406,  407, 409. 
Solubility  of  salts,  367. 
Specific  gravity,  247  -  249,  257. 


INDEX. 


733 


Formulae :  — 

Specific  gravity  and  mass,  92. 
Sp.  Gr.  and  specific  weight,  92. 
"        and  weight,  91. 
"        of  gases,  673. 
"       of  liquids  corrected  for  tem- 
perature, 665. 

"       of  solids   corrected  for  tem- 
perature, 663. 
"        of  vapors,  675,  676. 
"       referred  to  air  and  water,  93. 
"       weight  and  volume,  92. 
Specific  heat  of  gases  under  constant 

volume,  481. 

"  "    method  of  mixture,  468. 

Specific  weight,  90. 
Syphon,  321.  [586. 

Tension  and  temperature  of  vapors, 
"          "    volume  of  vapors,  588. 
"       of  aqueous  vapor,  581. 
Uniform  motions,  23. 
Uniformly  accelerated  motion,  24,  25. 

"        retarded  motions,  26,  2-7. 
Variation  of  gravity  with  height,  86. 
Velocity  of  sound,  482. 
Volume  of  alcohol,  etc.,  518. 
"      of  gases,  681. 
"      of  mercury,  511. 
"      of  water,  527.  [670. 

Weight  of  gas,  reduced  for  latitude, 
"     of  one  c~*  of  gas,  668, 669. 
"     of  bodies  in  air,  269. 
Woolf 's  apparatus,  319,  320. 
Franklin,  on  absorption  of  heat,  653. 
French  System  of  Weights,  89. 
Freezing  mixtures,  556. 
"       point,  548. 
"          "      of  water,  549. 
"          "  "      effect  of  salts  on,  549. 

Friction,  heat  of,  648. 
Fulcrum,  97. 
Furnace,  hot-air,  542. 
Fusion  of  solids,  548,  553.    (See  Melting  and 

Freezing  Points,  and  Heat  of  Fusion.) 
Fusion  of  solids,  vitreous,  548.  [557. 

"  "       change  of  volume  attending, 

GAMLEO,  proposition  of  composition  of  ve- 
locities, 28. 
Gallon,  imperial,  14. 
Gases,  absorption  of,  by  solids,  379. 

"       compressibility  of,  115,  273,  287. 

"      condensation  of.   (See  Condensation.) 

"      conduction  of  heat  by,  657. 

"      definition  of  quantity  of,  394. 

"      direction  of  pressure  of,  265. 

"      effusion  of.     (See  Effusion.)        [115. 

"      elasticity  of,  perfect  and  unlimited, 

"      expansion  of.     (See  Expansion.) 

"      fluidity  of,  263. 

"      formation  of  vapor  in,  636. 

"      how  distinguished  from  liquids,  273. 

"  vapors,  585. 

"      mechanical  condition  of,  263. 
method  of  weighing,  270. 

"      passage  of,  through  membranes,  425. 

"      permanent  elasticity  of,  274. 

"      pressure  due  to  gravity,  265. 

"      solubility  of.     (See  Solubility.) 

"       specific  gravity  of,  93,  273,  670. 

"      tension  of,  definition,  263. 

62* 


Gases,  transmission  of  pressure,  264. 
"      transpiration  of,  417. 
"      volume  of,  679.    (See  Weighing  and 

Measuring.) 
"         how  reduced  to  standard 

pressure,  313. 

"         moist,  how  reduced,  637. 
"      weight  of,  270,  667. 
Gasometers,  314. 
Gav-Lussac,  solubility  of  sulphate  of  soda, 

374,  375. 

Geometry,  subject-matter  of,  11. 
Glass,  annealing  of,  212. 
"      expansion  of,  at  different  tempera- 
tures, 498,  499. 

Glauber  Salts.    (See  Sulphate  of  Soda.) 
Gold-Leaf,  illustrates  divisibility  of  matter, 
manufacture  of,  206.  [109. 

Goniometer,  Application,  177. 
"  Reflective,  178. 

"          Babinet's,  183. 

Haidinger's,  183. 
Mitscherlich's,  182. 
Rudberg's,  182. 
Suckow's,  183. 
Wollaston's,  179. 
Goniometry,  Mill  r's  method  of,  181.     [384. 
Graham's  experiments  on  diffusion  of  liquids, 
"    of  gases,  420. 
effusion,  413. 
osmose,  389. 
transpiration,  417. 
Grailich  and  Pekarek's  Sckrometer,  209. 
Gramme,  definition  of,  89. 
Grassi,  on  compressibility  of  liquids,  217. 
Gravitation,  law  of,  86. 
Gravity,  acceleration  of,  65. 

"        Borda's  and  Cassini's  experiments 

on,  74. 

"        causes  of  variation  of  earth's,  77. 
"        centre  of,  60. 
"        definition  of,  56. 
"        direction  of  earth's,  67. 
"        intensity  of,  64. 
"  "  how  measured,  66. 

"  "  represented  by  g,  65. 

irregularities  of,  77. 
measured  by  pendulum,  73. 
point  of  application  of  earth's,  58. 
proportional  to  quantity  of  matter, 
resultant  of  forces  of,  59.  [65. 

"        value  of,  at  different  latitudes,  76. 
"        varies  with  distance,  85. 
"        (See  Specific  Gravity.) 
Gypsum,  form  of  crystals  of,  174. 

"          ratio  of  crystalline  axes  of,  123. 

HALLSTROM,  expansion  of  water,  523. 
Hardness,  definition  of,  208. 
"         how  measured,  208. 
"         of  crystals,  209. 
"         scale  of,  209. 
"         sclerometer,  209. 
Heat,  a  repulsive  force,  118. 
"     absorbed  by  expansion,  475,  480. 
"     an  expansive  force,  430. 
«     central,  647. 
"     definition  of,  426. 
"     mechanical  equivalent  of,  484,  633. 
"      theories  of,  426. 
"     (See  Conduction,  Radiant,  &  Sources.) 


734 


INDEX. 


Heat  of  Fusion,  555. 

44  "        freezing  mixture,  556. 

"  "        how  determined,  559. 

"  "        Person's  law,  560. 

Hemihedral  Forms,  128, 135,  138,  145,  149, 
Hemi-octahedrons,  163.  [161,  167. 

Hemi-prisms,  165. 
Hemitropes,  174. 

Holohedral  Form,  127, 133, 142, 147, 158, 163. 
Hopkins,  effect  of  pressure  on  melting-point, 
Hydrometer,  249.  [550. 

"  Baume"'s,  253. 

"  Fahrenheit's,  251. 

Nicholson's,  250. 
Eousseau's,  255. 
Hydrostatic   Balance,  248. 
"  Paradox,  228. 

"  Press,  220. 

Hygrometer,  639. 

"  Daniell's,  643. 

44  Deluc's,  645. 

44  Hair,  645. 

"  Regnault's,  642. 

"  Saussure's,  645. 

"  Wet-bulb,  644. 

Hygrometry,  636. 

"  Dalton's  laws,  638. 

"  dew-point,  641. 

drying  apparatus,  646. 
14  formation  of  mixed  vapors,  638. 

"         of  vapor  in  air,  636. 
relative  humidity  of  air,  640. 
tension  of  vapor  in  air,  636. 
"  volume  of  moist  gases,  how  re- 

duced, 637. 
Hypothesis,  how  related  to  law,  7. 

IMPENETRABILITY,  definition  of,  19. 
India-rubber,  adhesion  of,  343. 

used  for  joints,  343. 
Inertia,  definition  of,  32. 
Iodine,  crystallization  of,  120. 

JOULE,  mechanical  equivalent  of  heat,  484, 
633. 

KATER,  experiments  on  the  pendulum,  12,71. 
Kilogramme,  origin  and  history  of,  15. 
Klino-diagonal  axis,  123,  164. 
Kopp,  change  of  volume  in  fusion,  551. 

"      cubic  expansion,  496. 

44     expansion  of  liquids,  516. 

"     volume  of  water  at  different  tempera- 
tures, 526. 

LA  PLACE,  formula  of,  305. 

"  velocity  of  sound,  482. 

Latent  Heat.    ( See  Heat  of  Fusion.) 
Latent  Heat  of  Vapor,  603. 

"  "•        application  in  case  of 

steam,  611. 

"  "        Brix's  experiments  on, 

"  "        cryophorus,  609.    [604. 

"  "        determination  of,  603. 

"  "        illustrations  of,  608. 

"  "        in  equal  volumes,  606. 

"  "        in  steam    at    different 

temperatures,  606. 
"  "        Leslie's  experiment  on, 

609. 
"  "        porous  water-jars,  608. 


Latent  Heat  of  Vapor,  Regnault's    experi- 
ments on,  607. 
"      solid  carbonic  acid,  610. 
"      spheroidal  condition  of 

liquids,  611. 
"      Watt's  theory,  606. 
Latitude,  variation  of  gravity  with,  76. 

"  u        of  Aveight  of  gases  with, 

670. 

Lavoisier  and  Laplace,  measurement  of  lin- 
ear expansion,  494. 
Law,  criterion  of  its  validity,  8. 
Dalton's,  638. 
definition  of,  7. 
Mariotte's,  287. 
nature  of  a  physical,  7,  300. 
of  gravitation,  86. 
Person's,  560. 

relation  of,  to  Divine  Mind,  7. 
Watt's,  606. 
Laws  of  capillarity,  355. 
"        cleavage,  205. 
"        crystalline  symmetry,  132. 
"        diffusion  of  gases,  420. 
"  "          liquids,  383. 

"         Dulong,  484,  489. 
"        elasticity,  186. 
"        liquid  equilibrium,  229. 

"      pressure,  227. 
"        solution  of  gases,  392. 
"        torsion,  192. 
"        transpiration,  417. 
Length,  units  of,  English,  11.    French,  14. 
Leslie's  experiment,  609. 
Lever,  arms  of,  98. 

"      conditions  of  equilibrium  of,  98. 
44     general  theory  of,  97. 
"      three  kinds  of,  97. 
Leverage,  definition  of,  100. 
Light,  plane  of  polarization  rotated  by  crys- 
tals, 162,  167. 
Liquid  state,  117. 

Liquids,  adhesion  to  solids.    (See  Solids.) 
"        centre  of  pressure  of,  220. 
44        characteristic  properties  of,  215. 
"        compressibility  of,  114,  216. 
"        diffusion  of,  383.     (See  Diffusion.) 
"        direction  of  pressure  of,  219. 
"        elasticity  of,  115,  215. 
"        expansion  of.     (See  Expansion.) 
"        how  distinguished  from  gases.  273. 
"        laws  of  buoyancy  of,  235  -  247. 
"  "       equilibrium  of,  228-232. 

"  "       pressure  of,  224-227. 

14        mechanical  condition  of,  215. 
"        pressure  due  to  gravity,  223. 
"        principle  of  Archimedes,  235. 
"        specific  gravity  of,  247  et  seq.,  665. 
"        spheroidal  condition  of,  361. 
"        transmission  of  pressure,  218. 
"        volume  of,  666.    (See  Weighing  and 
"  Measuring.) 

Litre,  17. 

Locomotive  Boiler,  618. 
"  Engine,  628. 

Loewel's  experiments  on  solubility  of  carbo- 
nate of  soda,  376. 

"  "  on  solubility  of  sul- 

phate of  soda,  374. 

44  "on  supersaturated  so- 

lutions, 378. 


INDEX. 


735 


MAKRO-UIAGONAL  AXES,  123. 
Malleability,  205. 

order  of,  207.  [208. 

"  variations    with    temperature, 

Manometer,  Regnault's,  308. 

"  metallic,  of  Bourdon,  189. 

"  with  confined  air,  310. 

Marcet's  Globe,  574. 
Mariotte's  Flask,  323. 

"          Law,  application  of,  301. 

"  "    deviations  from,  290, 299, 532, 

586.602. 

"  "    experiments  on,   Arago  and 

Dulong,  293. 

»  "  "          Despretz,  291. 

"  "  "          Natterer,  299. 

"  "  "          Oersted,  290. 

"  "  "          Regnault,  295. 

"  "    history  of,  290. 

"    illustrations  of,  288. 
"  "    relation  to  expansion  of  gas- 

es, 532,  586. 

"  "    statement  of,  287. 

Mass,  definition  of,  18 
"     relation  to  density,  18. 
"     unit  of,  91. 

Matter,  compressibility  of,  113. 
"        definition  of,  3. 

"        divisibility  of,  an  accidental  prop- 
erty, 109. 

"        essential  nature  of,  not  understood,  3. 
"  "        and  accidental  properties 

of,  10. 

"        expansibility  of,  113. 
"        general  and  specific  properties  of,  3. 
"        illustrations  of  its  porosity,  110. 
"        physical  and  chemical  properties,  5. 
Maximum  density  of  water,  520. 

"  "     '         "        effects    of    salts 

on,  526. 

"  "  "        history    of    dis- 

covery of,  622. 

"  "  "        important  bear- 

ings of,  525. 
Measure,  English  system  of,  11.   (See  Yard.) 

"        French  system  of,  its  history,  14. 
Measuring.    (See  Weighing  and  Measuring.) 
Mechanics,  subject-matter  of,  32. 
Melting-Point,  '548. 

effect  of  pressure  on,  550. 
"  of  alloys,   determination  of, 

Meniscus,  form  of,  347,  349.  [554. 

Mercurial  Thermometers,  432. 

"  arbitrary  scale,  446. 

calibration  of,  443. 
"  change  of  zero-point, 

"  "^         comparison    of   dif- 

ferent, 439. 

"  "  construction  of  stan- 

dard, 442. 

"  "  defects  of,  436. 

"  "  filling  of,  433. 

graduation  of,  433. 
observations,      how 

corrected,  448. 

"  "  size  of  bulb  of,  445. 

Mercury  column,  how  measured,  280. 

14  "         expansion  of.     (See  Ex- 

pansion.) 
Metacentre,  definition  of,  244. 


Metals,  crystallization  of,  120. 
Metre,  an  arbitrary  measure,  16. 
"      origin  and  history  of,  14. 
"      subdivisions  of,  17. 
Mitscherlich,  expansion  of  crystals,  498. 

goniometer,  182. 
Modifications  of  crystals,  131. 

"  «  laws  of,  132. 

Mohs's  scale  of  hardness,  209. 
Molecular  forces,  two  classes  of,  117.    (See 

Forces.) 

Moment,  definition  of,  100. 
Momentum,  definition  of,  37. 
Motion,  a  relative  term,  21. 

"        an  essential  property  of  matter,  21. 

"        compound,  27. 

"         curvilinear,  how  resulting,  29. 

"        origin  of  idea  of,  21. 

"        parallelogram  of,  27. 

"        possible  in  several  directions  at  once, 

"        uniform,  and  varying,  23.  [22. 

"        uniformly  accelerated,  23. 

"  "      "  retarded,  26. 

[598. 

NATTERER,  apparatus  for  condensing  gases, 
"  experiments  on  compressibility 

of  gases,  299. 

Newton,  discovery  of  law  of  gravitation,  87. 
"  formula  for  velocity  of  sound,  482. 
"  opinion  on  atomic  theory,  110. 

ORTHO-DIAGONAL  Axis,  123. 
Osmometer,  387. 
Osmose,  387. 

"        explanation  of,  388. 

"        Graham's  experiments  on,  389. 

"        how  allied  to  chemical  affinity,  391. 

PARAMETERS  of  crystalline  planes,  124. 
Pendulum,  amplitude  of  oscillation,  68. 
BessePs  experiments  on,  76. 
"  Borda's    and    Cassini's    experi- 

ments on,  74,  76. 
"  centre  of  oscillation  of,  70. 

"  definition  of,  66. 

"  formula  of,  68,  69. 

"  Harrison's  gridiron,  505. 

how  affected  by  the  air,  75. 
isochronism  of,  68. 
"  Rater's  experiments  on,  12,  71. 

laws  of  oscillation  of,  69. 
"  Martin's  compensation,  506. 

"          measure  of  force  of  gravity,  73. 

"        of  time,  71. 

"  simple  and  compound,  66,  69. 

"  theory  of,  67. 

"          virtual  length  of,  70. 
Physical  changes,  how  distinguished  from 

chemical,  4. 
"        properties,  how  distinguished  from 

chemical,  5. 

Physics,  how  distinguished  from  Chemistry, 
Planes  of  cleavage,  119.  [5. 

"          similar,  126,  175. 
"         symbols  of  crystalline,  128. 
"         terminal  and  basal,  169. 
Plumb-Line,  use  of,  57. 
Pneumatic  Trough,  311,  680. 
Polyhedron,  121. 
Polymorphism,  184. 
Pores,  size  of,  Herschel's  opinion,  113. 


736 


INDEX. 


Porosity,  110. 

"         Florentine  experiments  on,  112. 

illustrations  of,  111. 
"         implies  compressibility,  113. 
Position  of  a  body,  how  defined,  20. 

"        origin  of  idea  of,  20. 
Pound,  Troy  and  Avoirdupois,  90. 

"      United  States  standard,  90. 
Power  of  a  force,  37,  52. 
Pressure  of  the  atmosphere,  266. 

"  measured  by  ba- 

rometer, 279. 

RADIANT  HEAT,  651. 

"        absorption  of,  652. 
"        analogous  to  light,  651. 
emission  of,  653.         [653. 
Franklin's      experiments, 
"        freezing  water  by  radia- 
tion, 654. 

"        hot-beds,  654. 
"        laws  of,  651. 

phenomena  of  dew,  653. 
"        radiation  of  cold,  651. 
"        reflection  of,  652. 
"        transmission  through  me- 
dia, 652. 
Refrigerator,  543. 

Regnault,  comparison  of  thermometers,  439. 
"         determination  of  tension  of  va- 
pors, 575.  [295. 
"         experiments  on    Mariotte's    law, 
"                   "           on  specific  heat,  466, 
[467,469,471,474,476. 
hygrometer,  642. 
hygrometry,  644,  645. 
latent  heat  of  aqueous  vapor,  607. 
method  of  weighing  gases,  270. 
specific  gravity  of  gases,  667. 

"  "        of  vapors,  676. 

"         weight  of  gases,  667. 
Relative  Weight.     (See  Weight.) 

"        specific  weight,  96. 
Rest,  a  relative  term,  21. 
Rhombohedron,  149. 
Rolling-Mill,  206. 
Rumford,  conduction  of  heat  in  liquids,  657. 

"          heat  of  friction,  648. 
Rupert's  Drops,  212. 
Rupture,  resistance  to,  201. 
"         law  of,  202. 

SAFETY-TUBES,  theory  of,  315. 

"        valve,  619. 

Savart,  elasticity  of  crystals,  196. 
Scalenohedron,  153. 
Sclerometer,  209. 
Section,  principal,  151,  159. 
Set,  definition  of,  116,  194. 
Silliman,  diffusion  apparatus,  423. 
Similar  axes,  125. 
"       edges,  181. 
"       planes,  126, 175. 
"       solid  angles,  181. 
Siphon,  theory  of,  320. 
Solid  state,  117. 
Solids,  absorption  of  liquids  by  porous,  363. 

of  gases  by,  379. 
adhesion  between,  342. 

"        to  liquids,  Gay-Lussac's  ex- 
periments, 345. 


Solids,  characteristic  properties  of,  119. 
"      compressibility  of,  113. 
"      conduction  of 'heat  in,  655. 
"      elasticity  of,  imperfect  and  limited, 
"      fusion  of.     (See  Fusion.)  [116. 

"      porosity  of,  110. 
"      specific  gravity  of,  91,  247,  662. 
"      volume  of,  664. 

"      weight  of,  87, 100,  661.     (See  Weigh- 
ing and  Measuring.) 

Solubility  of  carbonate  of  soda,  376,  377. 
"          of  sulphate  of  soda,  372  -  375. 
"          of  gases,  causes  of  variation,  398. 
"  "         coefficient  of  absorption, 

392. 

"  "         determination  of  coeffi- 

cient, 398. 
"  "         expression  by  empirical 

formulae,  393. 

"         mixed  gases,  405.    [394. 
"         variation  with  pressure, 
"  "         variation  with  tempera- 

ture, 393. 

"  "         (See  Absorption-Meter.) 

"         of  solids,  curves  of,  367. 

"         determination  of,  369. 
"  "         empirical    formulas    of, 

366. 
"  "         uninfluenced  by  fusion, 

369. 

"  "         variation  with  tempera- 

ture, 365. 
Solution,  how  distinguished  from  chemical 

change,  371. 
"        of  gases,  392. 
"        of  solids  in  liquids,  365. 
"        supersaturated,  376. 
Sources  of  Heat,  647. 

"      central  heat,  647. 
"  "      calculations  of  Fourier,  647. 

"  "      chemical,  649. 

"  "      condensation,  648. 

"  "       friction,  648. 

"  "      percussion,  648. 

"  "      sun,  647. 

Sp.  Gravity,  91,  247. 
"  bottle,  247. 

"  methods  of  determining,  247- 

257. 

"  of  gases,  93,  273.  [414. 

"  "        determined  by  effusion, 

"  "        referred  to  air,  93. 

"  relation  to  specific  weight  in 

French  system,  92. 
Sp.  Heat,  464. 

"        of  gases,  476,  478. 

"  »        under    constant  pressure, 

477. 

"  "        under  constant    pressure, 

does  not  vary  with  tem- 
perature or  pressure,  477. 
"  "        under    constant    volume, 

480. 

"  "        under    constant    volume, 

determination   from  ve- 
locity of  sound,  482. 
"  "        under    constant    volume, 

Dulong's     experiments, 
483. 

"  "        under    constant    volume, 

Duloug's  laws,  484,  489. 


INDEX. 


73T 


Sp.  Heat  of  platinum,  and  determination  of 

nigh  temperatures,  473. 
"        of  solids  and  liquids,  466. 
"  connected  with  their  chem- 

ical equivalents,  471. 
determination  of,  466,  467. 
"  greater  in  liquids  than  in 

solids,  475. 

greatest  in  water,  476. 
"        of  the  elements,  466. 
"        unit  of  heat,  464,  472. 
Sp.  Weight,  90. 

"  relative,  96. 

Spheroidal  condition  of  liquids,  361,  611. 
"  "  Boutigny's    experi- 

ments, 613. 

"  illustrations  of,  614. 

"  "  temperature  in,  612. 

"  "      freezing  of  water  in,  614. 

Spirit-Level,  232. 
Spring-Balance,  94, 189. 
Standards  of  measure.  ( See  Yard  and  Metre.) 
"        of   weight.     (See    Gramme    and 

Pound.) 

Statics,  definition  of,  34. 
Steam,  572.     (See  Vapors.) 

**      application  of  latent  heat  of,  611. 
"      bath,  591. 

"      expansion  at  formation  of,  603. 
"      latent  heat  of,  at  different  tempera- 
tures, 606,  632. 

"  "          "      Regnault's  results,  607. 

"          "      theory  of  Watt  as  to, 
"      mechanical  power  of,  631.          [606. 
"      volume  of,  631. 
Steam-Boiler,  615. 

"  appendages  of,  618. 

"  Cornish,  616. 

dimensions  of,  620. 

"          heating  surface, 
"  French  form  of,  617.        [616. 

fusible  plug,  620. 
locomotive,  617. 
requisites  of,  615. 
safety-valve,  619. 
Steam-Engine,  615. 

condenser,  625. 
"  cut-offs,  633. 

fly-wheel,  623. 
high-pressure,  628,  633. 
locomotive,  628. 
low-pressure,  621,  633. 
mechanical  power  of,  631. 
non-condensing,  628. 
parallel  motion,  624.  t 
"  the  eccentric,  625. 

Watt's  condensing,  621. 
Substances,  definition  of,  3. 
Sugar,  hemihedral  forms  of,  168.  [169. 

Sulphate  of  copper,  crystalline  form  of,  124, 

of  iron,  crystalline  form  of,  123. 
"       of  lime,  crystalline  form  of,  123. 
of  soda,  laws  of  solubility,  372,  375. 
"      osmotic  equivalent  of,  388. 
soluble  modifications  of,  374. 
"  "     supersaturated  solution  of. 

376. 
"  "     use  of,  in  freezing  mixtures, 

557. 

Sulphide  of  hydrogen,  coefficient  of  absorp- 
tion of,  399. 


Sulphur,  how  crystallized,  120. 

"        ratio  of  crystalline  axes  of,  123. 
Sulphurous  Acid,  coefficient  of  absorption  of. 

401. 

"     condensation  of,  593. 
Supersaturated  Solution,  376. 
Surface,  units  of.     English,  13.    French,  17. 
Syphon,  theory  of,  320. 
System,  dimetric,  122, 142. 
hexagonal,  122,  147. 
monoclinic,  123,  163. 
"        monometric,  121,  132. 
"        triclinic,  123,  168. 
"        trimetric,  123,  158. 
Systems  of  crystals,  121. 

TABLES:  — 

Absorption  of  gases  by  charcoal,  380  $ 
by  Meerschaum,  plaster  of  Paris,  and 
silk,  381. 
Boiling-points  of  condensed  gases,  592. 


liquids,  566. 
salir 


line  solutions,  568. 
Coefficients  of  compressibility  of  liquids, 
of  elasticity,  187.          [217. 
"  of  expansion  of  glass  at  dif- 

ferent temperatures,  497. 
of  expansion   of  mercury, 

510. 

Comparison  of  different  mercurial  ther- 
mometers. 439. 
of  mercurial  with  air-ther- 
mometers, 439. 
of  thermometers  filled  with 

different  liquids,  451. 
Compressibility  of  gases  by  Arago  and 
Dulong,  294. 
"      by  Natterer,  299. 
"  "      byRegnault,296. 

Conducting  power  of  metals,  by  Des- 
pretz,  659;  by  Wiedman  and  Franz, 
656. 

Determination  of  crystals,  176. 
Diffusion  of  solids  in  solution,  385. 
Dimension  of  steam-boilers,  621. 

"  of  the  earth,  83. 

Effect  of  pressure  on  melting-point,  550. 
Effusion  and  Diffusion  of  gases,  414. 
Expansion  of  matter  by  heat,  431. 
"          in  vaporization,  603. 
"          of  gases,  528. 
"          of  liquids,  517.  [519. 

"  "       above  boiling-point, 

Freezing-points  of  condensed  gases,  599. 
French  linear  measure,  17. 

"        system  of  weights,  89. 
Greatest  density  of  vapors,  601. 
Groups  of  equi-diffusive  substances,  386. 
Heat  of  combustion,  650. 

"      fusion,  556. 
Height  of  liquids  in  capillary  tubes,  358, 

361. 

Intensity  of  gravity  at  different  lati- 
tudes. 76. 
Latent  heat  of  aqueous  vapors,  by  Watt, 

606 ;  by  Regnault,  608. 
"          "    of  vapors,  605. 
Limit  of  elasticity,  195. 
Mechanical  power  of  steam,  631. 
Melting-points,  548. 

44  of  alloys,  550. 


738 


INDEX. 


Tables:  — 

Person's  law,  562. 

Pressure  and  specific  gravity  of  the  air 

at  increasing  altitudes,  306. 
-Scale  of  hardness,  209. 
Solubility  of  carbonate  of  soda,  377. 
"        of  chloride  of  potassium,  366. 
"        of  gases,  393. 
"        of  nitre,  366. 
"        of  sulphate  of  soda,  375. 
Sp.  Heat  of  elements,  466. 

"        of  equal  volumes  of  gases,  483. 
"        of  gases  and  vapors,  478. 
"        in  solid  and  liquid  state,  475. 
"        of  liquids  at  different  temper- 
atures, 474. 

of  modifications  of  carbon,  476. 
"        of  platinum  at  different  tem- 
peratures, 473. 

"        of  solids  at  different  tempera- 
tures, 473. 

"        of  water  at  different  tempera- 
tures, 472. 
Temperature  of  liquids  in  spheroidal 

condition,  612. 

Tenacity,  ductility,  malleability,  207. 
Tension  of  aqueous  vapors,  671. 
"       of  condensed  gases,  593. 
"  «  "      at  GO,  595. 

"       of  vapors  of  liquids,  583. 
Tints  of  heated  steel,  211. 
Transpirability  of  gases,  418. 
Weight  of  gases,  668. 
Tartaric  Acid,  nemihedral  forms  of,  167. 
Tartrate  of  soda  and  ammonia,  hemihedral 

forms  of,  162. 
Temperature,  absolute  zero,  564. 

definition  of,  463. 
"  determined  by  specific  heat  of 

platinum,  473. 

"  influence  of,  on  solubility,  366. 

"  lowest  observed,  452,  565. 

"  measured  by  a  thermometer, 

of  celestial  space,  564.     [432. 
"  obtained  with  condensed  gas- 

es, 610. 

"  thermal  equilibrium,  463. 

"  true,  539. 

Tempering,  211. 

of  bronze,  212. 
"  of  copper,  212. 

"  of  glass,  212. 

Tenacity,  203. 

"        means  of  measuring,  202. 
"        order  of,  207. 
Tension  of  gases.    (See  Gases.) 

"        of  vapors.    (See  Vapors.) 
Tetartohedral  Forms,  129,  156. 
Theory,  atomic,  110. 
Theories,  how  related  to  laws,  7. 
Thermometer,  air,  455,  534. 
"  alcohol,  451. 

"  filled  with  various  liquids,  451. 

"  fixed  points  of,  433. 

house,  450. 

maximum  and  minimum,  452. 
"  mercurial,  432. 

"  metallic,  of  Bre"guet,  504. 

"  Negretti  and  Zambra's,  453. 

"  Rutherford's,  452. 

"  scales  of,  435. 


Thermometer,  scales  of,  reduction  of.  436. 
"  Walferdin's,  454. 

"  water,  438. 

weight,  513. 

"  (See  also  Air,  and  Mercurial.) 

Thermo-multipHer,  Melloni's,  457. 
Thermoscopes,  Leslie's,  456. 

Rumford's,  457. 
Sanctorius's,  456. 
Time,  how  measured,  22. 
"      origin  of  the  idea  of,  22. 
"      units  of,  22. 

Tin,  ratio  of  crystalline  axes  of,  122. 
Torricelli's  experiments,  275. 
Torsion  Balance,  193. 

"        elasticity  of,  191. 
Transpiration  of  gases,  laws  of,  417. 
Troughton,  standard  yard,  13. 
Truncation,  131. 
Twin  crystals,  173. 

UNIT  of  force,  36,  93. 

"  heat,  464,  472. 

"  length,  11,  14,  17. 

"  mass,  91. 

"  surface,  13, 17. 

"  volume,  13, 17. 

"  weight,  89. 

VAPOR,  aqueous  tension  of,  571. 

"  "  "        Dalton's  appara- 

tus, 572. 

"        apparatus  of  Gay-Li;ssac,  574. 
"  Regnault,  575. 

"        empirical  formula?  for,  581. 

"        formation  in  atmosphere  of  gas,  636. 
(And  see  Hygrometry.) 

"        geometrical  curve  of,  580. 

"        laws  governing,  580. 

"        Marcet's  globe,  574. 

"        Papin's  digester,  591. 

"        (See  Latent  Heat  of  Vapor.) 
Vapors,  expansion  attending  formation  of, 

"        formation  of,  570,  582.  [603. 

"        greatest  density  of,  600. 

"        how  distinguished  from  gases,  585. 

"        maximum  tension  of,  584. 

u        smallest  density  of,  602. 

"        specific  gravity  of,  674  et  seq. 

"        tensions  of,  compared,  584. 

"        weight  of,  669. 
Velocities,  composition  of,  28. 
Velocity,  definition  of,  23. 
Vis  viva,  53. 
Volume,  definition  of,  10. 

"        how  estimated,  14. 

"        units  of.    English,  13.    French,  17. 
Volumeter,  Gay-Lussac's,  252. 

WASH-BOTTLE,  325. 

Water,  change  of  volume  in  freezing,  552. 

"       effect  of  pressure  on  melting-point, 
550. 

"       expansion  of.    (See  Expansion.) 

"       freezing-point  of,  549. 

"       maximum   density  of.    (See  Maxi- 
mum Density.) 

"       pump,  334.  [526. 

"       volume  of,  at  different  temperatures, 
Watt,  law  of,  606. 

"     steam-engine  of,  621. 


INDEX. 


739 


Weighing  and  Measuring,  661. 

Sp.  Gr.  of  gases,  Bunsen's  method, 
671. 

"  "        Regnault's  method, 

670. 

"       of  liquids,  91,  249,  seq. 

"  "        corrected  for  tem- 

perature, 665. 

"       of  solids,  91,  247. 

"  "        corrected  for  tem- 

perature, 662. 

"       of  vapors,  674.  seq.       [678. 

«  "       Deville's     method, 

"  "      Dumas's     method, 

675. 

"  "     Gay-Lussac's  meth- 

od, 678. 

"  •*     Regnault's  method, 

676. 
Volume  of  gases,  679. 

"        of  liquids,  666. 

"        of  solids,  664. 
Weight  of  gases,  270,667. 

"        of  solids,  87,  100,  661. 

"        of  vapors,  669. 


Weight,  absolute,  87. 

"  "        distinct  from  mass,  88. 

"  "        liable  to  variation,  89. 

"  "        measure    of    quantity    of 

matter,  88. 

"        of  a  body  in  air,  268. 
relative,  94. 

a  constant  quantity,  95. 
"        measured  by  the  balance, 

94. 

"        specific,  90. 
"        of  a  unit  of  mass,  91. 
Weights  described,  94. 
Wells's  theory  of  dew,  653. 
Welter's  tube,  317. 

Wertheim,  experiments  on  elasticity.  187. 
Wire-Mill,  205. 
Woolf 's  Bottles,  318. 


YARD,  act  of  Parliament  concerning,  11. 
"       American  standard,  13. 
"       origin  and  history  of,  11. 
"       standard,  destroyed  by  fire,  12. 


THE  END. 


I 


re  1 1417 


VERSltY  OF  CAtlFORN 


